Subgroups — C₅₃×#61610 #27269122

Order 13568.

2226 conjugacy classes of subgroups.

The subgroup lattice has 1942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3484	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3323	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3318	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3314	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3311	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3310	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3297	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3295	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3282	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×SD₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3275	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3267	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3266	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3265	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3265	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3224	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3222	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3200	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3198	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3196	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#3191	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#3123	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#3118	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#3012	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#3009	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#3003	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×C₅₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2976	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic
33	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
37	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
38	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
40	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
41	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
42	C₅₃×#563	—	2	1	no	—
43	C₅₃×#562	—	2	1	no	—
44	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
45	C₅₃×#554	—	2	1	no	—
46	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
47	C₅₃×#553	—	2	1	no	—
48	C₅₃×#553	C₂²	1	1	yes	characteristic, complemented
49	C₅₃×#552	C₂²	1	1	yes	characteristic, complemented
50	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#548	C₂²	1	1	yes	characteristic, complemented
52	C₅₃×#548	C₂²	1	1	yes	characteristic, complemented
53	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
54	C₅₃×#546	—	2	1	no	—
55	C₅₃×#546	—	2	1	no	—
56	C₅₃×#546	C₂²	1	1	yes	characteristic
57	C₅₃×#546	C₂²	1	1	yes	characteristic
58	C₅₃×#546	C₂²	1	1	yes	characteristic
59	C₅₃×#546	C₂²	1	1	yes	characteristic
60	D₄²×C₅₃	—	2	1	no	—
61	D₄²×C₅₃	—	2	1	no	—
62	D₄²×C₅₃	C₂²	1	1	yes	characteristic
63	D₄²×C₅₃	C₂²	1	1	yes	characteristic
64	D₄²×C₅₃	C₂²	1	1	yes	characteristic
65	D₄²×C₅₃	C₂²	1	1	yes	characteristic
66	C₅₃×#542	—	2	1	no	—
67	C₅₃×#542	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#541	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#539	—	2	1	no	—
70	C₅₃×#538	—	2	1	no	—
71	C₅₃×#538	—	2	1	no	—
72	C₅₃×#537	C₂²	1	1	yes	characteristic, complemented
73	C₅₃×#536	C₂²	1	1	yes	characteristic, complemented
74	C₅₃×#535	C₂²	1	1	yes	characteristic
75	C₅₃×#535	C₂²	1	1	yes	characteristic
76	C₅₃×#534	—	2	1	no	—
77	C₅₃×#534	—	2	1	no	—
78	C₅₃×#525	C₂²	1	1	yes	characteristic
79	C₅₃×#525	C₂²	1	1	yes	characteristic
80	C₅₃×#525	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
82	C₂×#120×C₅₃	—	2	1	no	—
83	C₂×#120×C₅₃	—	2	1	no	—
84	C₅₃×#518	C₂²	1	1	yes	characteristic
85	C₅₃×#497	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#496	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#495	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#492	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#490	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#489	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#488	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
105	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
106	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
107	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
108	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#469	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
114	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#466	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#466	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
135	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
136	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
137	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
138	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
139	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
140	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
141	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
142	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
143	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
144	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
145	C₅₃×#450	C₂²	1	1	yes	characteristic
146	C₅₃×#450	C₂²	1	1	yes	characteristic
147	C₅₃×#450	C₂²	1	1	yes	characteristic
148	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
149	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
150	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
151	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
152	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
153	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
154	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
155	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
156	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
157	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
158	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
159	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
160	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
161	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
162	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
163	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
164	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
165	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
166	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
167	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
168	C₅₃×#447	C₂²	1	1	yes	characteristic
169	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
170	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
171	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
172	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
173	C₅₃×#442	C₂²	1	1	yes	characteristic, complemented
174	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
175	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
176	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
177	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
178	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
179	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
180	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
181	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
182	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
183	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
184	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
185	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
186	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
187	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
188	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
189	C₅₃×#433	C₂²	1	1	yes	characteristic, complemented
190	C₅₃×#433	C₂²	1	1	yes	characteristic, complemented
191	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
192	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
193	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
194	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
195	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
196	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
197	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
198	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
199	C₅₃×#408	C₂²	1	1	yes	characteristic, complemented
200	C₅₃×#408	C₂²	1	1	yes	characteristic, complemented
201	C₅₃×#407	C₂²	1	1	yes	characteristic, complemented
202	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
203	C₂⁵×C₅₃	—	2	1	no	—
204	H(5,𝔽₂)×C₅₃	—	4	2	no	—
205	H(5,𝔽₂)×C₅₃	—	4	2	no	—
206	C₂×#41×C₅₃	—	2	1	no	—
207	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
208	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
209	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
210	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
211	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
212	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic, complemented
213	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
214	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
215	C₂²×D₄×C₅₃	—	2	1	no	—
216	C₂²×D₄×C₅₃	—	2	1	no	—
217	C₂²×D₄×C₅₃	—	2	1	no	—
218	C₂²×D₄×C₅₃	—	2	1	no	—
219	C₂²×D₄×C₅₃	—	2	1	no	—
220	C₂²×D₄×C₅₃	—	2	1	no	—
221	C₂²×D₄×C₅₃	—	2	1	no	—
222	C₂²×D₄×C₅₃	—	2	1	no	—
223	C₂²×D₄×C₅₃	—	2	1	no	—
224	C₂²×D₄×C₅₃	—	2	1	no	—
225	C₂²×D₄×C₅₃	—	4	2	no	—
226	C₂²×D₄×C₅₃	—	4	2	no	—
227	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
228	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
229	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
230	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
231	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
232	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
233	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
234	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
235	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
236	#137×C₅₃	—	4	2	no	—
237	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
238	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
239	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
240	#135×C₅₃	—	4	2	no	—
241	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
242	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
243	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
244	C₂×SD₁₆×C₅₃	—	4	2	no	—
245	C₂×SD₁₆×C₅₃	—	4	2	no	—
246	C₂×SD₁₆×C₅₃	—	4	2	no	—
247	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
248	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
249	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
250	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
251	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
252	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
