Subgroups — C₅₃×#61640 #27269152

Order 13568.

2110 conjugacy classes of subgroups.

The subgroup lattice has 1902 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×#3488	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3318	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3317	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3316	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3311	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3304	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3301	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3296	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3295	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3285	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3284	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3282	C₂	1	1	yes	maximal, characteristic, complemented
14	D₄×SD₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3271	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3270	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3267	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×#3204	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3201	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3188	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#3187	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#3125	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#3120	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×#3002	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×C₅₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2977	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic
33	C₂²×#41×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×#135×C₅₃	C₂²	1	1	yes	characteristic, complemented
37	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic, complemented
38	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₂²×Q₁₆×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	C₅₃×#550	C₂²	1	1	yes	characteristic
51	C₅₃×#550	C₂²	1	1	yes	characteristic
52	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
53	C₅₃×#548	C₂²	1	1	yes	characteristic
54	C₅₃×#548	C₂²	1	1	yes	characteristic
55	C₅₃×#548	C₂²	1	1	yes	characteristic, complemented
56	C₅₃×#548	C₂²	1	1	yes	characteristic, complemented
57	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
58	C₅₃×#546	—	2	1	no	—
59	C₅₃×#546	—	2	1	no	—
60	C₅₃×#546	C₂²	1	1	yes	characteristic
61	C₅₃×#546	C₂²	1	1	yes	characteristic
62	D₄²×C₅₃	—	2	1	no	—
63	D₄²×C₅₃	—	2	1	no	—
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	—	2	1	no	—
73	C₅₃×#537	C₂²	1	1	yes	characteristic
74	C₅₃×#537	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#536	C₂²	1	1	yes	characteristic, complemented
76	C₅₃×#535	—	2	1	no	—
77	C₅₃×#535	C₂²	1	1	yes	characteristic
78	C₅₃×#525	—	2	1	no	—
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×#121×C₅₃	—	2	1	no	—
83	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
84	C₅₃×#520	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×#484	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#483	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×#481	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×#481	C₂²	1	1	yes	characteristic, complemented
105	C₅₃×#479	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×#475	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×#467	C₂²	1	1	yes	characteristic, complemented
114	C₅₃×#466	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#466	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#465	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×#464	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×#462	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
138	C₅₃×#452	C₂²	1	1	yes	characteristic
139	C₅₃×#452	C₂²	1	1	yes	characteristic
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×#452	C₂²	1	1	yes	characteristic, complemented
145	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
146	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
147	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
148	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
149	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
150	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
151	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
152	C₅₃×#451	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
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×#449	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×#448	C₂²	1	1	yes	characteristic, complemented
169	C₅₃×#448	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×#441	C₂²	1	1	yes	characteristic, complemented
175	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
176	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
177	C₄×Q₁₆×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×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
181	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
182	C₅₃×#435	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	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
186	C₈×D₄×C₅₃	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×#417	C₂²	1	1	yes	characteristic, complemented
193	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
194	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
195	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
196	C₂×#103×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	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
202	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
203	H(5,𝔽₂)×C₅₃	—	4	2	no	—
204	H(5,𝔽₂)×C₅₃	—	4	2	no	—
205	C₂×#41×C₅₃	—	2	1	no	—
206	C₂×#41×C₅₃	—	2	1	no	—
207	C₂×#41×C₅₃	—	2	1	no	—
208	C₂×#41×C₅₃	—	4	2	no	—
209	C₂×#41×C₅₃	—	4	2	no	—
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
213	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
214	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
215	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
216	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
217	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
218	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
219	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
220	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
221	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
226	C₂²×D₄×C₅₃	—	2	1	no	—
227	C₂²×D₄×C₅₃	—	2	1	no	—
228	C₂²×D₄×C₅₃	—	2	1	no	—
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	C₂³×C₄×C₅₃	—	2	1	no	—
234	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
235	#137×C₅₃	—	4	2	no	—
236	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
237	#135×C₅₃	—	4	2	no	—
238	#135×C₅₃	—	4	2	no	—
239	#135×C₅₃	—	4	2	no	—
240	C₂×Q₁₆×C₅₃	—	4	2	no	—
241	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
242	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
243	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
244	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
245	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
246	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
247	C₂×SD₁₆×C₅₃	—	4	2	no	—
248	C₂×SD₁₆×C₅₃	—	4	2	no	—
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
260	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
261	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
262	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
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×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
268	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
269	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
270	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
271	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
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
275	C₄⋊Q₈×C₅₃	—	2	1	no	—
276	C₄⋊Q₈×C₅₃	—	2	1	no	—
277	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
278	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
279	#127×C₅₃	—	2	1	no	—
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
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	—	2	1	no	—
302	#124×C₅₃	C₂³	1	1	yes	characteristic
303	#124×C₅₃	C₂³	1	1	yes	characteristic
304	#124×C₅₃	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
316	#123×C₅₃	D₄	1	1	yes	characteristic
317	C₂²⋊Q₈×C₅₃	—	2	1	no	—
318	C₂²⋊Q₈×C₅₃	—	2	1	no	—
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	—	2	1	no	—
330	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
331	C₂²⋊Q₈×C₅₃	D₄	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
340	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
341	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
342	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
360	#121×C₅₃	—	2	1	no	—
361	#121×C₅₃	—	2	1	no	—
362	#121×C₅₃	—	2	1	no	—
363	#121×C₅₃	—	2	1	no	—
364	#121×C₅₃	—	2	1	no	—
365	#121×C₅₃	—	2	1	no	—
366	#121×C₅₃	—	2	1	no	—
367	#121×C₅₃	D₄	1	1	yes	characteristic
368	#121×C₅₃	D₄	1	1	yes	characteristic
369	#121×C₅₃	C₂³	1	1	yes	characteristic
370	#121×C₅₃	C₂³	1	1	yes	characteristic
371	#121×C₅₃	C₂³	1	1	yes	characteristic
372	#121×C₅₃	C₂³	1	1	yes	characteristic
373	#121×C₅₃	C₂³	1	1	yes	characteristic
374	#121×C₅₃	C₂³	1	1	yes	characteristic
375	#121×C₅₃	C₂³	1	1	yes	characteristic
376	#121×C₅₃	C₂³	1	1	yes	characteristic
377	#121×C₅₃	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
388	#120×C₅₃	D₄	1	1	yes	characteristic
389	C₄×Q₈×C₅₃	—	2	1	no	—
390	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
391	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
392	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
393	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
394	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
406	C₄×D₄×C₅₃	—	2	1	no	—
407	C₄×D₄×C₅₃	—	2	1	no	—
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
414	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
415	#117×C₅₃	—	2	1	no	—
416	#117×C₅₃	—	2	1	no	—
417	#117×C₅₃	C₂³	1	1	yes	characteristic
418	#117×C₅₃	C₂³	1	1	yes	characteristic
419	#117×C₅₃	C₂³	1	1	yes	characteristic
420	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
421	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
422	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
423	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
424	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
425	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
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
431	#107×C₅₃	C₂³	1	1	yes	characteristic
432	#106×C₅₃	C₂³	1	1	yes	characteristic
433	#106×C₅₃	C₂³	1	1	yes	characteristic
434	#106×C₅₃	C₂³	1	1	yes	characteristic
435	#106×C₅₃	C₂³	1	1	yes	characteristic
436	#106×C₅₃	C₂³	1	1	yes	characteristic
437	#106×C₅₃	C₂³	1	1	yes	characteristic
438	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
439	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
440	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
441	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
442	#103×C₅₃	C₂³	1	1	yes	characteristic
443	#103×C₅₃	C₂³	1	1	yes	characteristic
444	#103×C₅₃	C₂³	1	1	yes	characteristic
445	#103×C₅₃	C₂³	1	1	yes	characteristic
446	#103×C₅₃	C₂³	1	1	yes	characteristic
447	#103×C₅₃	C₂³	1	1	yes	characteristic
448	#103×C₅₃	C₂³	1	1	yes	characteristic
449	#103×C₅₃	C₂³	1	1	yes	characteristic
450	#103×C₅₃	C₂³	1	1	yes	characteristic
451	#103×C₅₃	C₂³	1	1	yes	characteristic
452	#103×C₅₃	C₂³	1	1	yes	characteristic
453	#103×C₅₃	C₂³	1	1	yes	characteristic
454	#103×C₅₃	C₂³	1	1	yes	characteristic
455	#103×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
469	#102×C₅₃	C₂³	1	1	yes	characteristic
470	#102×C₅₃	C₂³	1	1	yes	characteristic
471	#102×C₅₃	C₂³	1	1	yes	characteristic
472	#102×C₅₃	C₂³	1	1	yes	characteristic
473	#102×C₅₃	C₂³	1	1	yes	characteristic
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
483	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
484	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
485	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
486	#97×C₅₃	C₂³	1	1	yes	characteristic
487	#97×C₅₃	C₂³	1	1	yes	characteristic
488	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
489	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
495	#41×C₅₃	—	2	2	no	—
496	#41×C₅₃	—	2	2	no	—
497	#41×C₅₃	—	2	2	no	—
498	#41×C₅₃	—	2	2	no	—
499	#41×C₅₃	—	2	2	no	—
500	#41×C₅₃	—	2	2	no	—
501	#41×C₅₃	—	4	1	no	—
502	#41×C₅₃	—	4	1	no	—
503	#41×C₅₃	—	4	1	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	4	no	—
510	#41×C₅₃	—	4	4	no	—
511	#41×C₅₃	—	4	1	no	—
512	#41×C₅₃	—	4	1	no	—
513	#41×C₅₃	—	4	1	no	—
514	#41×C₅₃	—	4	1	no	—
515	#41×C₅₃	—	4	4	no	—
516	C₂×Q₈×C₅₃	—	2	1	no	—
517	C₂×Q₈×C₅₃	—	2	1	no	—
518	C₂×Q₈×C₅₃	—	2	1	no	—
519	C₂×Q₈×C₅₃	—	2	1	no	—
520	C₂×Q₈×C₅₃	—	2	2	no	—
521	C₂×Q₈×C₅₃	—	4	1	no	—
522	C₂×Q₈×C₅₃	—	4	1	no	—
523	C₂×Q₈×C₅₃	—	4	1	no	—
524	C₂×Q₈×C₅₃	—	4	1	no	—
525	C₂×Q₈×C₅₃	—	4	1	no	—
526	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
527	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
528	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
529	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
530	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
531	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
532	C₂×D₄×C₅₃	—	2	1	no	—
533	C₂×D₄×C₅₃	—	2	2	no	—
534	C₂×D₄×C₅₃	—	2	2	no	—
535	C₂×D₄×C₅₃	—	2	2	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	—	4	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	4	no	—
566	C₂×D₄×C₅₃	—	4	4	no	—
567	C₂×D₄×C₅₃	—	4	4	no	—
568	C₂×D₄×C₅₃	—	4	4	no	—
569	C₂×D₄×C₅₃	—	8	2	no	—
570	C₂×D₄×C₅₃	—	8	2	no	—
571	C₂×D₄×C₅₃	—	8	2	no	—
572	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
573	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
574	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
575	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
576	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
577	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
578	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
579	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
580	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
581	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
582	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
583	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
584	C₂²×C₄×C₅₃	—	2	1	no	—
585	C₂²×C₄×C₅₃	—	2	1	no	—
586	C₂²×C₄×C₅₃	—	2	1	no	—
587	C₂²×C₄×C₅₃	—	2	1	no	—
588	C₂²×C₄×C₅₃	—	2	1	no	—
589	C₂²×C₄×C₅₃	—	2	1	no	—
590	C₂²×C₄×C₅₃	—	2	1	no	—
591	C₂²×C₄×C₅₃	—	2	1	no	—
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	—	4	1	no	—
602	C₂²×C₄×C₅₃	—	4	1	no	—
603	C₂²×C₄×C₅₃	—	4	4	no	—
604	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
605	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
606	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
607	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
608	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
609	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
610	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
611	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
612	Q₁₆×C₅₃	—	2	2	no	—
613	Q₁₆×C₅₃	—	2	2	no	—
614	Q₁₆×C₅₃	—	2	2	no	—
615	Q₁₆×C₅₃	—	4	1	no	—
616	Q₁₆×C₅₃	—	4	1	no	—
617	Q₁₆×C₅₃	—	4	1	no	—
618	SD₁₆×C₅₃	—	2	2	no	—
619	SD₁₆×C₅₃	—	2	2	no	—
620	SD₁₆×C₅₃	—	2	2	no	—
621	SD₁₆×C₅₃	—	2	2	no	—
622	SD₁₆×C₅₃	—	4	1	no	—
623	SD₁₆×C₅₃	—	4	1	no	—
624	SD₁₆×C₅₃	—	4	1	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	D₈×C₅₃	—	2	2	no	—
633	D₈×C₅₃	—	4	1	no	—
634	D₈×C₅₃	—	4	1	no	—
635	D₈×C₅₃	—	4	1	no	—
636	M₁₆×C₅₃	—	4	1	no	—
637	M₁₆×C₅₃	—	4	1	no	—
638	C₂×C₈×C₅₃	—	4	1	no	—