253	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
254	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
255	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
256	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
257	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
258	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
259	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
260	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
261	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
262	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
263	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
264	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
265	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
266	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
267	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
268	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
269	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
270	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
271	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
272	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
273	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
274	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
275	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
276	C₄⋊Q₈×C₅₃	—	2	1	no	—
277	C₄⋊Q₈×C₅₃	—	2	1	no	—
278	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
279	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
280	#127×C₅₃	—	2	1	no	—
281	#127×C₅₃	C₂³	1	1	yes	characteristic
282	#127×C₅₃	C₂³	1	1	yes	characteristic
283	#126×C₅₃	—	2	1	no	—
284	#126×C₅₃	—	2	1	no	—
285	#126×C₅₃	—	2	1	no	—
286	#126×C₅₃	—	2	1	no	—
287	#126×C₅₃	—	2	1	no	—
288	#126×C₅₃	—	2	1	no	—
289	#126×C₅₃	—	2	1	no	—
290	#125×C₅₃	—	2	1	no	—
291	#125×C₅₃	—	2	1	no	—
292	#125×C₅₃	—	2	1	no	—
293	#125×C₅₃	—	2	1	no	—
294	#125×C₅₃	C₂³	1	1	yes	characteristic, complemented
295	#124×C₅₃	—	2	1	no	—
296	#124×C₅₃	—	2	1	no	—
297	#124×C₅₃	—	2	1	no	—
298	#124×C₅₃	—	2	1	no	—
299	#124×C₅₃	—	2	1	no	—
300	#124×C₅₃	—	2	1	no	—
301	#124×C₅₃	C₂³	1	1	yes	characteristic
302	#124×C₅₃	C₂³	1	1	yes	characteristic
303	#124×C₅₃	C₂³	1	1	yes	characteristic, complemented
304	#123×C₅₃	—	2	1	no	—
305	#123×C₅₃	—	2	1	no	—
306	#123×C₅₃	—	2	1	no	—
307	#123×C₅₃	—	2	1	no	—
308	#123×C₅₃	—	2	1	no	—
309	#123×C₅₃	—	2	1	no	—
310	#123×C₅₃	—	2	1	no	—
311	#123×C₅₃	—	2	1	no	—
312	#123×C₅₃	—	2	1	no	—
313	#123×C₅₃	—	2	1	no	—
314	#123×C₅₃	—	2	1	no	—
315	#123×C₅₃	—	2	1	no	—
316	#123×C₅₃	—	2	1	no	—
317	#123×C₅₃	D₄	1	1	yes	characteristic
318	#123×C₅₃	D₄	1	1	yes	characteristic
319	C₂²⋊Q₈×C₅₃	—	2	1	no	—
320	C₂²⋊Q₈×C₅₃	—	2	1	no	—
321	C₂²⋊Q₈×C₅₃	—	2	1	no	—
322	C₂²⋊Q₈×C₅₃	—	2	1	no	—
323	C₂²⋊Q₈×C₅₃	—	2	1	no	—
324	C₂²⋊Q₈×C₅₃	—	2	1	no	—
325	C₂²⋊Q₈×C₅₃	—	2	1	no	—
326	C₂²⋊Q₈×C₅₃	—	2	1	no	—
327	C₂²⋊Q₈×C₅₃	—	2	1	no	—
328	C₂²⋊Q₈×C₅₃	—	2	1	no	—
329	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
330	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
331	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
332	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
333	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
334	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
335	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
336	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
337	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
338	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
339	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
340	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
341	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
342	#121×C₅₃	—	2	1	no	—
343	#121×C₅₃	—	2	1	no	—
344	#121×C₅₃	—	2	1	no	—
345	#121×C₅₃	—	2	1	no	—
346	#121×C₅₃	—	2	1	no	—
347	#121×C₅₃	—	2	1	no	—
348	#121×C₅₃	—	2	1	no	—
349	#121×C₅₃	—	2	1	no	—
350	#121×C₅₃	—	2	1	no	—
351	#121×C₅₃	—	2	1	no	—
352	#121×C₅₃	—	2	1	no	—
353	#121×C₅₃	—	2	1	no	—
354	#121×C₅₃	—	2	1	no	—
355	#121×C₅₃	—	2	1	no	—
356	#121×C₅₃	—	2	1	no	—
357	#121×C₅₃	—	2	1	no	—
358	#121×C₅₃	—	2	1	no	—
359	#121×C₅₃	D₄	1	1	yes	characteristic
360	#121×C₅₃	D₄	1	1	yes	characteristic
361	#121×C₅₃	C₂³	1	1	yes	characteristic
362	#121×C₅₃	C₂³	1	1	yes	characteristic
363	#121×C₅₃	C₂³	1	1	yes	characteristic
364	#121×C₅₃	C₂³	1	1	yes	characteristic
365	#121×C₅₃	C₂³	1	1	yes	characteristic
366	#121×C₅₃	C₂³	1	1	yes	characteristic
367	#121×C₅₃	C₂³	1	1	yes	characteristic
368	#121×C₅₃	C₂³	1	1	yes	characteristic
369	#121×C₅₃	C₂³	1	1	yes	characteristic, complemented
370	#120×C₅₃	—	2	1	no	—
371	#120×C₅₃	—	2	1	no	—
372	#120×C₅₃	—	2	1	no	—
373	#120×C₅₃	—	2	1	no	—
374	#120×C₅₃	—	2	1	no	—
375	#120×C₅₃	—	2	1	no	—
376	#120×C₅₃	—	2	1	no	—
377	#120×C₅₃	—	2	1	no	—
378	#120×C₅₃	—	2	1	no	—
379	#120×C₅₃	—	2	1	no	—
380	#120×C₅₃	—	2	1	no	—
381	#120×C₅₃	—	2	1	no	—
382	#120×C₅₃	—	2	1	no	—
383	#120×C₅₃	—	2	1	no	—
384	#120×C₅₃	—	2	1	no	—
385	#120×C₅₃	—	2	1	no	—
386	#120×C₅₃	—	2	1	no	—
387	#120×C₅₃	—	2	1	no	—
388	#120×C₅₃	D₄	1	1	yes	characteristic
389	#120×C₅₃	D₄	1	1	yes	characteristic
390	C₄×Q₈×C₅₃	—	2	1	no	—
391	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
392	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
393	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
394	C₄×D₄×C₅₃	—	2	1	no	—
395	C₄×D₄×C₅₃	—	2	1	no	—
396	C₄×D₄×C₅₃	—	2	1	no	—
397	C₄×D₄×C₅₃	—	2	1	no	—
398	C₄×D₄×C₅₃	—	2	1	no	—
399	C₄×D₄×C₅₃	—	2	1	no	—
400	C₄×D₄×C₅₃	—	2	1	no	—
401	C₄×D₄×C₅₃	—	2	1	no	—
402	C₄×D₄×C₅₃	—	2	1	no	—
403	C₄×D₄×C₅₃	—	2	1	no	—
404	C₄×D₄×C₅₃	—	2	1	no	—
405	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
406	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
407	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
408	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
409	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
410	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
411	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
412	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
413	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
414	#117×C₅₃	—	2	1	no	—
415	#117×C₅₃	C₂³	1	1	yes	characteristic
416	#117×C₅₃	C₂³	1	1	yes	characteristic
417	#117×C₅₃	C₂³	1	1	yes	characteristic
418	#117×C₅₃	C₂³	1	1	yes	characteristic, complemented
419	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
420	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
421	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
422	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
423	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
424	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
425	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
426	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
427	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
428	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
429	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
430	#107×C₅₃	C₂³	1	1	yes	characteristic, complemented
431	#107×C₅₃	C₂³	1	1	yes	characteristic, complemented
432	#107×C₅₃	C₂³	1	1	yes	characteristic, complemented
433	#107×C₅₃	C₂³	1	1	yes	characteristic, complemented
434	#106×C₅₃	C₂³	1	1	yes	characteristic, complemented
435	#106×C₅₃	C₂³	1	1	yes	characteristic, complemented
436	#106×C₅₃	C₂³	1	1	yes	characteristic, complemented
437	#106×C₅₃	C₂³	1	1	yes	characteristic, complemented
438	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
439	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
440	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
441	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
442	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
443	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
444	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
445	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
446	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
447	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
448	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
449	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
450	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
451	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
452	#102×C₅₃	C₂³	1	1	yes	characteristic
453	#102×C₅₃	C₂³	1	1	yes	characteristic
454	#102×C₅₃	C₂³	1	1	yes	characteristic
455	#102×C₅₃	C₂³	1	1	yes	characteristic
456	#102×C₅₃	C₂³	1	1	yes	characteristic
457	#102×C₅₃	C₂³	1	1	yes	characteristic
458	#102×C₅₃	C₂³	1	1	yes	characteristic
459	#102×C₅₃	C₂³	1	1	yes	characteristic
460	#102×C₅₃	C₂³	1	1	yes	characteristic
461	#102×C₅₃	C₂³	1	1	yes	characteristic
462	#102×C₅₃	C₂³	1	1	yes	characteristic
463	#102×C₅₃	C₂³	1	1	yes	characteristic
464	#102×C₅₃	C₂³	1	1	yes	characteristic
465	#102×C₅₃	C₂³	1	1	yes	characteristic
466	#102×C₅₃	C₂³	1	1	yes	characteristic
467	#102×C₅₃	C₂³	1	1	yes	characteristic
468	#102×C₅₃	C₂³	1	1	yes	characteristic, complemented
469	#102×C₅₃	C₂³	1	1	yes	characteristic, complemented
470	#102×C₅₃	C₂³	1	1	yes	characteristic, complemented
471	#102×C₅₃	C₂³	1	1	yes	characteristic, complemented
472	#102×C₅₃	C₂³	1	1	yes	characteristic, complemented
473	#102×C₅₃	C₂³	1	1	yes	characteristic, complemented
474	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
475	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
476	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
477	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
478	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
479	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
480	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
481	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
482	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
483	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
484	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
485	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
486	#97×C₅₃	C₂³	1	1	yes	characteristic, complemented
487	#97×C₅₃	C₂³	1	1	yes	characteristic, complemented
488	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
489	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
490	C₂⁴×C₅₃	—	2	1	no	—
491	C₂⁴×C₅₃	—	2	1	no	—
492	C₂⁴×C₅₃	—	2	1	no	—
493	C₂⁴×C₅₃	—	2	1	no	—
494	C₂⁴×C₅₃	—	2	1	no	—
495	C₂⁴×C₅₃	—	2	1	no	—
496	C₂⁴×C₅₃	—	2	1	no	—
497	C₂⁴×C₅₃	—	2	1	no	—
498	C₂⁴×C₅₃	—	4	4	no	—
499	C₂⁴×C₅₃	—	8	2	no	—
500	C₂⁴×C₅₃	—	8	2	no	—
501	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
502	#41×C₅₃	—	2	2	no	—
503	#41×C₅₃	—	2	2	no	—
504	#41×C₅₃	—	4	1	no	—
505	#41×C₅₃	—	4	1	no	—
506	#41×C₅₃	—	4	1	no	—
507	#41×C₅₃	—	4	1	no	—
508	#41×C₅₃	—	4	1	no	—
509	#41×C₅₃	—	4	1	no	—
510	#41×C₅₃	—	4	1	no	—
511	#41×C₅₃	—	4	1	no	—
512	#41×C₅₃	—	4	1	no	—
513	#41×C₅₃	—	4	1	no	—
514	#41×C₅₃	—	4	4	no	—
515	C₂×Q₈×C₅₃	—	2	1	no	—
516	C₂×Q₈×C₅₃	—	2	1	no	—
517	C₂×Q₈×C₅₃	—	2	1	no	—