639	C₂×C₈×C₅₃	—	4	1	no	—
640	C₂×C₈×C₅₃	—	4	1	no	—
641	C₂×C₈×C₅₃	—	4	1	no	—
642	C₂×C₈×C₅₃	—	4	1	no	—
643	C₂×C₈×C₅₃	—	4	1	no	—
644	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
645	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
646	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
647	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₅₃	—	2	1	no	—
653	C₄⋊C₄×C₅₃	—	2	1	no	—
654	C₄⋊C₄×C₅₃	—	2	1	no	—
655	C₄⋊C₄×C₅₃	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	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	C₂²⋊C₄×C₅₃	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
720	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
721	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
722	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
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	C₄²×C₅₃	—	2	1	no	—
730	C₄²×C₅₃	—	2	1	no	—
731	C₄²×C₅₃	—	2	1	no	—
732	C₄²×C₅₃	—	2	1	no	—
733	C₄²×C₅₃	—	2	1	no	—
734	C₄²×C₅₃	—	2	1	no	—
735	C₄²×C₅₃	—	2	1	no	—
736	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
737	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
738	C₂³×C₅₃	—	2	1	no	—
739	C₂³×C₅₃	—	2	2	no	—
740	C₂³×C₅₃	—	2	1	no	—
741	C₂³×C₅₃	—	2	1	no	—
742	C₂³×C₅₃	—	2	1	no	—
743	C₂³×C₅₃	—	2	1	no	—
744	C₂³×C₅₃	—	4	1	no	—
745	C₂³×C₅₃	—	4	1	no	—
746	C₂³×C₅₃	—	4	2	no	—
747	C₂³×C₅₃	—	4	2	no	—
748	C₂³×C₅₃	—	4	2	no	—
749	C₂³×C₅₃	—	4	2	no	—
750	C₂³×C₅₃	—	4	2	no	—
751	C₂³×C₅₃	—	8	1	no	—
752	C₂³×C₅₃	—	8	1	no	—
753	C₂³×C₅₃	—	8	1	no	—
754	C₂³×C₅₃	—	8	1	no	—
755	C₂³×C₅₃	—	8	1	no	—
756	C₂³×C₅₃	—	8	1	no	—
757	C₂³×C₅₃	—	8	1	no	—
758	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
759	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
760	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
761	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
762	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
763	Q₈×C₅₃	—	2	1	no	—
764	Q₈×C₅₃	—	2	1	no	—
765	Q₈×C₅₃	—	2	1	no	—
766	Q₈×C₅₃	—	2	1	no	—
767	Q₈×C₅₃	—	2	1	no	—
768	Q₈×C₅₃	—	2	1	no	—
769	Q₈×C₅₃	—	2	1	no	—
770	Q₈×C₅₃	—	2	1	no	—
771	Q₈×C₅₃	—	2	1	no	—
772	Q₈×C₅₃	—	4	1	no	—
773	Q₈×C₅₃	—	4	2	no	—
774	Q₈×C₅₃	—	8	1	no	—
775	Q₈×C₅₃	—	8	1	no	—
776	Q₈×C₅₃	—	8	1	no	—
777	Q₈×C₅₃	H(5,𝔽₂)	1	2	yes	—
778	D₄×C₅₃	—	2	4	no	—
779	D₄×C₅₃	—	2	2	no	—
780	D₄×C₅₃	—	2	2	no	—
781	D₄×C₅₃	—	2	1	no	—
782	D₄×C₅₃	—	2	1	no	—
783	D₄×C₅₃	—	2	1	no	—
784	D₄×C₅₃	—	2	1	no	—
785	D₄×C₅₃	—	2	1	no	—
786	D₄×C₅₃	—	2	1	no	—
787	D₄×C₅₃	—	2	1	no	—
788	D₄×C₅₃	—	2	1	no	—
789	D₄×C₅₃	—	2	1	no	—
790	D₄×C₅₃	—	4	1	no	—
791	D₄×C₅₃	—	4	1	no	—
792	D₄×C₅₃	—	4	1	no	—
793	D₄×C₅₃	—	4	1	no	—
794	D₄×C₅₃	—	4	1	no	—
795	D₄×C₅₃	—	4	2	no	—
796	D₄×C₅₃	—	4	2	no	—
797	D₄×C₅₃	—	4	2	no	—
798	D₄×C₅₃	—	4	2	no	—
799	D₄×C₅₃	—	4	2	no	—
800	D₄×C₅₃	—	4	2	no	—
801	D₄×C₅₃	—	4	2	no	—
802	D₄×C₅₃	—	4	2	no	—
803	D₄×C₅₃	—	4	2	no	—
804	D₄×C₅₃	—	4	2	no	—
805	D₄×C₅₃	—	4	2	no	—
806	D₄×C₅₃	—	4	2	no	—
807	D₄×C₅₃	—	8	1	no	—
808	D₄×C₅₃	—	8	1	no	—
809	D₄×C₅₃	—	8	1	no	—
810	D₄×C₅₃	—	8	1	no	—
811	D₄×C₅₃	—	8	1	no	—
812	D₄×C₅₃	—	8	1	no	—
813	D₄×C₅₃	—	8	1	no	—
814	D₄×C₅₃	—	8	1	no	—
815	D₄×C₅₃	—	8	1	no	—
816	D₄×C₅₃	—	8	1	no	—
817	D₄×C₅₃	—	8	1	no	—
818	D₄×C₅₃	—	8	1	no	—
819	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
820	C₂×C₄×C₅₃	—	2	4	no	—
821	C₂×C₄×C₅₃	—	2	1	no	—
822	C₂×C₄×C₅₃	—	2	1	no	—
823	C₂×C₄×C₅₃	—	2	1	no	—
824	C₂×C₄×C₅₃	—	2	1	no	—
825	C₂×C₄×C₅₃	—	2	1	no	—
826	C₂×C₄×C₅₃	—	2	1	no	—
827	C₂×C₄×C₅₃	—	2	1	no	—
828	C₂×C₄×C₅₃	—	2	1	no	—
829	C₂×C₄×C₅₃	—	2	1	no	—
830	C₂×C₄×C₅₃	—	2	1	no	—
831	C₂×C₄×C₅₃	—	2	1	no	—
832	C₂×C₄×C₅₃	—	2	1	no	—
833	C₂×C₄×C₅₃	—	2	1	no	—
834	C₂×C₄×C₅₃	—	2	1	no	—
835	C₂×C₄×C₅₃	—	2	1	no	—
836	C₂×C₄×C₅₃	—	2	1	no	—
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	—	4	1	no	—
843	C₂×C₄×C₅₃	—	4	1	no	—
844	C₂×C₄×C₅₃	—	4	1	no	—
845	C₂×C₄×C₅₃	—	4	2	no	—
846	C₂×C₄×C₅₃	—	4	2	no	—
847	C₂×C₄×C₅₃	—	4	2	no	—
848	C₂×C₄×C₅₃	—	4	2	no	—
849	C₂×C₄×C₅₃	—	4	2	no	—
850	C₂×C₄×C₅₃	—	4	2	no	—
851	C₂×C₄×C₅₃	—	8	1	no	—
852	C₂×C₄×C₅₃	—	8	1	no	—
853	C₂×C₄×C₅₃	—	8	1	no	—
854	C₂×C₄×C₅₃	—	8	1	no	—
855	C₂×C₄×C₅₃	—	8	1	no	—
856	C₂×C₄×C₅₃	—	8	1	no	—
857	C₂×C₄×C₅₃	—	8	1	no	—
858	C₂×C₄×C₅₃	—	8	1	no	—
859	C₂×C₄×C₅₃	—	8	1	no	—
860	C₂×C₄×C₅₃	—	8	1	no	—
861	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
862	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
863	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
864	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
865	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
866	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
867	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
868	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
869	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
870	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
871	C₈×C₅₃	—	2	1	no	—
872	C₈×C₅₃	—	2	1	no	—
873	C₈×C₅₃	—	2	1	no	—
874	C₈×C₅₃	—	2	1	no	—
875	C₈×C₅₃	—	2	1	no	—
876	C₈×C₅₃	—	2	1	no	—
877	C₈×C₅₃	—	2	1	no	—
878	C₈×C₅₃	—	2	1	no	—
879	#61640	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
880	C₂²×C₅₃	—	2	1	no	—
881	C₂²×C₅₃	—	2	1	no	—
882	C₂²×C₅₃	—	2	1	no	—
883	C₂²×C₅₃	—	2	1	no	—
884	C₂²×C₅₃	—	2	1	no	—
885	C₂²×C₅₃	—	2	1	no	—
886	C₂²×C₅₃	—	2	1	no	—
887	C₂²×C₅₃	—	2	2	no	—
888	C₂²×C₅₃	—	2	1	no	—
889	C₂²×C₅₃	—	2	1	no	—
890	C₂²×C₅₃	—	2	1	no	—
891	C₂²×C₅₃	—	2	1	no	—
892	C₂²×C₅₃	—	2	1	no	—
893	C₂²×C₅₃	—	2	1	no	—
894	C₂²×C₅₃	—	2	1	no	—
895	C₂²×C₅₃	—	4	1	no	—
896	C₂²×C₅₃	—	4	1	no	—
897	C₂²×C₅₃	—	4	1	no	—
898	C₂²×C₅₃	—	4	1	no	—
899	C₂²×C₅₃	—	4	1	no	—
900	C₂²×C₅₃	—	4	1	no	—
901	C₂²×C₅₃	—	4	1	no	—
902	C₂²×C₅₃	—	4	1	no	—
903	C₂²×C₅₃	—	4	1	no	—
904	C₂²×C₅₃	—	4	1	no	—
905	C₂²×C₅₃	—	4	1	no	—
906	C₂²×C₅₃	—	4	1	no	—
907	C₂²×C₅₃	—	4	1	no	—
908	C₂²×C₅₃	—	4	1	no	—
909	C₂²×C₅₃	—	8	2	no	—
910	C₂²×C₅₃	—	8	4	no	—
911	C₂²×C₅₃	—	16	2	no	—
912	C₂²×C₅₃	—	16	2	no	—
913	C₂²×C₅₃	—	16	2	no	—
914	C₂²×C₅₃	#577	1	2	yes	—
915	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
916	C₄×C₅₃	—	2	1	no	—
917	C₄×C₅₃	—	2	1	no	—
918	C₄×C₅₃	—	2	1	no	—
919	C₄×C₅₃	—	2	2	no	—
920	C₄×C₅₃	—	2	1	no	—
921	C₄×C₅₃	—	2	1	no	—
922	C₄×C₅₃	—	2	1	no	—
923	C₄×C₅₃	—	2	1	no	—
924	C₄×C₅₃	—	2	1	no	—
925	C₄×C₅₃	—	2	1	no	—
926	C₄×C₅₃	—	4	1	no	—
927	C₄×C₅₃	—	4	1	no	—
928	C₄×C₅₃	—	4	1	no	—
929	C₄×C₅₃	—	4	1	no	—
930	C₄×C₅₃	—	4	1	no	—
931	C₄×C₅₃	—	4	1	no	—
932	C₄×C₅₃	—	4	1	no	—
933	C₄×C₅₃	—	4	1	no	—
934	C₄×C₅₃	—	4	1	no	—
935	C₄×C₅₃	—	4	1	no	—
936	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
937	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
938	#3541	C₂×C₅₃	1	1	yes	characteristic, complemented
939	#3488	C₂×C₅₃	1	1	yes	characteristic, complemented
940	#3318	C₂×C₅₃	1	1	yes	characteristic, complemented
941	#3317	C₂×C₅₃	1	1	yes	characteristic, complemented
942	#3316	C₂×C₅₃	1	1	yes	characteristic, complemented
943	#3311	C₂×C₅₃	1	1	yes	characteristic, complemented
944	#3304	C₂×C₅₃	1	1	yes	characteristic, complemented
945	#3301	C₂×C₅₃	1	1	yes	characteristic, complemented
946	#3296	C₂×C₅₃	1	1	yes	characteristic, complemented
947	#3295	C₂×C₅₃	1	1	yes	characteristic, complemented
948	#3285	C₂×C₅₃	1	1	yes	characteristic, complemented
949	#3284	C₂×C₅₃	1	1	yes	characteristic, complemented
950	#3282	C₂×C₅₃	1	1	yes	characteristic, complemented
951	D₄×SD₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
952	#3271	C₂×C₅₃	1	1	yes	characteristic, complemented
953	#3270	C₂×C₅₃	1	1	yes	characteristic, complemented
954	#3267	C₂×C₅₃	1	1	yes	characteristic, complemented
955	#3265	C₂×C₅₃	1	1	yes	characteristic, complemented
956	#3224	C₂×C₅₃	1	1	yes	characteristic, complemented
957	#3222	C₂×C₅₃	1	1	yes	characteristic, complemented
958	#3204	C₂×C₅₃	1	1	yes	characteristic, complemented
959	#3201	C₂×C₅₃	1	1	yes	characteristic, complemented
960	#3188	C₂×C₅₃	1	1	yes	characteristic, complemented
961	#3187	C₂×C₅₃	1	1	yes	characteristic, complemented
962	#3125	C₂×C₅₃	1	1	yes	characteristic, complemented
963	#3120	C₂×C₅₃	1	1	yes	characteristic, complemented
964	#3012	C₂×C₅₃	1	1	yes	characteristic, complemented
965	#3009	C₂×C₅₃	1	1	yes	characteristic, complemented
966	#3002	C₂×C₅₃	1	1	yes	characteristic, complemented
967	C₂×#452	C₂×C₅₃	1	1	yes	characteristic, complemented
968	#2977	C₂×C₅₃	1	1	yes	characteristic, complemented
969	C₂×C₅₃	—	2	2	no	—
970	C₂×C₅₃	—	4	1	no	—
971	C₂×C₅₃	—	4	1	no	—
972	C₂×C₅₃	—	4	1	no	—
973	C₂×C₅₃	—	4	1	no	—
974	C₂×C₅₃	—	4	2	no	—
975	C₂×C₅₃	—	8	1	no	—
976	C₂×C₅₃	—	8	1	no	—
977	C₂×C₅₃	—	8	1	no	—
978	C₂×C₅₃	—	8	1	no	—
979	C₂×C₅₃	#3484	1	1	yes	characteristic
980	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
981	C₂×C₅₃	#3584	1	1	yes	characteristic
982	C₂×H(5,𝔽₂)	C₂²×C₅₃	1	1	yes	characteristic
983	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
984	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
985	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
986	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic, complemented
987	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic, complemented
988	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic, complemented
989	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
990	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
991	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
992	#563	—	2	1	no	—
993	#562	—	2	1	no	—
994	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
995	#554	—	2	1	no	—
996	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
997	#553	—	2	1	no	—
998	#553	C₂²×C₅₃	1	1	yes	characteristic, complemented
999	#552	C₂²×C₅₃	1	1	yes	characteristic, complemented
1000	#550	C₂²×C₅₃	1	1	yes	characteristic
1001	#550	C₂²×C₅₃	1	1	yes	characteristic
1002	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1003	#548	C₂²×C₅₃	1	1	yes	characteristic
1004	#548	C₂²×C₅₃	1	1	yes	characteristic
1005	#548	C₂²×C₅₃	1	1	yes	characteristic, complemented
1006	#548	C₂²×C₅₃	1	1	yes	characteristic, complemented
1007	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
1008	#546	—	2	1	no	—
1009	#546	—	2	1	no	—
1010	#546	C₂²×C₅₃	1	1	yes	characteristic
1011	#546	C₂²×C₅₃	1	1	yes	characteristic
1012	D₄²	—	2	1	no	—
1013	D₄²	—	2	1	no	—
1014	D₄²	C₂²×C₅₃	1	1	yes	characteristic
1015	D₄²	C₂²×C₅₃	1	1	yes	characteristic
1016	#542	—	2	1	no	—
1017	#542	C₂²×C₅₃	1	1	yes	characteristic, complemented
1018	#541	C₂²×C₅₃	1	1	yes	characteristic, complemented
1019	#539	—	2	1	no	—
1020	#538	—	2	1	no	—
1021	#538	—	2	1	no	—
1022	#537	—	2	1	no	—
1023	#537	C₂²×C₅₃	1	1	yes	characteristic
1024	#537	C₂²×C₅₃	1	1	yes	characteristic, complemented
1025	#536	C₂²×C₅₃	1	1	yes	characteristic, complemented
1026	#535	—	2	1	no	—
1027	#535	C₂²×C₅₃	1	1	yes	characteristic
1028	#525	—	2	1	no	—
1029	#525	C₂²×C₅₃	1	1	yes	characteristic
1030	#525	C₂²×C₅₃	1	1	yes	characteristic, complemented
1031	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1032	C₂×#121	—	2	1	no	—
1033	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
1034	#520	C₂²×C₅₃	1	1	yes	characteristic
1035	#497	C₂²×C₅₃	1	1	yes	characteristic, complemented
1036	#496	C₂²×C₅₃	1	1	yes	characteristic, complemented
1037	#495	C₂²×C₅₃	1	1	yes	characteristic, complemented
1038	#492	C₂²×C₅₃	1	1	yes	characteristic, complemented
1039	#490	C₂²×C₅₃	1	1	yes	characteristic, complemented
1040	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
1041	#488	C₂²×C₅₃	1	1	yes	characteristic, complemented
1042	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
1043	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
1044	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
1045	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
1046	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
1047	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
1048	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
1049	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
1050	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
1051	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
1052	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
1053	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
1054	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
1055	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
1056	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
1057	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
1058	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
1059	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
1060	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
1061	#469	C₂²×C₅₃	1	1	yes	characteristic, complemented
1062	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1063	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
1064	#466	C₂²×C₅₃	1	1	yes	characteristic, complemented
1065	#466	C₂²×C₅₃	1	1	yes	characteristic, complemented
1066	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1067	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1068	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1069	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1070	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1071	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1072	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1073	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1074	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1075	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1076	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1077	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1078	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1079	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1080	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1081	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
1082	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1083	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1084	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1085	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1086	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1087	#452	C₂²×C₅₃	1	1	yes	characteristic
1088	#452	C₂²×C₅₃	1	1	yes	characteristic
1089	#452	C₂²×C₅₃	1	1	yes	characteristic
1090	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1091	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1092	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1093	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1094	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1095	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1096	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1097	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1098	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1099	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1100	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1101	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1102	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1103	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1104	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1105	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1106	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1107	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1108	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1109	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1110	#449	C₂²×C₅₃	1	1	yes	characteristic