518	C₂×Q₈×C₅₃	—	4	1	no	—
519	C₂×Q₈×C₅₃	—	4	1	no	—
520	C₂×Q₈×C₅₃	—	4	1	no	—
521	C₂×Q₈×C₅₃	—	4	1	no	—
522	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
523	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
524	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
525	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
526	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
527	C₂×D₄×C₅₃	—	2	2	no	—
528	C₂×D₄×C₅₃	—	2	2	no	—
529	C₂×D₄×C₅₃	—	2	2	no	—
530	C₂×D₄×C₅₃	—	2	2	no	—
531	C₂×D₄×C₅₃	—	2	2	no	—
532	C₂×D₄×C₅₃	—	2	2	no	—
533	C₂×D₄×C₅₃	—	2	2	no	—
534	C₂×D₄×C₅₃	—	2	2	no	—
535	C₂×D₄×C₅₃	—	2	1	no	—
536	C₂×D₄×C₅₃	—	2	1	no	—
537	C₂×D₄×C₅₃	—	2	1	no	—
538	C₂×D₄×C₅₃	—	2	1	no	—
539	C₂×D₄×C₅₃	—	2	1	no	—
540	C₂×D₄×C₅₃	—	2	1	no	—
541	C₂×D₄×C₅₃	—	2	1	no	—
542	C₂×D₄×C₅₃	—	2	1	no	—
543	C₂×D₄×C₅₃	—	2	1	no	—
544	C₂×D₄×C₅₃	—	2	1	no	—
545	C₂×D₄×C₅₃	—	2	1	no	—
546	C₂×D₄×C₅₃	—	2	1	no	—
547	C₂×D₄×C₅₃	—	2	1	no	—
548	C₂×D₄×C₅₃	—	2	1	no	—
549	C₂×D₄×C₅₃	—	2	1	no	—
550	C₂×D₄×C₅₃	—	2	1	no	—
551	C₂×D₄×C₅₃	—	2	1	no	—
552	C₂×D₄×C₅₃	—	2	1	no	—
553	C₂×D₄×C₅₃	—	2	1	no	—
554	C₂×D₄×C₅₃	—	2	1	no	—
555	C₂×D₄×C₅₃	—	2	1	no	—
556	C₂×D₄×C₅₃	—	2	1	no	—
557	C₂×D₄×C₅₃	—	2	1	no	—
558	C₂×D₄×C₅₃	—	2	1	no	—
559	C₂×D₄×C₅₃	—	2	1	no	—
560	C₂×D₄×C₅₃	—	2	1	no	—
561	C₂×D₄×C₅₃	—	4	1	no	—
562	C₂×D₄×C₅₃	—	4	1	no	—
563	C₂×D₄×C₅₃	—	4	1	no	—
564	C₂×D₄×C₅₃	—	4	1	no	—
565	C₂×D₄×C₅₃	—	4	1	no	—
566	C₂×D₄×C₅₃	—	4	1	no	—
567	C₂×D₄×C₅₃	—	4	1	no	—
568	C₂×D₄×C₅₃	—	4	1	no	—
569	C₂×D₄×C₅₃	—	4	4	no	—
570	C₂×D₄×C₅₃	—	4	4	no	—
571	C₂×D₄×C₅₃	—	4	4	no	—
572	C₂×D₄×C₅₃	—	4	4	no	—
573	C₂×D₄×C₅₃	—	4	4	no	—
574	C₂×D₄×C₅₃	—	4	4	no	—
575	C₂×D₄×C₅₃	—	8	2	no	—
576	C₂×D₄×C₅₃	—	8	2	no	—
577	C₂×D₄×C₅₃	—	8	2	no	—
578	C₂×D₄×C₅₃	—	8	2	no	—
579	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
580	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
581	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
582	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
583	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
584	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
585	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
586	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
587	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
588	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
589	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
590	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
591	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
592	C₂²×C₄×C₅₃	—	2	1	no	—
593	C₂²×C₄×C₅₃	—	2	1	no	—
594	C₂²×C₄×C₅₃	—	2	1	no	—
595	C₂²×C₄×C₅₃	—	2	1	no	—
596	C₂²×C₄×C₅₃	—	2	1	no	—
597	C₂²×C₄×C₅₃	—	2	1	no	—
598	C₂²×C₄×C₅₃	—	2	1	no	—
599	C₂²×C₄×C₅₃	—	2	1	no	—
600	C₂²×C₄×C₅₃	—	2	1	no	—
601	C₂²×C₄×C₅₃	—	2	1	no	—
602	C₂²×C₄×C₅₃	—	2	1	no	—
603	C₂²×C₄×C₅₃	—	2	1	no	—
604	C₂²×C₄×C₅₃	—	2	1	no	—
605	C₂²×C₄×C₅₃	—	2	1	no	—
606	C₂²×C₄×C₅₃	—	4	1	no	—
607	C₂²×C₄×C₅₃	—	4	1	no	—
608	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
609	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
610	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
611	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
612	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
613	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
614	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
615	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
616	Q₁₆×C₅₃	—	4	1	no	—
617	Q₁₆×C₅₃	—	4	1	no	—
618	Q₁₆×C₅₃	—	4	1	no	—
619	SD₁₆×C₅₃	—	2	2	no	—
620	SD₁₆×C₅₃	—	2	2	no	—
621	SD₁₆×C₅₃	—	2	2	no	—
622	SD₁₆×C₅₃	—	2	2	no	—
623	SD₁₆×C₅₃	—	2	2	no	—
624	SD₁₆×C₅₃	—	2	2	no	—
625	SD₁₆×C₅₃	—	4	1	no	—
626	SD₁₆×C₅₃	—	4	1	no	—
627	SD₁₆×C₅₃	—	4	1	no	—
628	SD₁₆×C₅₃	—	4	1	no	—
629	SD₁₆×C₅₃	—	4	1	no	—
630	SD₁₆×C₅₃	—	4	1	no	—
631	SD₁₆×C₅₃	—	4	1	no	—
632	SD₁₆×C₅₃	—	4	1	no	—
633	SD₁₆×C₅₃	—	4	1	no	—
634	SD₁₆×C₅₃	—	4	1	no	—
635	D₈×C₅₃	—	2	2	no	—
636	D₈×C₅₃	—	2	2	no	—
637	D₈×C₅₃	—	4	1	no	—
638	D₈×C₅₃	—	4	1	no	—
639	D₈×C₅₃	—	4	1	no	—
640	M₁₆×C₅₃	—	4	1	no	—
641	M₁₆×C₅₃	—	4	1	no	—
642	M₁₆×C₅₃	—	4	1	no	—
643	M₁₆×C₅₃	—	4	1	no	—
644	C₂×C₈×C₅₃	—	4	1	no	—
645	C₂×C₈×C₅₃	—	4	1	no	—
646	C₂×C₈×C₅₃	—	4	1	no	—
647	C₂×C₈×C₅₃	—	4	1	no	—
648	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
649	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
650	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
651	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
652	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
653	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
654	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
655	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
656	C₄⋊C₄×C₅₃	—	2	1	no	—
657	C₄⋊C₄×C₅₃	—	2	1	no	—
658	C₄⋊C₄×C₅₃	—	2	1	no	—
659	C₄⋊C₄×C₅₃	—	2	1	no	—
660	C₄⋊C₄×C₅₃	—	2	1	no	—
661	C₄⋊C₄×C₅₃	—	2	1	no	—
662	C₄⋊C₄×C₅₃	—	2	1	no	—
663	C₄⋊C₄×C₅₃	—	2	1	no	—
664	C₄⋊C₄×C₅₃	—	2	1	no	—
665	C₄⋊C₄×C₅₃	—	2	1	no	—
666	C₄⋊C₄×C₅₃	—	2	1	no	—
667	C₄⋊C₄×C₅₃	—	2	1	no	—
668	C₄⋊C₄×C₅₃	—	2	1	no	—
669	C₄⋊C₄×C₅₃	—	2	1	no	—
670	C₄⋊C₄×C₅₃	—	2	1	no	—
671	C₄⋊C₄×C₅₃	—	2	1	no	—
672	C₄⋊C₄×C₅₃	—	2	1	no	—
673	C₄⋊C₄×C₅₃	—	2	1	no	—
674	C₄⋊C₄×C₅₃	—	2	1	no	—
675	C₄⋊C₄×C₅₃	—	2	1	no	—
676	C₄⋊C₄×C₅₃	—	2	1	no	—
677	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
678	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
679	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
680	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
681	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
682	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
683	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
684	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
685	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
686	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
687	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
688	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
689	C₂²⋊C₄×C₅₃	—	2	1	no	—
690	C₂²⋊C₄×C₅₃	—	2	1	no	—
691	C₂²⋊C₄×C₅₃	—	2	1	no	—
692	C₂²⋊C₄×C₅₃	—	2	1	no	—
693	C₂²⋊C₄×C₅₃	—	2	1	no	—
694	C₂²⋊C₄×C₅₃	—	2	1	no	—
695	C₂²⋊C₄×C₅₃	—	2	1	no	—
696	C₂²⋊C₄×C₅₃	—	2	1	no	—
697	C₂²⋊C₄×C₅₃	—	2	1	no	—
698	C₂²⋊C₄×C₅₃	—	2	1	no	—
699	C₂²⋊C₄×C₅₃	—	2	1	no	—
700	C₂²⋊C₄×C₅₃	—	2	1	no	—
701	C₂²⋊C₄×C₅₃	—	2	1	no	—
702	C₂²⋊C₄×C₅₃	—	2	1	no	—
703	C₂²⋊C₄×C₅₃	—	2	1	no	—
704	C₂²⋊C₄×C₅₃	—	2	1	no	—
705	C₂²⋊C₄×C₅₃	—	2	1	no	—
706	C₂²⋊C₄×C₅₃	—	2	1	no	—
707	C₂²⋊C₄×C₅₃	—	2	1	no	—
708	C₂²⋊C₄×C₅₃	—	2	1	no	—
709	C₂²⋊C₄×C₅₃	—	2	1	no	—
710	C₂²⋊C₄×C₅₃	—	2	1	no	—
711	C₂²⋊C₄×C₅₃	—	2	1	no	—
712	C₂²⋊C₄×C₅₃	—	2	1	no	—
713	C₂²⋊C₄×C₅₃	—	2	1	no	—
714	C₂²⋊C₄×C₅₃	—	2	1	no	—
715	C₂²⋊C₄×C₅₃	—	2	1	no	—
716	C₂²⋊C₄×C₅₃	—	2	1	no	—
717	C₂²⋊C₄×C₅₃	—	2	1	no	—
718	C₂²⋊C₄×C₅₃	—	2	1	no	—
719	C₂²⋊C₄×C₅₃	—	2	1	no	—
720	C₂²⋊C₄×C₅₃	—	2	1	no	—
721	C₂²⋊C₄×C₅₃	—	2	1	no	—
722	C₂²⋊C₄×C₅₃	—	2	1	no	—
723	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
724	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
725	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
726	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
727	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
728	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
729	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
730	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
731	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
732	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
733	C₄²×C₅₃	—	2	1	no	—
734	C₄²×C₅₃	—	2	1	no	—
735	C₄²×C₅₃	—	2	1	no	—
736	C₄²×C₅₃	—	2	1	no	—
737	C₄²×C₅₃	—	2	1	no	—
738	C₄²×C₅₃	—	2	1	no	—
739	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
740	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
741	C₂³×C₅₃	—	2	4	no	—
742	C₂³×C₅₃	—	2	2	no	—
743	C₂³×C₅₃	—	2	1	no	—
744	C₂³×C₅₃	—	2	1	no	—
745	C₂³×C₅₃	—	2	1	no	—
746	C₂³×C₅₃	—	2	1	no	—
747	C₂³×C₅₃	—	2	1	no	—
748	C₂³×C₅₃	—	2	1	no	—
749	C₂³×C₅₃	—	4	1	no	—
750	C₂³×C₅₃	—	4	1	no	—
751	C₂³×C₅₃	—	4	2	no	—
752	C₂³×C₅₃	—	4	2	no	—
753	C₂³×C₅₃	—	4	2	no	—
754	C₂³×C₅₃	—	4	2	no	—
755	C₂³×C₅₃	—	4	2	no	—
756	C₂³×C₅₃	—	4	2	no	—
757	C₂³×C₅₃	—	4	2	no	—
758	C₂³×C₅₃	—	4	2	no	—
759	C₂³×C₅₃	—	4	2	no	—
760	C₂³×C₅₃	—	4	2	no	—
761	C₂³×C₅₃	—	4	2	no	—
762	C₂³×C₅₃	—	8	1	no	—
763	C₂³×C₅₃	—	8	1	no	—
764	C₂³×C₅₃	—	8	1	no	—
765	C₂³×C₅₃	—	8	1	no	—
766	C₂³×C₅₃	—	8	1	no	—
767	C₂³×C₅₃	—	8	1	no	—
768	C₂³×C₅₃	—	8	1	no	—
769	C₂³×C₅₃	—	8	1	no	—
770	C₂³×C₅₃	—	8	1	no	—
771	C₂³×C₅₃	—	8	1	no	—
772	C₂³×C₅₃	—	8	1	no	—
773	C₂³×C₅₃	—	8	1	no	—
774	C₂³×C₅₃	—	8	16	no	—
775	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
776	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
777	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
778	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
779	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
780	Q₈×C₅₃	—	2	1	no	—
781	Q₈×C₅₃	—	2	1	no	—
782	Q₈×C₅₃	—	2	1	no	—
783	Q₈×C₅₃	—	2	1	no	—
784	Q₈×C₅₃	—	2	1	no	—
785	Q₈×C₅₃	—	2	1	no	—
786	Q₈×C₅₃	—	2	1	no	—
787	Q₈×C₅₃	—	2	1	no	—
788	Q₈×C₅₃	—	4	1	no	—
789	Q₈×C₅₃	—	8	1	no	—
790	Q₈×C₅₃	—	8	1	no	—
791	Q₈×C₅₃	—	8	1	no	—
792	D₄×C₅₃	—	2	4	no	—
793	D₄×C₅₃	—	2	2	no	—
794	D₄×C₅₃	—	2	2	no	—
795	D₄×C₅₃	—	2	1	no	—
796	D₄×C₅₃	—	2	1	no	—
797	D₄×C₅₃	—	2	1	no	—
798	D₄×C₅₃	—	2	1	no	—
799	D₄×C₅₃	—	2	1	no	—
800	D₄×C₅₃	—	2	1	no	—
801	D₄×C₅₃	—	2	1	no	—
802	D₄×C₅₃	—	2	1	no	—
803	D₄×C₅₃	—	2	1	no	—
804	D₄×C₅₃	—	2	1	no	—
805	D₄×C₅₃	—	4	1	no	—
806	D₄×C₅₃	—	4	1	no	—
807	D₄×C₅₃	—	4	1	no	—
808	D₄×C₅₃	—	4	1	no	—
809	D₄×C₅₃	—	4	1	no	—
810	D₄×C₅₃	—	4	2	no	—
811	D₄×C₅₃	—	4	2	no	—
812	D₄×C₅₃	—	4	2	no	—
813	D₄×C₅₃	—	4	2	no	—
814	D₄×C₅₃	—	4	2	no	—
815	D₄×C₅₃	—	4	2	no	—
816	D₄×C₅₃	—	4	2	no	—
817	D₄×C₅₃	—	4	2	no	—
818	D₄×C₅₃	—	4	2	no	—
819	D₄×C₅₃	—	4	2	no	—
820	D₄×C₅₃	—	4	2	no	—
821	D₄×C₅₃	—	4	2	no	—
822	D₄×C₅₃	—	4	2	no	—
823	D₄×C₅₃	—	8	1	no	—
824	D₄×C₅₃	—	8	1	no	—
825	D₄×C₅₃	—	8	1	no	—
826	D₄×C₅₃	—	8	1	no	—
827	D₄×C₅₃	—	8	1	no	—
828	D₄×C₅₃	—	8	1	no	—
829	D₄×C₅₃	—	8	1	no	—
830	D₄×C₅₃	—	8	1	no	—
831	D₄×C₅₃	—	8	1	no	—
832	D₄×C₅₃	—	8	1	no	—
833	D₄×C₅₃	—	8	1	no	—
834	D₄×C₅₃	—	8	1	no	—
835	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
836	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
837	C₂×C₄×C₅₃	—	2	1	no	—
838	C₂×C₄×C₅₃	—	2	1	no	—
839	C₂×C₄×C₅₃	—	2	1	no	—
840	C₂×C₄×C₅₃	—	2	1	no	—
841	C₂×C₄×C₅₃	—	2	1	no	—
842	C₂×C₄×C₅₃	—	2	1	no	—
843	C₂×C₄×C₅₃	—	2	1	no	—
844	C₂×C₄×C₅₃	—	2	1	no	—
845	C₂×C₄×C₅₃	—	2	1	no	—
846	C₂×C₄×C₅₃	—	2	1	no	—
847	C₂×C₄×C₅₃	—	2	1	no	—
848	C₂×C₄×C₅₃	—	2	1	no	—
849	C₂×C₄×C₅₃	—	2	1	no	—
850	C₂×C₄×C₅₃	—	2	1	no	—
851	C₂×C₄×C₅₃	—	2	1	no	—
852	C₂×C₄×C₅₃	—	2	1	no	—
853	C₂×C₄×C₅₃	—	2	1	no	—
854	C₂×C₄×C₅₃	—	2	1	no	—
855	C₂×C₄×C₅₃	—	2	1	no	—
856	C₂×C₄×C₅₃	—	2	1	no	—
857	C₂×C₄×C₅₃	—	4	1	no	—
858	C₂×C₄×C₅₃	—	4	1	no	—
859	C₂×C₄×C₅₃	—	4	1	no	—
860	C₂×C₄×C₅₃	—	4	2	no	—
861	C₂×C₄×C₅₃	—	4	2	no	—
862	C₂×C₄×C₅₃	—	4	2	no	—
863	C₂×C₄×C₅₃	—	8	1	no	—
864	C₂×C₄×C₅₃	—	8	1	no	—
865	C₂×C₄×C₅₃	—	8	1	no	—
866	C₂×C₄×C₅₃	—	8	1	no	—
867	C₂×C₄×C₅₃	—	8	1	no	—
868	C₂×C₄×C₅₃	—	8	1	no	—
869	C₂×C₄×C₅₃	—	8	1	no	—
870	C₂×C₄×C₅₃	—	8	1	no	—
871	C₂×C₄×C₅₃	—	8	1	no	—
872	C₂×C₄×C₅₃	—	8	1	no	—
873	C₂×C₄×C₅₃	—	8	1	no	—
874	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
875	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
876	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
877	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
878	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
879	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
880	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
881	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
882	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
883	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
884	C₈×C₅₃	—	2	1	no	—
885	C₈×C₅₃	—	2	1	no	—
886	C₈×C₅₃	—	2	1	no	—
887	C₈×C₅₃	—	2	1	no	—
888	C₈×C₅₃	—	2	1	no	—
889	C₈×C₅₃	—	2	1	no	—
890	C₈×C₅₃	—	2	1	no	—
891	C₈×C₅₃	—	2	1	no	—
892	#61610	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
893	C₂²×C₅₃	—	2	1	no	—
894	C₂²×C₅₃	—	2	1	no	—
895	C₂²×C₅₃	—	2	1	no	—
896	C₂²×C₅₃	—	2	1	no	—
897	C₂²×C₅₃	—	2	1	no	—
898	C₂²×C₅₃	—	2	1	no	—
899	C₂²×C₅₃	—	2	1	no	—
900	C₂²×C₅₃	—	2	1	no	—
901	C₂²×C₅₃	—	2	1	no	—
902	C₂²×C₅₃	—	2	1	no	—
903	C₂²×C₅₃	—	2	2	no	—
904	C₂²×C₅₃	—	2	2	no	—
905	C₂²×C₅₃	—	2	1	no	—
906	C₂²×C₅₃	—	2	1	no	—
907	C₂²×C₅₃	—	2	1	no	—
908	C₂²×C₅₃	—	2	1	no	—
909	C₂²×C₅₃	—	4	4	no	—
910	C₂²×C₅₃	—	4	1	no	—
911	C₂²×C₅₃	—	4	1	no	—
912	C₂²×C₅₃	—	4	1	no	—
913	C₂²×C₅₃	—	4	1	no	—
914	C₂²×C₅₃	—	4	1	no	—
915	C₂²×C₅₃	—	4	1	no	—
916	C₂²×C₅₃	—	4	1	no	—
917	C₂²×C₅₃	—	4	1	no	—
918	C₂²×C₅₃	—	4	1	no	—
919	C₂²×C₅₃	—	4	1	no	—
920	C₂²×C₅₃	—	4	1	no	—
921	C₂²×C₅₃	—	4	1	no	—
922	C₂²×C₅₃	—	4	1	no	—
923	C₂²×C₅₃	—	4	1	no	—
924	C₂²×C₅₃	—	4	1	no	—
925	C₂²×C₅₃	—	4	1	no	—
926	C₂²×C₅₃	—	8	4	no	—
927	C₂²×C₅₃	—	8	4	no	—
928	C₂²×C₅₃	—	8	4	no	—
929	C₂²×C₅₃	—	8	4	no	—
930	C₂²×C₅₃	—	8	4	no	—
931	C₂²×C₅₃	—	8	4	no	—
932	C₂²×C₅₃	—	16	2	no	—
933	C₂²×C₅₃	—	16	2	no	—
934	C₂²×C₅₃	#577	1	2	yes	—
935	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
936	C₄×C₅₃	—	2	1	no	—
937	C₄×C₅₃	—	2	1	no	—
938	C₄×C₅₃	—	2	1	no	—
939	C₄×C₅₃	—	2	1	no	—
940	C₄×C₅₃	—	2	1	no	—
941	C₄×C₅₃	—	2	1	no	—
942	C₄×C₅₃	—	2	1	no	—
943	C₄×C₅₃	—	2	1	no	—
944	C₄×C₅₃	—	2	1	no	—
945	C₄×C₅₃	—	4	1	no	—
946	C₄×C₅₃	—	4	1	no	—
947	C₄×C₅₃	—	4	1	no	—
948	C₄×C₅₃	—	4	1	no	—
949	C₄×C₅₃	—	4	1	no	—
950	C₄×C₅₃	—	4	1	no	—
951	C₄×C₅₃	—	4	1	no	—
952	C₄×C₅₃	—	4	1	no	—
953	C₄×C₅₃	—	4	1	no	—
954	C₄×C₅₃	—	4	1	no	—
955	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
956	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
957	#3541	C₂×C₅₃	1	1	yes	characteristic, complemented
958	#3484	C₂×C₅₃	1	1	yes	characteristic, complemented
959	#3324	C₂×C₅₃	1	1	yes	characteristic, complemented
960	#3323	C₂×C₅₃	1	1	yes	characteristic, complemented
961	#3318	C₂×C₅₃	1	1	yes	characteristic, complemented
962	#3314	C₂×C₅₃	1	1	yes	characteristic, complemented
963	#3311	C₂×C₅₃	1	1	yes	characteristic, complemented
964	#3310	C₂×C₅₃	1	1	yes	characteristic, complemented
965	#3297	C₂×C₅₃	1	1	yes	characteristic, complemented
966	#3295	C₂×C₅₃	1	1	yes	characteristic, complemented
967	#3282	C₂×C₅₃	1	1	yes	characteristic, complemented
968	D₄×SD₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
969	#3275	C₂×C₅₃	1	1	yes	characteristic, complemented
970	#3272	C₂×C₅₃	1	1	yes	characteristic, complemented
971	#3267	C₂×C₅₃	1	1	yes	characteristic, complemented
972	#3266	C₂×C₅₃	1	1	yes	characteristic, complemented
973	#3265	C₂×C₅₃	1	1	yes	characteristic, complemented
974	#3265	C₂×C₅₃	1	1	yes	characteristic, complemented
975	#3224	C₂×C₅₃	1	1	yes	characteristic, complemented
976	#3222	C₂×C₅₃	1	1	yes	characteristic, complemented
977	#3200	C₂×C₅₃	1	1	yes	characteristic, complemented
978	#3198	C₂×C₅₃	1	1	yes	characteristic, complemented
979	#3196	C₂×C₅₃	1	1	yes	characteristic, complemented
980	#3191	C₂×C₅₃	1	1	yes	characteristic, complemented
981	#3123	C₂×C₅₃	1	1	yes	characteristic, complemented
982	#3118	C₂×C₅₃	1	1	yes	characteristic, complemented
983	#3012	C₂×C₅₃	1	1	yes	characteristic, complemented
984	#3009	C₂×C₅₃	1	1	yes	characteristic, complemented
985	#3003	C₂×C₅₃	1	1	yes	characteristic, complemented
986	C₂×#450	C₂×C₅₃	1	1	yes	characteristic, complemented
987	#2976	C₂×C₅₃	1	1	yes	characteristic, complemented
988	C₂×C₅₃	—	2	2	no	—
989	C₂×C₅₃	—	4	1	no	—
990	C₂×C₅₃	—	4	1	no	—
991	C₂×C₅₃	—	4	1	no	—
992	C₂×C₅₃	—	4	1	no	—
993	C₂×C₅₃	—	4	2	no	—
994	C₂×C₅₃	—	4	2	no	—
995	C₂×C₅₃	—	8	1	no	—
996	C₂×C₅₃	—	8	1	no	—
997	C₂×C₅₃	—	8	1	no	—
998	C₂×C₅₃	—	8	1	no	—
999	C₂×C₅₃	#3484	1	1	yes	characteristic
1000	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
1001	C₂×C₅₃	#3585	1	1	yes	characteristic
1002	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic
1003	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
1004	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
1005	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
1006	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
1007	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
1008	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic, complemented
1009	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1010	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1011	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1012	#563	—	2	1	no	—
1013	#562	—	2	1	no	—
1014	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
1015	#554	—	2	1	no	—
1016	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
1017	#553	—	2	1	no	—
1018	#553	C₂²×C₅₃	1	1	yes	characteristic, complemented
1019	#552	C₂²×C₅₃	1	1	yes	characteristic, complemented
1020	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1021	#548	C₂²×C₅₃	1	1	yes	characteristic, complemented
1022	#548	C₂²×C₅₃	1	1	yes	characteristic, complemented
1023	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
1024	#546	—	2	1	no	—
1025	#546	—	2	1	no	—
1026	#546	C₂²×C₅₃	1	1	yes	characteristic
1027	#546	C₂²×C₅₃	1	1	yes	characteristic
1028	#546	C₂²×C₅₃	1	1	yes	characteristic
1029	#546	C₂²×C₅₃	1	1	yes	characteristic
1030	D₄²	—	2	1	no	—
1031	D₄²	—	2	1	no	—
1032	D₄²	C₂²×C₅₃	1	1	yes	characteristic
1033	D₄²	C₂²×C₅₃	1	1	yes	characteristic
1034	D₄²	C₂²×C₅₃	1	1	yes	characteristic
1035	D₄²	C₂²×C₅₃	1	1	yes	characteristic
1036	#542	—	2	1	no	—
1037	#542	C₂²×C₅₃	1	1	yes	characteristic, complemented
1038	#541	C₂²×C₅₃	1	1	yes	characteristic, complemented
1039	#539	—	2	1	no	—
1040	#538	—	2	1	no	—
1041	#538	—	2	1	no	—
1042	#537	C₂²×C₅₃	1	1	yes	characteristic, complemented
1043	#536	C₂²×C₅₃	1	1	yes	characteristic, complemented
1044	#535	C₂²×C₅₃	1	1	yes	characteristic
1045	#535	C₂²×C₅₃	1	1	yes	characteristic
1046	#534	—	2	1	no	—
1047	#534	—	2	1	no	—
1048	#525	C₂²×C₅₃	1	1	yes	characteristic
1049	#525	C₂²×C₅₃	1	1	yes	characteristic
1050	#525	C₂²×C₅₃	1	1	yes	characteristic, complemented
1051	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1052	C₂×#120	—	2	1	no	—
1053	C₂×#120	—	2	1	no	—
1054	#518	C₂²×C₅₃	1	1	yes	characteristic
1055	#497	C₂²×C₅₃	1	1	yes	characteristic, complemented
1056	#496	C₂²×C₅₃	1	1	yes	characteristic, complemented
1057	#495	C₂²×C₅₃	1	1	yes	characteristic, complemented
1058	#492	C₂²×C₅₃	1	1	yes	characteristic, complemented
1059	#490	C₂²×C₅₃	1	1	yes	characteristic, complemented
1060	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
1061	#488	C₂²×C₅₃	1	1	yes	characteristic, complemented
1062	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
1063	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
1064	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
1065	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
1066	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
1067	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
1068	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
1069	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
1070	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
1071	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
1072	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
1073	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
1074	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
1075	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
1076	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
1077	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
1078	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
1079	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
1080	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
1081	#469	C₂²×C₅₃	1	1	yes	characteristic, complemented
1082	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1083	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1084	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1085	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1086	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1087	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
1088	#466	C₂²×C₅₃	1	1	yes	characteristic, complemented
1089	#466	C₂²×C₅₃	1	1	yes	characteristic, complemented
1090	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1091	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1092	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1093	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1094	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1095	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1096	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1097	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1098	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1099	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1100	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1101	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1102	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1103	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1104	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1105	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1106	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1107	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1108	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1109	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1110	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1111	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1112	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1113	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1114	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1115	#450	C₂²×C₅₃	1	1	yes	characteristic
1116	#450	C₂²×C₅₃	1	1	yes	characteristic
1117	#450	C₂²×C₅₃	1	1	yes	characteristic