1111	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1112	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1113	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1114	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1115	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1116	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1117	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1118	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1119	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1120	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1121	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1122	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1123	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1124	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1125	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1126	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1127	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1128	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1129	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1130	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1131	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1132	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1133	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1134	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1135	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1136	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1137	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1138	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1139	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1140	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1141	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
1142	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
1143	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1144	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1145	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1146	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
1147	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
1148	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
1149	#408	C₂²×C₅₃	1	1	yes	characteristic, complemented
1150	#408	C₂²×C₅₃	1	1	yes	characteristic, complemented
1151	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1152	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1153	C₅₃	#61640	1	1	yes	characteristic, direct product factor, Sylow
1154	H(5,𝔽₂)	—	4	2	no	—
1155	H(5,𝔽₂)	—	4	2	no	—
1156	C₂×#41	—	2	1	no	—
1157	C₂×#41	—	2	1	no	—
1158	C₂×#41	—	2	1	no	—
1159	C₂×#41	—	4	2	no	—
1160	C₂×#41	—	4	2	no	—
1161	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1162	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1163	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1164	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1165	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1166	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1167	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1168	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1169	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1170	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1171	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1172	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1173	C₂²×D₄	—	2	1	no	—
1174	C₂²×D₄	—	2	1	no	—
1175	C₂²×D₄	—	2	1	no	—
1176	C₂²×D₄	—	2	1	no	—
1177	C₂²×D₄	—	2	1	no	—
1178	C₂²×D₄	—	2	1	no	—
1179	C₂²×D₄	—	2	1	no	—
1180	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1181	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1182	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1183	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1184	C₂³×C₄	—	2	1	no	—
1185	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1186	#137	—	4	2	no	—
1187	AGL(1,ℤ/8)	—	4	2	no	—
1188	#135	—	4	2	no	—
1189	#135	—	4	2	no	—
1190	#135	—	4	2	no	—
1191	C₂×Q₁₆	—	4	2	no	—
1192	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1193	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1194	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1195	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1196	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1197	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1198	C₂×SD₁₆	—	4	2	no	—
1199	C₂×SD₁₆	—	4	2	no	—
1200	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1201	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1202	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1203	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1204	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1205	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1206	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1207	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1208	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1209	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1210	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1211	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1212	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1213	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1214	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1215	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1216	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1217	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1218	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1219	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1220	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1221	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1222	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1223	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1224	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1225	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1226	C₄⋊Q₈	—	2	1	no	—
1227	C₄⋊Q₈	—	2	1	no	—
1228	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1229	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1230	#127	—	2	1	no	—
1231	#127	—	2	1	no	—
1232	#127	C₂³×C₅₃	1	1	yes	characteristic
1233	#127	C₂³×C₅₃	1	1	yes	characteristic
1234	#126	—	2	1	no	—
1235	#126	—	2	1	no	—
1236	#126	—	2	1	no	—
1237	#126	—	2	1	no	—
1238	#126	—	2	1	no	—
1239	#126	—	2	1	no	—
1240	#126	—	2	1	no	—
1241	#125	—	2	1	no	—
1242	#125	—	2	1	no	—
1243	#125	—	2	1	no	—
1244	#125	—	2	1	no	—
1245	#125	C₂³×C₅₃	1	1	yes	characteristic
1246	#124	—	2	1	no	—
1247	#124	—	2	1	no	—
1248	#124	—	2	1	no	—
1249	#124	—	2	1	no	—
1250	#124	—	2	1	no	—
1251	#124	—	2	1	no	—
1252	#124	—	2	1	no	—
1253	#124	C₂³×C₅₃	1	1	yes	characteristic
1254	#124	C₂³×C₅₃	1	1	yes	characteristic
1255	#124	C₂³×C₅₃	1	1	yes	characteristic
1256	#123	—	2	1	no	—
1257	#123	—	2	1	no	—
1258	#123	—	2	1	no	—
1259	#123	—	2	1	no	—
1260	#123	—	2	1	no	—
1261	#123	—	2	1	no	—
1262	#123	—	2	1	no	—
1263	#123	—	2	1	no	—
1264	#123	—	2	1	no	—
1265	#123	—	2	1	no	—
1266	#123	D₄×C₅₃	1	1	yes	characteristic
1267	#123	D₄×C₅₃	1	1	yes	characteristic
1268	C₂²⋊Q₈	—	2	1	no	—
1269	C₂²⋊Q₈	—	2	1	no	—
1270	C₂²⋊Q₈	—	2	1	no	—
1271	C₂²⋊Q₈	—	2	1	no	—
1272	C₂²⋊Q₈	—	2	1	no	—
1273	C₂²⋊Q₈	—	2	1	no	—
1274	C₂²⋊Q₈	—	2	1	no	—
1275	C₂²⋊Q₈	—	2	1	no	—
1276	C₂²⋊Q₈	—	2	1	no	—
1277	C₂²⋊Q₈	—	2	1	no	—
1278	C₂²⋊Q₈	—	2	1	no	—
1279	C₂²⋊Q₈	—	2	1	no	—
1280	C₂²⋊Q₈	—	2	1	no	—
1281	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
1282	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
1283	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1284	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1285	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1286	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1287	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1288	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1289	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1290	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1291	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1292	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1293	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1294	#121	—	2	1	no	—