1118	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1119	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1120	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1121	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1122	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1123	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1124	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1125	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1126	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1127	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1128	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1129	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1130	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1131	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1132	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1133	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1134	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1135	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1136	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1137	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1138	#447	C₂²×C₅₃	1	1	yes	characteristic
1139	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1140	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1141	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1142	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1143	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1144	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1145	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1146	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1147	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1148	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1149	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1150	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1151	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
1152	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
1153	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1154	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1155	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1156	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1157	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1158	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1159	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1160	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1161	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
1162	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
1163	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
1164	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
1165	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1166	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
1167	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
1168	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
1169	#408	C₂²×C₅₃	1	1	yes	characteristic, complemented
1170	#408	C₂²×C₅₃	1	1	yes	characteristic, complemented
1171	#407	C₂²×C₅₃	1	1	yes	characteristic, complemented
1172	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1173	C₅₃	#61610	1	1	yes	characteristic, direct product factor, Sylow
1174	C₂⁵	—	2	1	no	—
1175	H(5,𝔽₂)	—	4	2	no	—
1176	H(5,𝔽₂)	—	4	2	no	—
1177	C₂×#41	—	2	1	no	—
1178	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1179	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1180	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1181	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1182	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1183	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic, complemented
1184	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1185	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
1186	C₂²×D₄	—	2	1	no	—
1187	C₂²×D₄	—	2	1	no	—
1188	C₂²×D₄	—	2	1	no	—
1189	C₂²×D₄	—	2	1	no	—
1190	C₂²×D₄	—	2	1	no	—
1191	C₂²×D₄	—	2	1	no	—
1192	C₂²×D₄	—	2	1	no	—
1193	C₂²×D₄	—	2	1	no	—
1194	C₂²×D₄	—	2	1	no	—
1195	C₂²×D₄	—	2	1	no	—
1196	C₂²×D₄	—	4	2	no	—
1197	C₂²×D₄	—	4	2	no	—
1198	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1199	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1200	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1201	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1202	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1203	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1204	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1205	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1206	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1207	#137	—	4	2	no	—
1208	AGL(1,ℤ/8)	—	4	2	no	—
1209	AGL(1,ℤ/8)	—	4	2	no	—
1210	AGL(1,ℤ/8)	—	4	2	no	—
1211	#135	—	4	2	no	—
1212	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic, complemented
1213	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic, complemented
1214	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic, complemented
1215	C₂×SD₁₆	—	4	2	no	—
1216	C₂×SD₁₆	—	4	2	no	—
1217	C₂×SD₁₆	—	4	2	no	—
1218	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1219	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1220	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1221	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1222	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1223	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1224	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1225	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1226	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1227	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1228	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1229	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1230	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic, complemented
1231	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic, complemented
1232	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic, complemented
1233	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic, complemented
1234	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1235	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1236	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1237	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1238	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
1239	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1240	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1241	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic, complemented
1242	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic, complemented
1243	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1244	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1245	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
1246	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
1247	C₄⋊Q₈	—	2	1	no	—
1248	C₄⋊Q₈	—	2	1	no	—
1249	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
1250	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
1251	#127	—	2	1	no	—
1252	#127	C₂³×C₅₃	1	1	yes	characteristic
1253	#127	C₂³×C₅₃	1	1	yes	characteristic
1254	#126	—	2	1	no	—
1255	#126	—	2	1	no	—
1256	#126	—	2	1	no	—
1257	#126	—	2	1	no	—
1258	#126	—	2	1	no	—
1259	#126	—	2	1	no	—
1260	#126	—	2	1	no	—
1261	#125	—	2	1	no	—
1262	#125	—	2	1	no	—
1263	#125	—	2	1	no	—
1264	#125	—	2	1	no	—
1265	#125	C₂³×C₅₃	1	1	yes	characteristic, complemented
1266	#124	—	2	1	no	—
1267	#124	—	2	1	no	—
1268	#124	—	2	1	no	—
1269	#124	—	2	1	no	—
1270	#124	—	2	1	no	—
1271	#124	—	2	1	no	—
1272	#124	C₂³×C₅₃	1	1	yes	characteristic
1273	#124	C₂³×C₅₃	1	1	yes	characteristic
1274	#124	C₂³×C₅₃	1	1	yes	characteristic, complemented
1275	#123	—	2	1	no	—
1276	#123	—	2	1	no	—
1277	#123	—	2	1	no	—
1278	#123	—	2	1	no	—
1279	#123	—	2	1	no	—
1280	#123	—	2	1	no	—
1281	#123	—	2	1	no	—
1282	#123	—	2	1	no	—
1283	#123	—	2	1	no	—
1284	#123	—	2	1	no	—
1285	#123	—	2	1	no	—
1286	#123	—	2	1	no	—
1287	#123	—	2	1	no	—
1288	#123	D₄×C₅₃	1	1	yes	characteristic
1289	#123	D₄×C₅₃	1	1	yes	characteristic
1290	C₂²⋊Q₈	—	2	1	no	—
1291	C₂²⋊Q₈	—	2	1	no	—
1292	C₂²⋊Q₈	—	2	1	no	—
1293	C₂²⋊Q₈	—	2	1	no	—
1294	C₂²⋊Q₈	—	2	1	no	—
1295	C₂²⋊Q₈	—	2	1	no	—
1296	C₂²⋊Q₈	—	2	1	no	—
1297	C₂²⋊Q₈	—	2	1	no	—
1298	C₂²⋊Q₈	—	2	1	no	—
1299	C₂²⋊Q₈	—	2	1	no	—
1300	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
1301	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
1302	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1303	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1304	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1305	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1306	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1307	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1308	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1309	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1310	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
1311	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
1312	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
1313	#121	—	2	1	no	—
1314	#121	—	2	1	no	—
1315	#121	—	2	1	no	—
1316	#121	—	2	1	no	—
1317	#121	—	2	1	no	—
1318	#121	—	2	1	no	—
1319	#121	—	2	1	no	—
1320	#121	—	2	1	no	—
1321	#121	—	2	1	no	—
1322	#121	—	2	1	no	—
1323	#121	—	2	1	no	—
1324	#121	—	2	1	no	—
1325	#121	—	2	1	no	—
1326	#121	—	2	1	no	—
1327	#121	—	2	1	no	—
1328	#121	—	2	1	no	—
1329	#121	—	2	1	no	—
1330	#121	D₄×C₅₃	1	1	yes	characteristic
1331	#121	D₄×C₅₃	1	1	yes	characteristic
1332	#121	C₂³×C₅₃	1	1	yes	characteristic
1333	#121	C₂³×C₅₃	1	1	yes	characteristic
1334	#121	C₂³×C₅₃	1	1	yes	characteristic
1335	#121	C₂³×C₅₃	1	1	yes	characteristic
1336	#121	C₂³×C₅₃	1	1	yes	characteristic
1337	#121	C₂³×C₅₃	1	1	yes	characteristic
1338	#121	C₂³×C₅₃	1	1	yes	characteristic
1339	#121	C₂³×C₅₃	1	1	yes	characteristic
1340	#121	C₂³×C₅₃	1	1	yes	characteristic, complemented
1341	#120	—	2	1	no	—
1342	#120	—	2	1	no	—
1343	#120	—	2	1	no	—
1344	#120	—	2	1	no	—
1345	#120	—	2	1	no	—
1346	#120	—	2	1	no	—
1347	#120	—	2	1	no	—
1348	#120	—	2	1	no	—
1349	#120	—	2	1	no	—
1350	#120	—	2	1	no	—
1351	#120	—	2	1	no	—
1352	#120	—	2	1	no	—
1353	#120	—	2	1	no	—
1354	#120	—	2	1	no	—
1355	#120	—	2	1	no	—
1356	#120	—	2	1	no	—
1357	#120	—	2	1	no	—
1358	#120	—	2	1	no	—
1359	#120	D₄×C₅₃	1	1	yes	characteristic
1360	#120	D₄×C₅₃	1	1	yes	characteristic
1361	C₄×Q₈	—	2	1	no	—
1362	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
1363	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
1364	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
1365	C₄×D₄	—	2	1	no	—
1366	C₄×D₄	—	2	1	no	—
1367	C₄×D₄	—	2	1	no	—
1368	C₄×D₄	—	2	1	no	—
1369	C₄×D₄	—	2	1	no	—
1370	C₄×D₄	—	2	1	no	—
1371	C₄×D₄	—	2	1	no	—
1372	C₄×D₄	—	2	1	no	—
1373	C₄×D₄	—	2	1	no	—
1374	C₄×D₄	—	2	1	no	—
1375	C₄×D₄	—	2	1	no	—
1376	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1377	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1378	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1379	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1380	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1381	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1382	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1383	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1384	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic, complemented
1385	#117	—	2	1	no	—
1386	#117	C₂³×C₅₃	1	1	yes	characteristic
1387	#117	C₂³×C₅₃	1	1	yes	characteristic
1388	#117	C₂³×C₅₃	1	1	yes	characteristic
1389	#117	C₂³×C₅₃	1	1	yes	characteristic, complemented
1390	C₂×C₄⋊C₄	—	2	1	no	—
1391	C₂×C₄⋊C₄	—	2	1	no	—
1392	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1393	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic, complemented
1394	C₂×C₂²⋊C₄	—	2	1	no	—
1395	C₂×C₂²⋊C₄	—	2	1	no	—
1396	C₂×C₂²⋊C₄	—	2	1	no	—
1397	C₂×C₂²⋊C₄	—	2	1	no	—
1398	C₂×C₂²⋊C₄	—	2	1	no	—
1399	C₂×C₂²⋊C₄	—	2	1	no	—
1400	C₂×C₂²⋊C₄	—	2	1	no	—
1401	#107	C₂³×C₅₃	1	1	yes	characteristic, complemented
1402	#107	C₂³×C₅₃	1	1	yes	characteristic, complemented
1403	#107	C₂³×C₅₃	1	1	yes	characteristic, complemented
1404	#107	C₂³×C₅₃	1	1	yes	characteristic, complemented
1405	#106	C₂³×C₅₃	1	1	yes	characteristic, complemented
1406	#106	C₂³×C₅₃	1	1	yes	characteristic, complemented
1407	#106	C₂³×C₅₃	1	1	yes	characteristic, complemented
1408	#106	C₂³×C₅₃	1	1	yes	characteristic, complemented
1409	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
1410	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
1411	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
1412	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
1413	#103	C₂³×C₅₃	1	1	yes	characteristic, complemented
1414	#103	C₂³×C₅₃	1	1	yes	characteristic, complemented
1415	#103	C₂³×C₅₃	1	1	yes	characteristic, complemented
1416	#103	C₂³×C₅₃	1	1	yes	characteristic, complemented
1417	#103	C₂³×C₅₃	1	1	yes	characteristic, complemented
1418	#103	C₂³×C₅₃	1	1	yes	characteristic, complemented
1419	#103	C₂³×C₅₃	1	1	yes	characteristic, complemented
1420	#103	C₂³×C₅₃	1	1	yes	characteristic, complemented
1421	#103	C₂³×C₅₃	1	1	yes	characteristic, complemented
1422	#103	C₂³×C₅₃	1	1	yes	characteristic, complemented
1423	#102	C₂³×C₅₃	1	1	yes	characteristic
1424	#102	C₂³×C₅₃	1	1	yes	characteristic
1425	#102	C₂³×C₅₃	1	1	yes	characteristic
1426	#102	C₂³×C₅₃	1	1	yes	characteristic
1427	#102	C₂³×C₅₃	1	1	yes	characteristic
1428	#102	C₂³×C₅₃	1	1	yes	characteristic
1429	#102	C₂³×C₅₃	1	1	yes	characteristic
1430	#102	C₂³×C₅₃	1	1	yes	characteristic
1431	#102	C₂³×C₅₃	1	1	yes	characteristic
1432	#102	C₂³×C₅₃	1	1	yes	characteristic
1433	#102	C₂³×C₅₃	1	1	yes	characteristic
1434	#102	C₂³×C₅₃	1	1	yes	characteristic
1435	#102	C₂³×C₅₃	1	1	yes	characteristic
1436	#102	C₂³×C₅₃	1	1	yes	characteristic
1437	#102	C₂³×C₅₃	1	1	yes	characteristic
1438	#102	C₂³×C₅₃	1	1	yes	characteristic
1439	#102	C₂³×C₅₃	1	1	yes	characteristic, complemented
1440	#102	C₂³×C₅₃	1	1	yes	characteristic, complemented
1441	#102	C₂³×C₅₃	1	1	yes	characteristic, complemented
1442	#102	C₂³×C₅₃	1	1	yes	characteristic, complemented
1443	#102	C₂³×C₅₃	1	1	yes	characteristic, complemented
1444	#102	C₂³×C₅₃	1	1	yes	characteristic, complemented
1445	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1446	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1447	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1448	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1449	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1450	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1451	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1452	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1453	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
1454	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
1455	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
1456	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
1457	#97	C₂³×C₅₃	1	1	yes	characteristic, complemented
1458	#97	C₂³×C₅₃	1	1	yes	characteristic, complemented
1459	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
1460	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic, complemented
1461	C₂⁴	—	2	1	no	—
1462	C₂⁴	—	2	1	no	—
1463	C₂⁴	—	2	1	no	—
1464	C₂⁴	—	2	1	no	—
1465	C₂⁴	—	2	1	no	—
1466	C₂⁴	—	2	1	no	—
1467	C₂⁴	—	2	1	no	—
1468	C₂⁴	—	2	1	no	—
1469	C₂⁴	—	4	4	no	—
1470	C₂⁴	—	8	2	no	—
1471	C₂⁴	—	8	2	no	—
1472	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
1473	#41	—	2	2	no	—
1474	#41	—	2	2	no	—
1475	#41	—	4	1	no	—
1476	#41	—	4	1	no	—
1477	#41	—	4	1	no	—
1478	#41	—	4	1	no	—
1479	#41	—	4	1	no	—
1480	#41	—	4	1	no	—
1481	#41	—	4	1	no	—
1482	#41	—	4	1	no	—
1483	#41	—	4	1	no	—
1484	#41	—	4	1	no	—
1485	#41	—	4	4	no	—
1486	C₂×Q₈	—	2	1	no	—
1487	C₂×Q₈	—	2	1	no	—
1488	C₂×Q₈	—	2	1	no	—
1489	C₂×Q₈	—	4	1	no	—
1490	C₂×Q₈	—	4	1	no	—
1491	C₂×Q₈	—	4	1	no	—
1492	C₂×Q₈	—	4	1	no	—
1493	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1494	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1495	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1496	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1497	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1498	C₂×D₄	—	2	2	no	—
1499	C₂×D₄	—	2	2	no	—
1500	C₂×D₄	—	2	2	no	—
1501	C₂×D₄	—	2	2	no	—
1502	C₂×D₄	—	2	2	no	—
1503	C₂×D₄	—	2	2	no	—
1504	C₂×D₄	—	2	2	no	—
1505	C₂×D₄	—	2	2	no	—
1506	C₂×D₄	—	2	1	no	—
1507	C₂×D₄	—	2	1	no	—
1508	C₂×D₄	—	2	1	no	—
1509	C₂×D₄	—	2	1	no	—
1510	C₂×D₄	—	2	1	no	—
1511	C₂×D₄	—	2	1	no	—
1512	C₂×D₄	—	2	1	no	—
1513	C₂×D₄	—	2	1	no	—
1514	C₂×D₄	—	2	1	no	—
1515	C₂×D₄	—	2	1	no	—
1516	C₂×D₄	—	2	1	no	—
1517	C₂×D₄	—	2	1	no	—
1518	C₂×D₄	—	2	1	no	—
1519	C₂×D₄	—	2	1	no	—
1520	C₂×D₄	—	2	1	no	—
1521	C₂×D₄	—	2	1	no	—
1522	C₂×D₄	—	2	1	no	—
1523	C₂×D₄	—	2	1	no	—
1524	C₂×D₄	—	2	1	no	—
1525	C₂×D₄	—	2	1	no	—
1526	C₂×D₄	—	2	1	no	—
1527	C₂×D₄	—	2	1	no	—
1528	C₂×D₄	—	2	1	no	—
1529	C₂×D₄	—	2	1	no	—
1530	C₂×D₄	—	2	1	no	—
1531	C₂×D₄	—	2	1	no	—
1532	C₂×D₄	—	4	1	no	—
1533	C₂×D₄	—	4	1	no	—
1534	C₂×D₄	—	4	1	no	—
1535	C₂×D₄	—	4	1	no	—
1536	C₂×D₄	—	4	1	no	—
1537	C₂×D₄	—	4	1	no	—
1538	C₂×D₄	—	4	1	no	—
1539	C₂×D₄	—	4	1	no	—
1540	C₂×D₄	—	4	4	no	—
1541	C₂×D₄	—	4	4	no	—
1542	C₂×D₄	—	4	4	no	—
1543	C₂×D₄	—	4	4	no	—
1544	C₂×D₄	—	4	4	no	—
1545	C₂×D₄	—	4	4	no	—
1546	C₂×D₄	—	8	2	no	—
1547	C₂×D₄	—	8	2	no	—
1548	C₂×D₄	—	8	2	no	—
1549	C₂×D₄	—	8	2	no	—
1550	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1551	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1552	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1553	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1554	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1555	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1556	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1557	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1558	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1559	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1560	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1561	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1562	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1563	C₂²×C₄	—	2	1	no	—
1564	C₂²×C₄	—	2	1	no	—
1565	C₂²×C₄	—	2	1	no	—
1566	C₂²×C₄	—	2	1	no	—
1567	C₂²×C₄	—	2	1	no	—
1568	C₂²×C₄	—	2	1	no	—
1569	C₂²×C₄	—	2	1	no	—
1570	C₂²×C₄	—	2	1	no	—
1571	C₂²×C₄	—	2	1	no	—
1572	C₂²×C₄	—	2	1	no	—
1573	C₂²×C₄	—	2	1	no	—
1574	C₂²×C₄	—	2	1	no	—
1575	C₂²×C₄	—	2	1	no	—
1576	C₂²×C₄	—	2	1	no	—
1577	C₂²×C₄	—	4	1	no	—
1578	C₂²×C₄	—	4	1	no	—
1579	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1580	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1581	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1582	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1583	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1584	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1585	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1586	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1587	Q₁₆	—	4	1	no	—
1588	Q₁₆	—	4	1	no	—
1589	Q₁₆	—	4	1	no	—
1590	SD₁₆	—	2	2	no	—
1591	SD₁₆	—	2	2	no	—
1592	SD₁₆	—	2	2	no	—
1593	SD₁₆	—	2	2	no	—
1594	SD₁₆	—	2	2	no	—
1595	SD₁₆	—	2	2	no	—
1596	SD₁₆	—	4	1	no	—
1597	SD₁₆	—	4	1	no	—
1598	SD₁₆	—	4	1	no	—
1599	SD₁₆	—	4	1	no	—
1600	SD₁₆	—	4	1	no	—
1601	SD₁₆	—	4	1	no	—
1602	SD₁₆	—	4	1	no	—
1603	SD₁₆	—	4	1	no	—
1604	SD₁₆	—	4	1	no	—
1605	SD₁₆	—	4	1	no	—
1606	D₈	—	2	2	no	—
1607	D₈	—	2	2	no	—
1608	D₈	—	4	1	no	—
1609	D₈	—	4	1	no	—
1610	D₈	—	4	1	no	—
1611	M₁₆	—	4	1	no	—
1612	M₁₆	—	4	1	no	—
1613	M₁₆	—	4	1	no	—
1614	M₁₆	—	4	1	no	—
1615	C₂×C₈	—	4	1	no	—
1616	C₂×C₈	—	4	1	no	—
1617	C₂×C₈	—	4	1	no	—
1618	C₂×C₈	—	4	1	no	—
1619	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1620	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1621	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1622	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1623	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1624	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1625	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1626	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1627	C₄⋊C₄	—	2	1	no	—
1628	C₄⋊C₄	—	2	1	no	—
1629	C₄⋊C₄	—	2	1	no	—
1630	C₄⋊C₄	—	2	1	no	—
1631	C₄⋊C₄	—	2	1	no	—
1632	C₄⋊C₄	—	2	1	no	—
1633	C₄⋊C₄	—	2	1	no	—
1634	C₄⋊C₄	—	2	1	no	—
1635	C₄⋊C₄	—	2	1	no	—
1636	C₄⋊C₄	—	2	1	no	—
1637	C₄⋊C₄	—	2	1	no	—
1638	C₄⋊C₄	—	2	1	no	—
1639	C₄⋊C₄	—	2	1	no	—
1640	C₄⋊C₄	—	2	1	no	—
1641	C₄⋊C₄	—	2	1	no	—
1642	C₄⋊C₄	—	2	1	no	—
1643	C₄⋊C₄	—	2	1	no	—
1644	C₄⋊C₄	—	2	1	no	—
1645	C₄⋊C₄	—	2	1	no	—
1646	C₄⋊C₄	—	2	1	no	—
1647	C₄⋊C₄	—	2	1	no	—
1648	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1649	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1650	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1651	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1652	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1653	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1654	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1655	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1656	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1657	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1658	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1659	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1660	C₂²⋊C₄	—	2	1	no	—
1661	C₂²⋊C₄	—	2	1	no	—
1662	C₂²⋊C₄	—	2	1	no	—
1663	C₂²⋊C₄	—	2	1	no	—
1664	C₂²⋊C₄	—	2	1	no	—
1665	C₂²⋊C₄	—	2	1	no	—
1666	C₂²⋊C₄	—	2	1	no	—
1667	C₂²⋊C₄	—	2	1	no	—
1668	C₂²⋊C₄	—	2	1	no	—
1669	C₂²⋊C₄	—	2	1	no	—
1670	C₂²⋊C₄	—	2	1	no	—
1671	C₂²⋊C₄	—	2	1	no	—
1672	C₂²⋊C₄	—	2	1	no	—
1673	C₂²⋊C₄	—	2	1	no	—
1674	C₂²⋊C₄	—	2	1	no	—
1675	C₂²⋊C₄	—	2	1	no	—
1676	C₂²⋊C₄	—	2	1	no	—
1677	C₂²⋊C₄	—	2	1	no	—
1678	C₂²⋊C₄	—	2	1	no	—
1679	C₂²⋊C₄	—	2	1	no	—