1295	#121	—	2	1	no	—
1296	#121	—	2	1	no	—
1297	#121	—	2	1	no	—
1298	#121	—	2	1	no	—
1299	#121	—	2	1	no	—
1300	#121	—	2	1	no	—
1301	#121	—	2	1	no	—
1302	#121	—	2	1	no	—
1303	#121	—	2	1	no	—
1304	#121	—	2	1	no	—
1305	#121	—	2	1	no	—
1306	#121	—	2	1	no	—
1307	#121	—	2	1	no	—
1308	#121	—	2	1	no	—
1309	#121	—	2	1	no	—
1310	#121	—	2	1	no	—
1311	#121	—	2	1	no	—
1312	#121	—	2	1	no	—
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	D₄×C₅₃	1	1	yes	characteristic
1319	#121	D₄×C₅₃	1	1	yes	characteristic
1320	#121	C₂³×C₅₃	1	1	yes	characteristic
1321	#121	C₂³×C₅₃	1	1	yes	characteristic
1322	#121	C₂³×C₅₃	1	1	yes	characteristic
1323	#121	C₂³×C₅₃	1	1	yes	characteristic
1324	#121	C₂³×C₅₃	1	1	yes	characteristic
1325	#121	C₂³×C₅₃	1	1	yes	characteristic
1326	#121	C₂³×C₅₃	1	1	yes	characteristic
1327	#121	C₂³×C₅₃	1	1	yes	characteristic
1328	#121	C₂³×C₅₃	1	1	yes	characteristic
1329	#120	—	2	1	no	—
1330	#120	—	2	1	no	—
1331	#120	—	2	1	no	—
1332	#120	—	2	1	no	—
1333	#120	—	2	1	no	—
1334	#120	—	2	1	no	—
1335	#120	—	2	1	no	—
1336	#120	—	2	1	no	—
1337	#120	—	2	1	no	—
1338	#120	D₄×C₅₃	1	1	yes	characteristic
1339	#120	D₄×C₅₃	1	1	yes	characteristic
1340	C₄×Q₈	—	2	1	no	—
1341	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1342	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1343	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1344	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1345	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1346	C₄×D₄	—	2	1	no	—
1347	C₄×D₄	—	2	1	no	—
1348	C₄×D₄	—	2	1	no	—
1349	C₄×D₄	—	2	1	no	—
1350	C₄×D₄	—	2	1	no	—
1351	C₄×D₄	—	2	1	no	—
1352	C₄×D₄	—	2	1	no	—
1353	C₄×D₄	—	2	1	no	—
1354	C₄×D₄	—	2	1	no	—
1355	C₄×D₄	—	2	1	no	—
1356	C₄×D₄	—	2	1	no	—
1357	C₄×D₄	—	2	1	no	—
1358	C₄×D₄	—	2	1	no	—
1359	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1360	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1361	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1362	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1363	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1364	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1365	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1366	#117	—	2	1	no	—
1367	#117	—	2	1	no	—
1368	#117	C₂³×C₅₃	1	1	yes	characteristic
1369	#117	C₂³×C₅₃	1	1	yes	characteristic
1370	#117	C₂³×C₅₃	1	1	yes	characteristic
1371	C₂×C₄⋊C₄	—	2	1	no	—
1372	C₂×C₄⋊C₄	—	2	1	no	—
1373	C₂×C₄⋊C₄	—	2	1	no	—
1374	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1375	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1376	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1377	C₂×C₂²⋊C₄	—	2	1	no	—
1378	C₂×C₂²⋊C₄	—	2	1	no	—
1379	C₂×C₂²⋊C₄	—	2	1	no	—
1380	C₂×C₂²⋊C₄	—	2	1	no	—
1381	#107	C₂³×C₅₃	1	1	yes	characteristic
1382	#107	C₂³×C₅₃	1	1	yes	characteristic
1383	#106	C₂³×C₅₃	1	1	yes	characteristic
1384	#106	C₂³×C₅₃	1	1	yes	characteristic
1385	#106	C₂³×C₅₃	1	1	yes	characteristic
1386	#106	C₂³×C₅₃	1	1	yes	characteristic
1387	#106	C₂³×C₅₃	1	1	yes	characteristic
1388	#106	C₂³×C₅₃	1	1	yes	characteristic
1389	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1390	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1391	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1392	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1393	#103	C₂³×C₅₃	1	1	yes	characteristic
1394	#103	C₂³×C₅₃	1	1	yes	characteristic
1395	#103	C₂³×C₅₃	1	1	yes	characteristic
1396	#103	C₂³×C₅₃	1	1	yes	characteristic
1397	#103	C₂³×C₅₃	1	1	yes	characteristic
1398	#103	C₂³×C₅₃	1	1	yes	characteristic
1399	#103	C₂³×C₅₃	1	1	yes	characteristic
1400	#103	C₂³×C₅₃	1	1	yes	characteristic
1401	#103	C₂³×C₅₃	1	1	yes	characteristic
1402	#103	C₂³×C₅₃	1	1	yes	characteristic
1403	#103	C₂³×C₅₃	1	1	yes	characteristic
1404	#103	C₂³×C₅₃	1	1	yes	characteristic
1405	#103	C₂³×C₅₃	1	1	yes	characteristic
1406	#103	C₂³×C₅₃	1	1	yes	characteristic
1407	#102	C₂³×C₅₃	1	1	yes	characteristic
1408	#102	C₂³×C₅₃	1	1	yes	characteristic
1409	#102	C₂³×C₅₃	1	1	yes	characteristic
1410	#102	C₂³×C₅₃	1	1	yes	characteristic
1411	#102	C₂³×C₅₃	1	1	yes	characteristic
1412	#102	C₂³×C₅₃	1	1	yes	characteristic
1413	#102	C₂³×C₅₃	1	1	yes	characteristic
1414	#102	C₂³×C₅₃	1	1	yes	characteristic
1415	#102	C₂³×C₅₃	1	1	yes	characteristic
1416	#102	C₂³×C₅₃	1	1	yes	characteristic
1417	#102	C₂³×C₅₃	1	1	yes	characteristic
1418	#102	C₂³×C₅₃	1	1	yes	characteristic
1419	#102	C₂³×C₅₃	1	1	yes	characteristic
1420	#102	C₂³×C₅₃	1	1	yes	characteristic
1421	#102	C₂³×C₅₃	1	1	yes	characteristic
1422	#102	C₂³×C₅₃	1	1	yes	characteristic
1423	#102	C₂³×C₅₃	1	1	yes	characteristic
1424	#102	C₂³×C₅₃	1	1	yes	characteristic
1425	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1426	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1427	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1428	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1429	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1430	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1431	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1432	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1433	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1434	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1435	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1436	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1437	#97	C₂³×C₅₃	1	1	yes	characteristic
1438	#97	C₂³×C₅₃	1	1	yes	characteristic
1439	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1440	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1441	C₂⁴	—	2	1	no	—
1442	C₂⁴	—	2	1	no	—
1443	C₂⁴	—	2	1	no	—
1444	C₂⁴	—	2	1	no	—
1445	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
1446	#41	—	2	2	no	—
1447	#41	—	2	2	no	—
1448	#41	—	2	2	no	—
1449	#41	—	2	2	no	—
1450	#41	—	2	2	no	—
1451	#41	—	2	2	no	—
1452	#41	—	4	1	no	—
1453	#41	—	4	1	no	—
1454	#41	—	4	1	no	—
1455	#41	—	4	1	no	—
1456	#41	—	4	1	no	—
1457	#41	—	4	1	no	—
1458	#41	—	4	1	no	—
1459	#41	—	4	1	no	—
1460	#41	—	4	4	no	—
1461	#41	—	4	4	no	—
1462	#41	—	4	1	no	—
1463	#41	—	4	1	no	—
1464	#41	—	4	1	no	—
1465	#41	—	4	1	no	—
1466	#41	—	4	4	no	—
1467	C₂×Q₈	—	2	1	no	—
1468	C₂×Q₈	—	2	1	no	—
1469	C₂×Q₈	—	2	1	no	—
1470	C₂×Q₈	—	2	1	no	—
1471	C₂×Q₈	—	2	2	no	—
1472	C₂×Q₈	—	4	1	no	—
1473	C₂×Q₈	—	4	1	no	—
1474	C₂×Q₈	—	4	1	no	—
1475	C₂×Q₈	—	4	1	no	—
1476	C₂×Q₈	—	4	1	no	—
1477	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1478	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1479	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1480	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1481	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1482	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1483	C₂×D₄	—	2	1	no	—
1484	C₂×D₄	—	2	2	no	—
1485	C₂×D₄	—	2	2	no	—
1486	C₂×D₄	—	2	2	no	—
1487	C₂×D₄	—	2	1	no	—
1488	C₂×D₄	—	2	1	no	—
1489	C₂×D₄	—	2	1	no	—
1490	C₂×D₄	—	2	1	no	—
1491	C₂×D₄	—	2	1	no	—
1492	C₂×D₄	—	2	1	no	—
1493	C₂×D₄	—	2	1	no	—
1494	C₂×D₄	—	2	1	no	—
1495	C₂×D₄	—	2	1	no	—
1496	C₂×D₄	—	2	1	no	—
1497	C₂×D₄	—	2	1	no	—
1498	C₂×D₄	—	2	1	no	—
1499	C₂×D₄	—	2	1	no	—
1500	C₂×D₄	—	2	1	no	—
1501	C₂×D₄	—	2	1	no	—
1502	C₂×D₄	—	2	1	no	—
1503	C₂×D₄	—	2	1	no	—
1504	C₂×D₄	—	2	1	no	—
1505	C₂×D₄	—	2	1	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	—	4	1	no	—
1512	C₂×D₄	—	4	1	no	—
1513	C₂×D₄	—	4	1	no	—
1514	C₂×D₄	—	4	1	no	—
1515	C₂×D₄	—	4	1	no	—
1516	C₂×D₄	—	4	4	no	—
1517	C₂×D₄	—	4	4	no	—
1518	C₂×D₄	—	4	4	no	—
1519	C₂×D₄	—	4	4	no	—
1520	C₂×D₄	—	8	2	no	—
1521	C₂×D₄	—	8	2	no	—
1522	C₂×D₄	—	8	2	no	—