1680	C₂²⋊C₄	—	2	1	no	—
1681	C₂²⋊C₄	—	2	1	no	—
1682	C₂²⋊C₄	—	2	1	no	—
1683	C₂²⋊C₄	—	2	1	no	—
1684	C₂²⋊C₄	—	2	1	no	—
1685	C₂²⋊C₄	—	2	1	no	—
1686	C₂²⋊C₄	—	2	1	no	—
1687	C₂²⋊C₄	—	2	1	no	—
1688	C₂²⋊C₄	—	2	1	no	—
1689	C₂²⋊C₄	—	2	1	no	—
1690	C₂²⋊C₄	—	2	1	no	—
1691	C₂²⋊C₄	—	2	1	no	—
1692	C₂²⋊C₄	—	2	1	no	—
1693	C₂²⋊C₄	—	2	1	no	—
1694	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1695	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1696	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1697	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1698	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1699	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1700	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1701	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1702	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1703	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1704	C₄²	—	2	1	no	—
1705	C₄²	—	2	1	no	—
1706	C₄²	—	2	1	no	—
1707	C₄²	—	2	1	no	—
1708	C₄²	—	2	1	no	—
1709	C₄²	—	2	1	no	—
1710	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1711	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1712	C₂³	—	2	4	no	—
1713	C₂³	—	2	2	no	—
1714	C₂³	—	2	1	no	—
1715	C₂³	—	2	1	no	—
1716	C₂³	—	2	1	no	—
1717	C₂³	—	2	1	no	—
1718	C₂³	—	2	1	no	—
1719	C₂³	—	2	1	no	—
1720	C₂³	—	4	1	no	—
1721	C₂³	—	4	1	no	—
1722	C₂³	—	4	2	no	—
1723	C₂³	—	4	2	no	—
1724	C₂³	—	4	2	no	—
1725	C₂³	—	4	2	no	—
1726	C₂³	—	4	2	no	—
1727	C₂³	—	4	2	no	—
1728	C₂³	—	4	2	no	—
1729	C₂³	—	4	2	no	—
1730	C₂³	—	4	2	no	—
1731	C₂³	—	4	2	no	—
1732	C₂³	—	4	2	no	—
1733	C₂³	—	8	1	no	—
1734	C₂³	—	8	1	no	—
1735	C₂³	—	8	1	no	—
1736	C₂³	—	8	1	no	—
1737	C₂³	—	8	1	no	—
1738	C₂³	—	8	1	no	—
1739	C₂³	—	8	1	no	—
1740	C₂³	—	8	1	no	—
1741	C₂³	—	8	1	no	—
1742	C₂³	—	8	1	no	—
1743	C₂³	—	8	1	no	—
1744	C₂³	—	8	1	no	—
1745	C₂³	—	8	16	no	—
1746	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1747	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1748	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1749	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1750	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1751	Q₈	—	2	1	no	—
1752	Q₈	—	2	1	no	—
1753	Q₈	—	2	1	no	—
1754	Q₈	—	2	1	no	—
1755	Q₈	—	2	1	no	—
1756	Q₈	—	2	1	no	—
1757	Q₈	—	2	1	no	—
1758	Q₈	—	2	1	no	—
1759	Q₈	—	4	1	no	—
1760	Q₈	—	8	1	no	—
1761	Q₈	—	8	1	no	—
1762	Q₈	—	8	1	no	—
1763	D₄	—	2	4	no	—
1764	D₄	—	2	2	no	—
1765	D₄	—	2	2	no	—
1766	D₄	—	2	1	no	—
1767	D₄	—	2	1	no	—
1768	D₄	—	2	1	no	—
1769	D₄	—	2	1	no	—
1770	D₄	—	2	1	no	—
1771	D₄	—	2	1	no	—
1772	D₄	—	2	1	no	—
1773	D₄	—	2	1	no	—
1774	D₄	—	2	1	no	—
1775	D₄	—	2	1	no	—
1776	D₄	—	4	1	no	—
1777	D₄	—	4	1	no	—
1778	D₄	—	4	1	no	—
1779	D₄	—	4	1	no	—
1780	D₄	—	4	1	no	—
1781	D₄	—	4	2	no	—
1782	D₄	—	4	2	no	—
1783	D₄	—	4	2	no	—
1784	D₄	—	4	2	no	—
1785	D₄	—	4	2	no	—
1786	D₄	—	4	2	no	—
1787	D₄	—	4	2	no	—
1788	D₄	—	4	2	no	—
1789	D₄	—	4	2	no	—
1790	D₄	—	4	2	no	—
1791	D₄	—	4	2	no	—
1792	D₄	—	4	2	no	—
1793	D₄	—	4	2	no	—
1794	D₄	—	8	1	no	—
1795	D₄	—	8	1	no	—
1796	D₄	—	8	1	no	—
1797	D₄	—	8	1	no	—
1798	D₄	—	8	1	no	—
1799	D₄	—	8	1	no	—
1800	D₄	—	8	1	no	—
1801	D₄	—	8	1	no	—
1802	D₄	—	8	1	no	—
1803	D₄	—	8	1	no	—
1804	D₄	—	8	1	no	—
1805	D₄	—	8	1	no	—
1806	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1807	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1808	C₂×C₄	—	2	1	no	—
1809	C₂×C₄	—	2	1	no	—
1810	C₂×C₄	—	2	1	no	—
1811	C₂×C₄	—	2	1	no	—
1812	C₂×C₄	—	2	1	no	—
1813	C₂×C₄	—	2	1	no	—
1814	C₂×C₄	—	2	1	no	—
1815	C₂×C₄	—	2	1	no	—
1816	C₂×C₄	—	2	1	no	—
1817	C₂×C₄	—	2	1	no	—
1818	C₂×C₄	—	2	1	no	—
1819	C₂×C₄	—	2	1	no	—
1820	C₂×C₄	—	2	1	no	—
1821	C₂×C₄	—	2	1	no	—
1822	C₂×C₄	—	2	1	no	—
1823	C₂×C₄	—	2	1	no	—
1824	C₂×C₄	—	2	1	no	—
1825	C₂×C₄	—	2	1	no	—
1826	C₂×C₄	—	2	1	no	—
1827	C₂×C₄	—	2	1	no	—
1828	C₂×C₄	—	4	1	no	—
1829	C₂×C₄	—	4	1	no	—
1830	C₂×C₄	—	4	1	no	—
1831	C₂×C₄	—	4	2	no	—
1832	C₂×C₄	—	4	2	no	—
1833	C₂×C₄	—	4	2	no	—
1834	C₂×C₄	—	8	1	no	—
1835	C₂×C₄	—	8	1	no	—
1836	C₂×C₄	—	8	1	no	—
1837	C₂×C₄	—	8	1	no	—
1838	C₂×C₄	—	8	1	no	—
1839	C₂×C₄	—	8	1	no	—
1840	C₂×C₄	—	8	1	no	—
1841	C₂×C₄	—	8	1	no	—
1842	C₂×C₄	—	8	1	no	—
1843	C₂×C₄	—	8	1	no	—
1844	C₂×C₄	—	8	1	no	—
1845	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1846	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1847	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1848	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1849	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1850	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1851	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1852	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1853	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1854	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1855	C₈	—	2	1	no	—
1856	C₈	—	2	1	no	—
1857	C₈	—	2	1	no	—
1858	C₈	—	2	1	no	—
1859	C₈	—	2	1	no	—
1860	C₈	—	2	1	no	—
1861	C₈	—	2	1	no	—
1862	C₈	—	2	1	no	—
1863	C₂²	—	2	1	no	—
1864	C₂²	—	2	1	no	—
1865	C₂²	—	2	1	no	—
1866	C₂²	—	2	1	no	—
1867	C₂²	—	2	1	no	—
1868	C₂²	—	2	1	no	—
1869	C₂²	—	2	2	no	—
1870	C₂²	—	2	2	no	—
1871	C₂²	—	2	1	no	—
1872	C₂²	—	2	1	no	—
1873	C₂²	—	2	1	no	—
1874	C₂²	—	2	1	no	—
1875	C₂²	—	2	1	no	—
1876	C₂²	—	2	1	no	—
1877	C₂²	—	2	1	no	—
1878	C₂²	—	2	1	no	—
1879	C₂²	—	4	4	no	—
1880	C₂²	—	4	1	no	—
1881	C₂²	—	4	1	no	—
1882	C₂²	—	4	1	no	—
1883	C₂²	—	4	1	no	—
1884	C₂²	—	4	1	no	—
1885	C₂²	—	4	1	no	—
1886	C₂²	—	4	1	no	—
1887	C₂²	—	4	1	no	—
1888	C₂²	—	4	1	no	—
1889	C₂²	—	4	1	no	—
1890	C₂²	—	4	1	no	—
1891	C₂²	—	4	1	no	—
1892	C₂²	—	4	1	no	—
1893	C₂²	—	4	1	no	—
1894	C₂²	—	4	1	no	—
1895	C₂²	—	4	1	no	—
1896	C₂²	—	8	4	no	—
1897	C₂²	—	8	4	no	—
1898	C₂²	—	8	4	no	—
1899	C₂²	—	8	4	no	—
1900	C₂²	—	8	4	no	—
1901	C₂²	—	8	4	no	—
1902	C₂²	—	16	2	no	—
1903	C₂²	—	16	2	no	—
1904	C₂²	C₅₃×#577	1	2	yes	—
1905	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1906	C₄	—	2	1	no	—
1907	C₄	—	2	1	no	—
1908	C₄	—	2	1	no	—
1909	C₄	—	2	1	no	—
1910	C₄	—	2	1	no	—
1911	C₄	—	2	1	no	—
1912	C₄	—	2	1	no	—
1913	C₄	—	2	1	no	—
1914	C₄	—	2	1	no	—
1915	C₄	—	4	1	no	—
1916	C₄	—	4	1	no	—
1917	C₄	—	4	1	no	—
1918	C₄	—	4	1	no	—
1919	C₄	—	4	1	no	—
1920	C₄	—	4	1	no	—
1921	C₄	—	4	1	no	—
1922	C₄	—	4	1	no	—
1923	C₄	—	4	1	no	—
1924	C₄	—	4	1	no	—
1925	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1926	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1927	C₂	—	2	2	no	—
1928	C₂	—	4	1	no	—
1929	C₂	—	4	1	no	—
1930	C₂	—	4	1	no	—
1931	C₂	—	4	1	no	—
1932	C₂	—	4	2	no	—
1933	C₂	—	4	2	no	—
1934	C₂	—	8	1	no	—
1935	C₂	—	8	1	no	—
1936	C₂	—	8	1	no	—
1937	C₂	—	8	1	no	—
1938	C₂	C₅₃×#3484	1	1	yes	characteristic
1939	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
1940	C₂	C₅₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₅₃×#525 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅₃×#3541	C₂	semidirect
2. C₅₃×#3484	C₂	semidirect
3. C₅₃×#3324	C₂	semidirect
4. C₅₃×#3323	C₂	semidirect
5. C₅₃×#3318	C₂	semidirect
6. C₅₃×#3314	C₂	semidirect
7. C₅₃×#3311	C₂	semidirect
8. C₅₃×#3310	C₂	semidirect
9. C₅₃×#3297	C₂	semidirect
10. C₅₃×#3295	C₂	semidirect
11. C₅₃×#3282	C₂	semidirect
12. D₄×SD₁₆×C₅₃	C₂	semidirect
13. C₅₃×#3275	C₂	semidirect
14. C₅₃×#3272	C₂	semidirect
15. C₅₃×#3267	C₂	semidirect
16. C₅₃×#3266	C₂	semidirect
17. C₅₃×#3265	C₂	semidirect
18. C₅₃×#3265	C₂	semidirect
19. C₅₃×#3224	C₂	semidirect
20. C₅₃×#3222	C₂	semidirect
21. C₅₃×#3200	C₂	semidirect
22. C₅₃×#3198	C₂	semidirect
23. C₅₃×#3196	C₂	semidirect
24. C₅₃×#3191	C₂	semidirect
25. C₅₃×#3123	C₂	semidirect
26. C₅₃×#3118	C₂	semidirect
27. C₅₃×#3012	C₂	semidirect
28. C₅₃×#3009	C₂	semidirect
29. C₅₃×#3003	C₂	semidirect
30. C₂×C₅₃×#450	C₂	semidirect
31. C₅₃×#2976	C₂	semidirect
34. C₂×#137×C₅₃	C₂²	semidirect
35. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
36. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
37. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
38. C₂×#135×C₅₃	C₂²	semidirect
39. C₂²×SD₁₆×C₅₃	C₂²	semidirect
40. C₂²×SD₁₆×C₅₃	C₂²	semidirect
41. C₂²×SD₁₆×C₅₃	C₂²	semidirect
44. C₅₃×#556	C₂²	semidirect
46. C₅₃×#554	C₂²	semidirect
48. C₅₃×#553	C₂²	semidirect
49. C₅₃×#552	C₂²	semidirect
50. D₄×Q₈×C₅₃	C₂²	semidirect
51. C₅₃×#548	C₂²	semidirect
52. C₅₃×#548	C₂²	semidirect
53. C₅₃×#547	C₂²	semidirect
67. C₅₃×#542	C₂²	semidirect
68. C₅₃×#541	C₂²	semidirect
72. C₅₃×#537	C₂²	semidirect
73. C₅₃×#536	C₂²	semidirect
80. C₅₃×#525	C₂²	semidirect
81. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
85. C₅₃×#497	C₂²	semidirect
86. C₅₃×#496	C₂²	semidirect
87. C₅₃×#495	C₂²	semidirect
88. C₅₃×#492	C₂²	semidirect
89. C₅₃×#490	C₂²	semidirect
90. C₅₃×#489	C₂²	semidirect
91. C₅₃×#488	C₂²	semidirect
92. C₅₃×#486	C₂²	semidirect
93. C₅₃×#485	C₂²	semidirect
94. C₅₃×#485	C₂²	semidirect
95. C₅₃×#485	C₂²	semidirect
96. C₅₃×#485	C₂²	semidirect
97. C₅₃×#484	C₂²	semidirect
98. C₅₃×#482	C₂²	semidirect
99. C₅₃×#482	C₂²	semidirect
100. C₅₃×#482	C₂²	semidirect
101. C₅₃×#482	C₂²	semidirect
102. C₅₃×#481	C₂²	semidirect
103. C₅₃×#481	C₂²	semidirect
104. C₅₃×#480	C₂²	semidirect
105. C₅₃×#478	C₂²	semidirect
106. C₅₃×#478	C₂²	semidirect
107. C₅₃×#476	C₂²	semidirect
108. C₅₃×#474	C₂²	semidirect
109. C₅₃×#470	C₂²	semidirect
110. C₅₃×#470	C₂²	semidirect
111. C₅₃×#469	C₂²	semidirect
112. C₅₃×#468	C₂²	semidirect
113. C₅₃×#468	C₂²	semidirect
114. C₅₃×#468	C₂²	semidirect
115. C₅₃×#468	C₂²	semidirect
116. C₅₃×#468	C₂²	semidirect
117. C₅₃×#467	C₂²	semidirect
118. C₅₃×#466	C₂²	semidirect
119. C₅₃×#466	C₂²	semidirect
120. C₅₃×#465	C₂²	semidirect
121. C₅₃×#465	C₂²	semidirect
122. C₅₃×#465	C₂²	semidirect
123. C₅₃×#465	C₂²	semidirect
124. C₅₃×#465	C₂²	semidirect
125. C₅₃×#464	C₂²	semidirect
126. C₅₃×#464	C₂²	semidirect
127. C₅₃×#464	C₂²	semidirect
128. C₅₃×#463	C₂²	semidirect
129. C₅₃×#463	C₂²	semidirect
130. C₅₃×#463	C₂²	semidirect
131. C₅₃×#461	C₂²	semidirect
132. C₅₃×#461	C₂²	semidirect
133. C₅₃×#460	C₂²	semidirect
134. C₅₃×#460	C₂²	semidirect
135. C₅₃×#460	C₂²	semidirect
136. C₅₃×#459	C₂²	semidirect
137. C₅₃×#452	C₂²	semidirect
138. C₅₃×#452	C₂²	semidirect
139. C₅₃×#452	C₂²	semidirect
140. C₅₃×#452	C₂²	semidirect
141. C₅₃×#452	C₂²	semidirect
142. C₅₃×#452	C₂²	semidirect
143. C₅₃×#452	C₂²	semidirect
144. C₅₃×#451	C₂²	semidirect
148. C₅₃×#450	C₂²	semidirect
149. C₅₃×#450	C₂²	semidirect
150. C₅₃×#450	C₂²	semidirect
151. C₅₃×#450	C₂²	semidirect
152. C₅₃×#450	C₂²	semidirect
153. C₅₃×#450	C₂²	semidirect
154. C₅₃×#450	C₂²	semidirect
155. C₅₃×#450	C₂²	semidirect
156. C₅₃×#450	C₂²	semidirect
157. C₅₃×#450	C₂²	semidirect
158. C₅₃×#450	C₂²	semidirect
159. C₅₃×#450	C₂²	semidirect
160. C₅₃×#449	C₂²	semidirect
161. C₅₃×#449	C₂²	semidirect
162. C₅₃×#449	C₂²	semidirect
163. C₅₃×#449	C₂²	semidirect
164. C₅₃×#449	C₂²	semidirect
165. C₅₃×#448	C₂²	semidirect
166. C₅₃×#448	C₂²	semidirect
167. C₅₃×#448	C₂²	semidirect
169. C₅₃×#447	C₂²	semidirect
170. C₅₃×#447	C₂²	semidirect
171. C₅₃×#447	C₂²	semidirect
172. C₅₃×#447	C₂²	semidirect
173. C₅₃×#442	C₂²	semidirect
174. C₅₃×#440	C₂²	semidirect
175. C₅₃×#440	C₂²	semidirect
176. C₅₃×#440	C₂²	semidirect
177. C₄×SD₁₆×C₅₃	C₂²	semidirect
178. C₄×SD₁₆×C₅₃	C₂²	semidirect
179. C₄×SD₁₆×C₅₃	C₂²	semidirect
180. C₄×D₈×C₅₃	C₂²	semidirect
181. C₅₃×#436	C₂²	semidirect
182. C₅₃×#436	C₂²	semidirect
183. C₅₃×#435	C₂²	semidirect
184. C₅₃×#435	C₂²	semidirect
185. C₅₃×#435	C₂²	semidirect
186. C₅₃×#435	C₂²	semidirect
187. C₈×D₄×C₅₃	C₂²	semidirect
188. C₈×D₄×C₅₃	C₂²	semidirect
189. C₅₃×#433	C₂²	semidirect
190. C₅₃×#433	C₂²	semidirect
191. C₅₃×#418	C₂²	semidirect
192. C₅₃×#418	C₂²	semidirect
193. C₅₃×#418	C₂²	semidirect
194. C₅₃×#417	C₂²	semidirect
195. C₅₃×#416	C₂²	semidirect
196. C₂×#102×C₅₃	C₂²	semidirect
197. C₂×#102×C₅₃	C₂²	semidirect
198. C₂×#102×C₅₃	C₂²	semidirect
199. C₅₃×#408	C₂²	semidirect
200. C₅₃×#408	C₂²	semidirect
201. C₅₃×#407	C₂²	semidirect
202. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
212. C₂×#41×C₅₃	C₂³	semidirect
214. C₂²×Q₈×C₅₃	C₂³	semidirect
241. C₂×Q₁₆×C₅₃	C₂³	semidirect
242. C₂×Q₁₆×C₅₃	C₂³	semidirect
243. C₂×Q₁₆×C₅₃	C₂³	semidirect
259. C₂×SD₁₆×C₅₃	C₂³	semidirect
260. C₂×SD₁₆×C₅₃	C₂³	semidirect
261. C₂×SD₁₆×C₅₃	C₂³	semidirect
262. C₂×SD₁₆×C₅₃	C₂³	semidirect
267. C₂×D₈×C₅₃	C₂³	semidirect
270. C₂×M₁₆×C₅₃	C₂³	semidirect
271. C₂×M₁₆×C₅₃	C₂³	semidirect
274. C₂²×C₈×C₅₃	C₂³	semidirect
275. C₂²×C₈×C₅₃	C₂³	semidirect
278. C₄⋊Q₈×C₅₃	C₂³	semidirect
279. C₄⋊Q₈×C₅₃	C₂³	semidirect
294. #125×C₅₃	C₂³	semidirect
303. #124×C₅₃	C₂³	semidirect
339. C₂²⋊Q₈×C₅₃	C₂³	semidirect
340. C₂²⋊Q₈×C₅₃	C₂³	semidirect
341. C₂²⋊Q₈×C₅₃	C₂³	semidirect
369. #121×C₅₃	C₂³	semidirect
391. C₄×Q₈×C₅₃	C₂³	semidirect
392. C₄×Q₈×C₅₃	C₂³	semidirect
393. C₄×Q₈×C₅₃	C₂³	semidirect
413. C₄×D₄×C₅₃	C₂³	semidirect
418. #117×C₅₃	C₂³	semidirect
422. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
430. #107×C₅₃	C₂³	semidirect
431. #107×C₅₃	C₂³	semidirect
432. #107×C₅₃	C₂³	semidirect
433. #107×C₅₃	C₂³	semidirect
434. #106×C₅₃	C₂³	semidirect
435. #106×C₅₃	C₂³	semidirect
436. #106×C₅₃	C₂³	semidirect
437. #106×C₅₃	C₂³	semidirect
438. C₄⋊C₈×C₅₃	C₂³	semidirect
439. C₄⋊C₈×C₅₃	C₂³	semidirect
440. C₄⋊C₈×C₅₃	C₂³	semidirect
441. C₄⋊C₈×C₅₃	C₂³	semidirect
442. #103×C₅₃	C₂³	semidirect
443. #103×C₅₃	C₂³	semidirect
444. #103×C₅₃	C₂³	semidirect
445. #103×C₅₃	C₂³	semidirect
446. #103×C₅₃	C₂³	semidirect
447. #103×C₅₃	C₂³	semidirect
448. #103×C₅₃	C₂³	semidirect
449. #103×C₅₃	C₂³	semidirect
450. #103×C₅₃	C₂³	semidirect
451. #103×C₅₃	C₂³	semidirect
468. #102×C₅₃	C₂³	semidirect
469. #102×C₅₃	C₂³	semidirect
470. #102×C₅₃	C₂³	semidirect
471. #102×C₅₃	C₂³	semidirect
472. #102×C₅₃	C₂³	semidirect
473. #102×C₅₃	C₂³	semidirect
482. C₂²⋊C₈×C₅₃	C₂³	semidirect
483. C₂²⋊C₈×C₅₃	C₂³	semidirect
484. C₂²⋊C₈×C₅₃	C₂³	semidirect
485. C₂²⋊C₈×C₅₃	C₂³	semidirect
486. #97×C₅₃	C₂³	semidirect
487. #97×C₅₃	C₂³	semidirect
488. C₄×C₈×C₅₃	C₂³	semidirect
489. C₄×C₈×C₅₃	C₂³	semidirect
892. #61610	C₅₃	direct (N × H)
957. #3541	C₂×C₅₃	semidirect
958. #3484	C₂×C₅₃	semidirect
959. #3324	C₂×C₅₃	semidirect
960. #3323	C₂×C₅₃	semidirect
961. #3318	C₂×C₅₃	semidirect
962. #3314	C₂×C₅₃	semidirect
963. #3311	C₂×C₅₃	semidirect
964. #3310	C₂×C₅₃	semidirect
965. #3297	C₂×C₅₃	semidirect
966. #3295	C₂×C₅₃	semidirect
967. #3282	C₂×C₅₃	semidirect
968. D₄×SD₁₆	C₂×C₅₃	semidirect
969. #3275	C₂×C₅₃	semidirect
970. #3272	C₂×C₅₃	semidirect
971. #3267	C₂×C₅₃	semidirect
972. #3266	C₂×C₅₃	semidirect
973. #3265	C₂×C₅₃	semidirect
974. #3265	C₂×C₅₃	semidirect
975. #3224	C₂×C₅₃	semidirect
976. #3222	C₂×C₅₃	semidirect
977. #3200	C₂×C₅₃	semidirect
978. #3198	C₂×C₅₃	semidirect
979. #3196	C₂×C₅₃	semidirect
980. #3191	C₂×C₅₃	semidirect
981. #3123	C₂×C₅₃	semidirect
982. #3118	C₂×C₅₃	semidirect
983. #3012	C₂×C₅₃	semidirect
984. #3009	C₂×C₅₃	semidirect
985. #3003	C₂×C₅₃	semidirect
986. C₂×#450	C₂×C₅₃	semidirect
987. #2976	C₂×C₅₃	semidirect
1004. C₂×#137	C₂²×C₅₃	semidirect
1005. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
1006. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
1007. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
1008. C₂×#135	C₂²×C₅₃	semidirect
1009. C₂²×SD₁₆	C₂²×C₅₃	semidirect
1010. C₂²×SD₁₆	C₂²×C₅₃	semidirect
1011. C₂²×SD₁₆	C₂²×C₅₃	semidirect
1014. #556	C₂²×C₅₃	semidirect
1016. #554	C₂²×C₅₃	semidirect
1018. #553	C₂²×C₅₃	semidirect
1019. #552	C₂²×C₅₃	semidirect
1020. D₄×Q₈	C₂²×C₅₃	semidirect
1021. #548	C₂²×C₅₃	semidirect
1022. #548	C₂²×C₅₃	semidirect
1023. #547	C₂²×C₅₃	semidirect
1037. #542	C₂²×C₅₃	semidirect
1038. #541	C₂²×C₅₃	semidirect
1042. #537	C₂²×C₅₃	semidirect
1043. #536	C₂²×C₅₃	semidirect
1050. #525	C₂²×C₅₃	semidirect
1051. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
1055. #497	C₂²×C₅₃	semidirect
1056. #496	C₂²×C₅₃	semidirect
1057. #495	C₂²×C₅₃	semidirect
1058. #492	C₂²×C₅₃	semidirect
1059. #490	C₂²×C₅₃	semidirect
1060. #489	C₂²×C₅₃	semidirect
1061. #488	C₂²×C₅₃	semidirect
1062. #486	C₂²×C₅₃	semidirect
1063. #485	C₂²×C₅₃	semidirect
1064. #485	C₂²×C₅₃	semidirect
1065. #485	C₂²×C₅₃	semidirect
1066. #485	C₂²×C₅₃	semidirect
1067. #484	C₂²×C₅₃	semidirect
1068. #482	C₂²×C₅₃	semidirect
1069. #482	C₂²×C₅₃	semidirect
1070. #482	C₂²×C₅₃	semidirect
1071. #482	C₂²×C₅₃	semidirect
1072. #481	C₂²×C₅₃	semidirect
1073. #481	C₂²×C₅₃	semidirect
1074. #480	C₂²×C₅₃	semidirect
1075. #478	C₂²×C₅₃	semidirect
1076. #478	C₂²×C₅₃	semidirect
1077. #476	C₂²×C₅₃	semidirect
1078. #474	C₂²×C₅₃	semidirect
1079. #470	C₂²×C₅₃	semidirect
1080. #470	C₂²×C₅₃	semidirect
1081. #469	C₂²×C₅₃	semidirect
1082. #468	C₂²×C₅₃	semidirect
1083. #468	C₂²×C₅₃	semidirect
1084. #468	C₂²×C₅₃	semidirect
1085. #468	C₂²×C₅₃	semidirect
1086. #468	C₂²×C₅₃	semidirect
1087. #467	C₂²×C₅₃	semidirect
1088. #466	C₂²×C₅₃	semidirect
1089. #466	C₂²×C₅₃	semidirect
1090. #465	C₂²×C₅₃	semidirect
1091. #465	C₂²×C₅₃	semidirect
1092. #465	C₂²×C₅₃	semidirect
1093. #465	C₂²×C₅₃	semidirect
1094. #465	C₂²×C₅₃	semidirect
1095. #464	C₂²×C₅₃	semidirect
1096. #464	C₂²×C₅₃	semidirect
1097. #464	C₂²×C₅₃	semidirect
1098. #463	C₂²×C₅₃	semidirect
1099. #463	C₂²×C₅₃	semidirect
1100. #463	C₂²×C₅₃	semidirect
1101. #461	C₂²×C₅₃	semidirect
1102. #461	C₂²×C₅₃	semidirect
1103. #460	C₂²×C₅₃	semidirect
1104. #460	C₂²×C₅₃	semidirect
1105. #460	C₂²×C₅₃	semidirect
1106. #459	C₂²×C₅₃	semidirect
1107. #452	C₂²×C₅₃	semidirect
1108. #452	C₂²×C₅₃	semidirect
1109. #452	C₂²×C₅₃	semidirect
1110. #452	C₂²×C₅₃	semidirect
1111. #452	C₂²×C₅₃	semidirect
1112. #452	C₂²×C₅₃	semidirect
1113. #452	C₂²×C₅₃	semidirect
1114. #451	C₂²×C₅₃	semidirect
1118. #450	C₂²×C₅₃	semidirect
1119. #450	C₂²×C₅₃	semidirect
1120. #450	C₂²×C₅₃	semidirect
1121. #450	C₂²×C₅₃	semidirect
1122. #450	C₂²×C₅₃	semidirect
1123. #450	C₂²×C₅₃	semidirect
1124. #450	C₂²×C₅₃	semidirect
1125. #450	C₂²×C₅₃	semidirect
1126. #450	C₂²×C₅₃	semidirect
1127. #450	C₂²×C₅₃	semidirect
1128. #450	C₂²×C₅₃	semidirect
1129. #450	C₂²×C₅₃	semidirect
1130. #449	C₂²×C₅₃	semidirect
1131. #449	C₂²×C₅₃	semidirect
1132. #449	C₂²×C₅₃	semidirect
1133. #449	C₂²×C₅₃	semidirect
1134. #449	C₂²×C₅₃	semidirect
1135. #448	C₂²×C₅₃	semidirect
1136. #448	C₂²×C₅₃	semidirect
1137. #448	C₂²×C₅₃	semidirect
1139. #447	C₂²×C₅₃	semidirect
1140. #447	C₂²×C₅₃	semidirect
1141. #447	C₂²×C₅₃	semidirect
1142. #447	C₂²×C₅₃	semidirect
1143. #442	C₂²×C₅₃	semidirect
1144. #440	C₂²×C₅₃	semidirect
1145. #440	C₂²×C₅₃	semidirect
1146. #440	C₂²×C₅₃	semidirect
1147. C₄×SD₁₆	C₂²×C₅₃	semidirect
1148. C₄×SD₁₆	C₂²×C₅₃	semidirect
1149. C₄×SD₁₆	C₂²×C₅₃	semidirect
1150. C₄×D₈	C₂²×C₅₃	semidirect
1151. #436	C₂²×C₅₃	semidirect
1152. #436	C₂²×C₅₃	semidirect
1153. #435	C₂²×C₅₃	semidirect
1154. #435	C₂²×C₅₃	semidirect
1155. #435	C₂²×C₅₃	semidirect
1156. #435	C₂²×C₅₃	semidirect
1157. C₈×D₄	C₂²×C₅₃	semidirect
1158. C₈×D₄	C₂²×C₅₃	semidirect
1159. #433	C₂²×C₅₃	semidirect
1160. #433	C₂²×C₅₃	semidirect
1161. #418	C₂²×C₅₃	semidirect
1162. #418	C₂²×C₅₃	semidirect
1163. #418	C₂²×C₅₃	semidirect
1164. #417	C₂²×C₅₃	semidirect
1165. #416	C₂²×C₅₃	semidirect
1166. C₂×#102	C₂²×C₅₃	semidirect
1167. C₂×#102	C₂²×C₅₃	semidirect
1168. C₂×#102	C₂²×C₅₃	semidirect
1169. #408	C₂²×C₅₃	semidirect
1170. #408	C₂²×C₅₃	semidirect
1171. #407	C₂²×C₅₃	semidirect
1172. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
1173. C₅₃	#61610	direct (N × H)
1183. C₂×#41	C₂³×C₅₃	semidirect
1185. C₂²×Q₈	C₂³×C₅₃	semidirect
1212. C₂×Q₁₆	C₂³×C₅₃	semidirect
1213. C₂×Q₁₆	C₂³×C₅₃	semidirect
1214. C₂×Q₁₆	C₂³×C₅₃	semidirect
1230. C₂×SD₁₆	C₂³×C₅₃	semidirect
1231. C₂×SD₁₆	C₂³×C₅₃	semidirect
1232. C₂×SD₁₆	C₂³×C₅₃	semidirect
1233. C₂×SD₁₆	C₂³×C₅₃	semidirect
1238. C₂×D₈	C₂³×C₅₃	semidirect
1241. C₂×M₁₆	C₂³×C₅₃	semidirect
1242. C₂×M₁₆	C₂³×C₅₃	semidirect
1245. C₂²×C₈	C₂³×C₅₃	semidirect
1246. C₂²×C₈	C₂³×C₅₃	semidirect
1249. C₄⋊Q₈	C₂³×C₅₃	semidirect
1250. C₄⋊Q₈	C₂³×C₅₃	semidirect
1265. #125	C₂³×C₅₃	semidirect
1274. #124	C₂³×C₅₃	semidirect
1310. C₂²⋊Q₈	C₂³×C₅₃	semidirect
1311. C₂²⋊Q₈	C₂³×C₅₃	semidirect
1312. C₂²⋊Q₈	C₂³×C₅₃	semidirect
1340. #121	C₂³×C₅₃	semidirect
1362. C₄×Q₈	C₂³×C₅₃	semidirect
1363. C₄×Q₈	C₂³×C₅₃	semidirect
1364. C₄×Q₈	C₂³×C₅₃	semidirect
1384. C₄×D₄	C₂³×C₅₃	semidirect
1389. #117	C₂³×C₅₃	semidirect
1393. C₂×C₄⋊C₄	C₂³×C₅₃	semidirect
1401. #107	C₂³×C₅₃	semidirect
1402. #107	C₂³×C₅₃	semidirect
1403. #107	C₂³×C₅₃	semidirect
1404. #107	C₂³×C₅₃	semidirect
1405. #106	C₂³×C₅₃	semidirect
1406. #106	C₂³×C₅₃	semidirect
1407. #106	C₂³×C₅₃	semidirect
1408. #106	C₂³×C₅₃	semidirect
1409. C₄⋊C₈	C₂³×C₅₃	semidirect
1410. C₄⋊C₈	C₂³×C₅₃	semidirect
1411. C₄⋊C₈	C₂³×C₅₃	semidirect
1412. C₄⋊C₈	C₂³×C₅₃	semidirect
1413. #103	C₂³×C₅₃	semidirect
1414. #103	C₂³×C₅₃	semidirect
1415. #103	C₂³×C₅₃	semidirect
1416. #103	C₂³×C₅₃	semidirect
1417. #103	C₂³×C₅₃	semidirect
1418. #103	C₂³×C₅₃	semidirect
1419. #103	C₂³×C₅₃	semidirect
1420. #103	C₂³×C₅₃	semidirect
1421. #103	C₂³×C₅₃	semidirect
1422. #103	C₂³×C₅₃	semidirect
1439. #102	C₂³×C₅₃	semidirect
1440. #102	C₂³×C₅₃	semidirect
1441. #102	C₂³×C₅₃	semidirect
1442. #102	C₂³×C₅₃	semidirect
1443. #102	C₂³×C₅₃	semidirect
1444. #102	C₂³×C₅₃	semidirect
1453. C₂²⋊C₈	C₂³×C₅₃	semidirect
1454. C₂²⋊C₈	C₂³×C₅₃	semidirect
1455. C₂²⋊C₈	C₂³×C₅₃	semidirect
1456. C₂²⋊C₈	C₂³×C₅₃	semidirect
1457. #97	C₂³×C₅₃	semidirect
1458. #97	C₂³×C₅₃	semidirect
1459. C₄×C₈	C₂³×C₅₃	semidirect
1460. C₄×C₈	C₂³×C₅₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅₃×#3541	2
C₅₃×#3484	2
C₅₃×#3324	2
C₅₃×#3323	2
C₅₃×#3318	2
C₅₃×#3314	2
C₅₃×#3311	2
C₅₃×#3310	2
C₅₃×#3297	2
C₅₃×#3295	2
C₅₃×#3282	2
D₄×SD₁₆×C₅₃	2
C₅₃×#3275	2
C₅₃×#3272	2
C₅₃×#3267	2
C₅₃×#3266	2
C₅₃×#3265	2
C₅₃×#3224	2
C₅₃×#3222	2
C₅₃×#3200	2
C₅₃×#3198	2
C₅₃×#3196	2
C₅₃×#3191	2
C₅₃×#3123	2
C₅₃×#3118	2
C₅₃×#3012	2
C₅₃×#3009	2
C₅₃×#3003	2
C₂×C₅₃×#450	2
C₅₃×#2976	2
#61610	53

Subgroups — C53×#61610 #27269122

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61610 #27269122