1523	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1524	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1525	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1526	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1527	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1528	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1529	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1530	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1531	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1532	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1533	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1534	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1535	C₂²×C₄	—	2	1	no	—
1536	C₂²×C₄	—	2	1	no	—
1537	C₂²×C₄	—	2	1	no	—
1538	C₂²×C₄	—	2	1	no	—
1539	C₂²×C₄	—	2	1	no	—
1540	C₂²×C₄	—	2	1	no	—
1541	C₂²×C₄	—	2	1	no	—
1542	C₂²×C₄	—	2	1	no	—
1543	C₂²×C₄	—	2	1	no	—
1544	C₂²×C₄	—	2	1	no	—
1545	C₂²×C₄	—	2	1	no	—
1546	C₂²×C₄	—	2	1	no	—
1547	C₂²×C₄	—	2	1	no	—
1548	C₂²×C₄	—	2	1	no	—
1549	C₂²×C₄	—	2	1	no	—
1550	C₂²×C₄	—	2	1	no	—
1551	C₂²×C₄	—	2	1	no	—
1552	C₂²×C₄	—	4	1	no	—
1553	C₂²×C₄	—	4	1	no	—
1554	C₂²×C₄	—	4	4	no	—
1555	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1556	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1557	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1558	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1559	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1560	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1561	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1562	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1563	Q₁₆	—	2	2	no	—
1564	Q₁₆	—	2	2	no	—
1565	Q₁₆	—	2	2	no	—
1566	Q₁₆	—	4	1	no	—
1567	Q₁₆	—	4	1	no	—
1568	Q₁₆	—	4	1	no	—
1569	SD₁₆	—	2	2	no	—
1570	SD₁₆	—	2	2	no	—
1571	SD₁₆	—	2	2	no	—
1572	SD₁₆	—	2	2	no	—
1573	SD₁₆	—	4	1	no	—
1574	SD₁₆	—	4	1	no	—
1575	SD₁₆	—	4	1	no	—
1576	SD₁₆	—	4	1	no	—
1577	SD₁₆	—	4	1	no	—
1578	SD₁₆	—	4	1	no	—
1579	SD₁₆	—	4	1	no	—
1580	SD₁₆	—	4	1	no	—
1581	SD₁₆	—	4	1	no	—
1582	SD₁₆	—	4	1	no	—
1583	D₈	—	2	2	no	—
1584	D₈	—	4	1	no	—
1585	D₈	—	4	1	no	—
1586	D₈	—	4	1	no	—
1587	M₁₆	—	4	1	no	—
1588	M₁₆	—	4	1	no	—
1589	C₂×C₈	—	4	1	no	—
1590	C₂×C₈	—	4	1	no	—
1591	C₂×C₈	—	4	1	no	—
1592	C₂×C₈	—	4	1	no	—
1593	C₂×C₈	—	4	1	no	—
1594	C₂×C₈	—	4	1	no	—
1595	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1596	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1597	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1598	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1599	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1600	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1601	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1602	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1603	C₄⋊C₄	—	2	1	no	—
1604	C₄⋊C₄	—	2	1	no	—
1605	C₄⋊C₄	—	2	1	no	—
1606	C₄⋊C₄	—	2	1	no	—
1607	C₄⋊C₄	—	2	1	no	—
1608	C₄⋊C₄	—	2	1	no	—
1609	C₄⋊C₄	—	2	1	no	—
1610	C₄⋊C₄	—	2	1	no	—
1611	C₄⋊C₄	—	2	1	no	—
1612	C₄⋊C₄	—	2	1	no	—
1613	C₄⋊C₄	—	2	1	no	—
1614	C₄⋊C₄	—	2	1	no	—
1615	C₄⋊C₄	—	2	1	no	—
1616	C₄⋊C₄	—	2	1	no	—
1617	C₄⋊C₄	—	2	1	no	—
1618	C₄⋊C₄	—	2	1	no	—
1619	C₄⋊C₄	—	2	1	no	—
1620	C₄⋊C₄	—	2	1	no	—
1621	C₄⋊C₄	—	2	1	no	—
1622	C₄⋊C₄	—	2	1	no	—
1623	C₄⋊C₄	—	2	1	no	—
1624	C₄⋊C₄	—	2	1	no	—
1625	C₄⋊C₄	—	2	1	no	—
1626	C₄⋊C₄	—	2	1	no	—
1627	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1628	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1629	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1630	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1631	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1632	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1633	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1634	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1635	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1636	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1637	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1638	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1639	C₂²⋊C₄	—	2	1	no	—
1640	C₂²⋊C₄	—	2	1	no	—
1641	C₂²⋊C₄	—	2	1	no	—
1642	C₂²⋊C₄	—	2	1	no	—
1643	C₂²⋊C₄	—	2	1	no	—
1644	C₂²⋊C₄	—	2	1	no	—
1645	C₂²⋊C₄	—	2	1	no	—
1646	C₂²⋊C₄	—	2	1	no	—
1647	C₂²⋊C₄	—	2	1	no	—
1648	C₂²⋊C₄	—	2	1	no	—
1649	C₂²⋊C₄	—	2	1	no	—
1650	C₂²⋊C₄	—	2	1	no	—
1651	C₂²⋊C₄	—	2	1	no	—
1652	C₂²⋊C₄	—	2	1	no	—
1653	C₂²⋊C₄	—	2	1	no	—
1654	C₂²⋊C₄	—	2	1	no	—
1655	C₂²⋊C₄	—	2	1	no	—
1656	C₂²⋊C₄	—	2	1	no	—
1657	C₂²⋊C₄	—	2	1	no	—
1658	C₂²⋊C₄	—	2	1	no	—
1659	C₂²⋊C₄	—	2	1	no	—
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	C₂×D₄×C₅₃	1	1	yes	characteristic
1671	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1672	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1673	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1674	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1675	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1676	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1677	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1678	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1679	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1680	C₄²	—	2	1	no	—
1681	C₄²	—	2	1	no	—
1682	C₄²	—	2	1	no	—
1683	C₄²	—	2	1	no	—
1684	C₄²	—	2	1	no	—
1685	C₄²	—	2	1	no	—
1686	C₄²	—	2	1	no	—
1687	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1688	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1689	C₂³	—	2	1	no	—
1690	C₂³	—	2	2	no	—
1691	C₂³	—	2	1	no	—
1692	C₂³	—	2	1	no	—
1693	C₂³	—	2	1	no	—
1694	C₂³	—	2	1	no	—
1695	C₂³	—	4	1	no	—
1696	C₂³	—	4	1	no	—
1697	C₂³	—	4	2	no	—
1698	C₂³	—	4	2	no	—
1699	C₂³	—	4	2	no	—
1700	C₂³	—	4	2	no	—
1701	C₂³	—	4	2	no	—
1702	C₂³	—	8	1	no	—
1703	C₂³	—	8	1	no	—
1704	C₂³	—	8	1	no	—
1705	C₂³	—	8	1	no	—
1706	C₂³	—	8	1	no	—
1707	C₂³	—	8	1	no	—
1708	C₂³	—	8	1	no	—
1709	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1710	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1711	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1712	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1713	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1714	Q₈	—	2	1	no	—
1715	Q₈	—	2	1	no	—
1716	Q₈	—	2	1	no	—
1717	Q₈	—	2	1	no	—
1718	Q₈	—	2	1	no	—
1719	Q₈	—	2	1	no	—
1720	Q₈	—	2	1	no	—
1721	Q₈	—	2	1	no	—
1722	Q₈	—	2	1	no	—
1723	Q₈	—	4	1	no	—
1724	Q₈	—	4	2	no	—
1725	Q₈	—	8	1	no	—
1726	Q₈	—	8	1	no	—
1727	Q₈	—	8	1	no	—
1728	Q₈	H(5,𝔽₂)×C₅₃	1	2	yes	—
1729	D₄	—	2	4	no	—
1730	D₄	—	2	2	no	—
1731	D₄	—	2	2	no	—
1732	D₄	—	2	1	no	—
1733	D₄	—	2	1	no	—
1734	D₄	—	2	1	no	—
1735	D₄	—	2	1	no	—
1736	D₄	—	2	1	no	—
1737	D₄	—	2	1	no	—
1738	D₄	—	2	1	no	—
1739	D₄	—	2	1	no	—
1740	D₄	—	2	1	no	—
1741	D₄	—	4	1	no	—
1742	D₄	—	4	1	no	—
1743	D₄	—	4	1	no	—
1744	D₄	—	4	1	no	—
1745	D₄	—	4	1	no	—
1746	D₄	—	4	2	no	—
1747	D₄	—	4	2	no	—
1748	D₄	—	4	2	no	—
1749	D₄	—	4	2	no	—
1750	D₄	—	4	2	no	—
1751	D₄	—	4	2	no	—
1752	D₄	—	4	2	no	—
1753	D₄	—	4	2	no	—
1754	D₄	—	4	2	no	—
1755	D₄	—	4	2	no	—
1756	D₄	—	4	2	no	—
1757	D₄	—	4	2	no	—
1758	D₄	—	8	1	no	—
1759	D₄	—	8	1	no	—
1760	D₄	—	8	1	no	—
1761	D₄	—	8	1	no	—
1762	D₄	—	8	1	no	—
1763	D₄	—	8	1	no	—
1764	D₄	—	8	1	no	—
1765	D₄	—	8	1	no	—
1766	D₄	—	8	1	no	—
1767	D₄	—	8	1	no	—
1768	D₄	—	8	1	no	—
1769	D₄	—	8	1	no	—
1770	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1771	C₂×C₄	—	2	4	no	—
1772	C₂×C₄	—	2	1	no	—
1773	C₂×C₄	—	2	1	no	—
1774	C₂×C₄	—	2	1	no	—
1775	C₂×C₄	—	2	1	no	—
1776	C₂×C₄	—	2	1	no	—
1777	C₂×C₄	—	2	1	no	—
1778	C₂×C₄	—	2	1	no	—
1779	C₂×C₄	—	2	1	no	—
1780	C₂×C₄	—	2	1	no	—
1781	C₂×C₄	—	2	1	no	—
1782	C₂×C₄	—	2	1	no	—
1783	C₂×C₄	—	2	1	no	—
1784	C₂×C₄	—	2	1	no	—
1785	C₂×C₄	—	2	1	no	—
1786	C₂×C₄	—	2	1	no	—
1787	C₂×C₄	—	2	1	no	—
1788	C₂×C₄	—	2	1	no	—
1789	C₂×C₄	—	2	1	no	—
1790	C₂×C₄	—	2	1	no	—
1791	C₂×C₄	—	2	1	no	—
1792	C₂×C₄	—	2	1	no	—
1793	C₂×C₄	—	4	1	no	—
1794	C₂×C₄	—	4	1	no	—
1795	C₂×C₄	—	4	1	no	—
1796	C₂×C₄	—	4	2	no	—
1797	C₂×C₄	—	4	2	no	—
1798	C₂×C₄	—	4	2	no	—
1799	C₂×C₄	—	4	2	no	—
1800	C₂×C₄	—	4	2	no	—
1801	C₂×C₄	—	4	2	no	—
1802	C₂×C₄	—	8	1	no	—
1803	C₂×C₄	—	8	1	no	—
1804	C₂×C₄	—	8	1	no	—
1805	C₂×C₄	—	8	1	no	—
1806	C₂×C₄	—	8	1	no	—
1807	C₂×C₄	—	8	1	no	—
1808	C₂×C₄	—	8	1	no	—
1809	C₂×C₄	—	8	1	no	—
1810	C₂×C₄	—	8	1	no	—
1811	C₂×C₄	—	8	1	no	—
1812	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1813	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1814	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1815	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1816	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1817	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1818	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1819	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1820	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1821	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1822	C₈	—	2	1	no	—
1823	C₈	—	2	1	no	—
1824	C₈	—	2	1	no	—
1825	C₈	—	2	1	no	—
1826	C₈	—	2	1	no	—
1827	C₈	—	2	1	no	—
1828	C₈	—	2	1	no	—
1829	C₈	—	2	1	no	—
1830	C₂²	—	2	1	no	—
1831	C₂²	—	2	1	no	—
1832	C₂²	—	2	1	no	—
1833	C₂²	—	2	2	no	—
1834	C₂²	—	2	1	no	—
1835	C₂²	—	2	1	no	—
1836	C₂²	—	2	1	no	—
1837	C₂²	—	2	1	no	—
1838	C₂²	—	2	1	no	—
1839	C₂²	—	2	1	no	—
1840	C₂²	—	2	1	no	—
1841	C₂²	—	2	1	no	—
1842	C₂²	—	2	1	no	—
1843	C₂²	—	2	1	no	—
1844	C₂²	—	2	1	no	—
1845	C₂²	—	4	1	no	—
1846	C₂²	—	4	1	no	—
1847	C₂²	—	4	1	no	—
1848	C₂²	—	4	1	no	—
1849	C₂²	—	4	1	no	—
1850	C₂²	—	4	1	no	—
1851	C₂²	—	4	1	no	—
1852	C₂²	—	4	1	no	—
1853	C₂²	—	4	1	no	—
1854	C₂²	—	4	1	no	—
1855	C₂²	—	4	1	no	—
1856	C₂²	—	4	1	no	—
1857	C₂²	—	4	1	no	—
1858	C₂²	—	4	1	no	—
1859	C₂²	—	8	2	no	—
1860	C₂²	—	8	4	no	—
1861	C₂²	—	16	2	no	—
1862	C₂²	—	16	2	no	—
1863	C₂²	—	16	2	no	—
1864	C₂²	C₅₃×#577	1	2	yes	—
1865	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1866	C₄	—	2	1	no	—
1867	C₄	—	2	2	no	—
1868	C₄	—	2	1	no	—
1869	C₄	—	2	1	no	—
1870	C₄	—	2	1	no	—
1871	C₄	—	2	1	no	—
1872	C₄	—	2	1	no	—
1873	C₄	—	2	1	no	—
1874	C₄	—	2	1	no	—
1875	C₄	—	2	1	no	—
1876	C₄	—	4	1	no	—
1877	C₄	—	4	1	no	—
1878	C₄	—	4	1	no	—
1879	C₄	—	4	1	no	—
1880	C₄	—	4	1	no	—
1881	C₄	—	4	1	no	—
1882	C₄	—	4	1	no	—
1883	C₄	—	4	1	no	—
1884	C₄	—	4	1	no	—
1885	C₄	—	4	1	no	—
1886	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1887	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1888	C₂	—	2	2	no	—
1889	C₂	—	4	1	no	—
1890	C₂	—	4	1	no	—
1891	C₂	—	4	1	no	—
1892	C₂	—	4	1	no	—
1893	C₂	—	4	2	no	—
1894	C₂	—	8	1	no	—
1895	C₂	—	8	1	no	—
1896	C₂	—	8	1	no	—
1897	C₂	—	8	1	no	—
1898	C₂	C₅₃×#3484	1	1	yes	characteristic
1899	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
1900	C₂	C₅₃×#3584	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×#3488	C₂	semidirect
3. C₅₃×#3318	C₂	semidirect
4. C₅₃×#3317	C₂	semidirect
5. C₅₃×#3316	C₂	semidirect
6. C₅₃×#3311	C₂	semidirect
7. C₅₃×#3304	C₂	semidirect
8. C₅₃×#3301	C₂	semidirect
9. C₅₃×#3296	C₂	semidirect
10. C₅₃×#3295	C₂	semidirect
11. C₅₃×#3285	C₂	semidirect
12. C₅₃×#3284	C₂	semidirect
13. C₅₃×#3282	C₂	semidirect
14. D₄×SD₁₆×C₅₃	C₂	semidirect
15. C₅₃×#3271	C₂	semidirect
16. C₅₃×#3270	C₂	semidirect
17. C₅₃×#3267	C₂	semidirect
18. C₅₃×#3265	C₂	semidirect
19. C₅₃×#3224	C₂	semidirect
20. C₅₃×#3222	C₂	semidirect
21. C₅₃×#3204	C₂	semidirect
22. C₅₃×#3201	C₂	semidirect
23. C₅₃×#3188	C₂	semidirect
24. C₅₃×#3187	C₂	semidirect
25. C₅₃×#3125	C₂	semidirect
26. C₅₃×#3120	C₂	semidirect
27. C₅₃×#3012	C₂	semidirect
28. C₅₃×#3009	C₂	semidirect
29. C₅₃×#3002	C₂	semidirect
30. C₂×C₅₃×#452	C₂	semidirect
31. C₅₃×#2977	C₂	semidirect
34. C₂×#137×C₅₃	C₂²	semidirect
35. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
36. C₂×#135×C₅₃	C₂²	semidirect
37. C₂×#135×C₅₃	C₂²	semidirect
38. C₂×#135×C₅₃	C₂²	semidirect
39. C₂²×Q₁₆×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
52. D₄×Q₈×C₅₃	C₂²	semidirect
55. C₅₃×#548	C₂²	semidirect
56. C₅₃×#548	C₂²	semidirect
57. C₅₃×#547	C₂²	semidirect
67. C₅₃×#542	C₂²	semidirect
68. C₅₃×#541	C₂²	semidirect
74. C₅₃×#537	C₂²	semidirect
75. 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×#484	C₂²	semidirect
95. C₅₃×#483	C₂²	semidirect
96. C₅₃×#483	C₂²	semidirect
97. C₅₃×#483	C₂²	semidirect
98. C₅₃×#482	C₂²	semidirect
99. C₅₃×#482	C₂²	semidirect
100. C₅₃×#482	C₂²	semidirect
101. C₅₃×#481	C₂²	semidirect
102. C₅₃×#481	C₂²	semidirect
103. C₅₃×#481	C₂²	semidirect
104. C₅₃×#481	C₂²	semidirect
105. C₅₃×#479	C₂²	semidirect
106. C₅₃×#478	C₂²	semidirect
107. C₅₃×#476	C₂²	semidirect
108. C₅₃×#475	C₂²	semidirect
109. C₅₃×#470	C₂²	semidirect
110. C₅₃×#470	C₂²	semidirect
111. C₅₃×#469	C₂²	semidirect
112. C₅₃×#468	C₂²	semidirect
113. C₅₃×#467	C₂²	semidirect
114. C₅₃×#466	C₂²	semidirect
115. C₅₃×#466	C₂²	semidirect
116. C₅₃×#465	C₂²	semidirect
117. C₅₃×#465	C₂²	semidirect
118. C₅₃×#465	C₂²	semidirect
119. C₅₃×#465	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×#464	C₂²	semidirect
129. C₅₃×#463	C₂²	semidirect
130. C₅₃×#463	C₂²	semidirect
131. C₅₃×#462	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
140. C₅₃×#452	C₂²	semidirect
141. C₅₃×#452	C₂²	semidirect
142. C₅₃×#452	C₂²	semidirect
143. C₅₃×#452	C₂²	semidirect
144. C₅₃×#452	C₂²	semidirect
145. C₅₃×#452	C₂²	semidirect
146. C₅₃×#452	C₂²	semidirect
147. C₅₃×#452	C₂²	semidirect
148. C₅₃×#452	C₂²	semidirect
149. C₅₃×#452	C₂²	semidirect
150. C₅₃×#452	C₂²	semidirect
151. C₅₃×#451	C₂²	semidirect
152. C₅₃×#451	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
161. C₅₃×#449	C₂²	semidirect
162. C₅₃×#449	C₂²	semidirect
163. C₅₃×#449	C₂²	semidirect
164. C₅₃×#449	C₂²	semidirect
165. C₅₃×#449	C₂²	semidirect
166. C₅₃×#448	C₂²	semidirect
167. C₅₃×#448	C₂²	semidirect
168. C₅₃×#448	C₂²	semidirect
169. C₅₃×#448	C₂²	semidirect
170. C₅₃×#447	C₂²	semidirect
171. C₅₃×#447	C₂²	semidirect
172. C₅₃×#447	C₂²	semidirect
173. C₅₃×#442	C₂²	semidirect
174. C₅₃×#441	C₂²	semidirect
175. C₅₃×#441	C₂²	semidirect
176. C₅₃×#440	C₂²	semidirect
177. C₄×Q₁₆×C₅₃	C₂²	semidirect
178. C₄×SD₁₆×C₅₃	C₂²	semidirect
179. C₄×SD₁₆×C₅₃	C₂²	semidirect
180. C₄×SD₁₆×C₅₃	C₂²	semidirect
181. C₅₃×#435	C₂²	semidirect
182. C₅₃×#435	C₂²	semidirect
183. C₅₃×#435	C₂²	semidirect
184. C₅₃×#435	C₂²	semidirect
185. C₈×D₄×C₅₃	C₂²	semidirect
186. C₈×D₄×C₅₃	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×#417	C₂²	semidirect
193. C₅₃×#416	C₂²	semidirect
194. C₅₃×#416	C₂²	semidirect
195. C₅₃×#416	C₂²	semidirect
196. C₂×#103×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. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
202. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
879. #61640	C₅₃	direct (N × H)
938. #3541	C₂×C₅₃	semidirect
939. #3488	C₂×C₅₃	semidirect
940. #3318	C₂×C₅₃	semidirect
941. #3317	C₂×C₅₃	semidirect
942. #3316	C₂×C₅₃	semidirect
943. #3311	C₂×C₅₃	semidirect
944. #3304	C₂×C₅₃	semidirect
945. #3301	C₂×C₅₃	semidirect
946. #3296	C₂×C₅₃	semidirect
947. #3295	C₂×C₅₃	semidirect
948. #3285	C₂×C₅₃	semidirect
949. #3284	C₂×C₅₃	semidirect
950. #3282	C₂×C₅₃	semidirect
951. D₄×SD₁₆	C₂×C₅₃	semidirect
952. #3271	C₂×C₅₃	semidirect
953. #3270	C₂×C₅₃	semidirect
954. #3267	C₂×C₅₃	semidirect
955. #3265	C₂×C₅₃	semidirect
956. #3224	C₂×C₅₃	semidirect
957. #3222	C₂×C₅₃	semidirect
958. #3204	C₂×C₅₃	semidirect
959. #3201	C₂×C₅₃	semidirect
960. #3188	C₂×C₅₃	semidirect
961. #3187	C₂×C₅₃	semidirect
962. #3125	C₂×C₅₃	semidirect
963. #3120	C₂×C₅₃	semidirect
964. #3012	C₂×C₅₃	semidirect
965. #3009	C₂×C₅₃	semidirect
966. #3002	C₂×C₅₃	semidirect
967. C₂×#452	C₂×C₅₃	semidirect
968. #2977	C₂×C₅₃	semidirect
984. C₂×#137	C₂²×C₅₃	semidirect
985. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
986. C₂×#135	C₂²×C₅₃	semidirect
987. C₂×#135	C₂²×C₅₃	semidirect
988. C₂×#135	C₂²×C₅₃	semidirect
989. C₂²×Q₁₆	C₂²×C₅₃	semidirect
990. C₂²×SD₁₆	C₂²×C₅₃	semidirect
991. C₂²×SD₁₆	C₂²×C₅₃	semidirect
994. #556	C₂²×C₅₃	semidirect
996. #554	C₂²×C₅₃	semidirect
998. #553	C₂²×C₅₃	semidirect
999. #552	C₂²×C₅₃	semidirect
1002. D₄×Q₈	C₂²×C₅₃	semidirect
1005. #548	C₂²×C₅₃	semidirect
1006. #548	C₂²×C₅₃	semidirect
1007. #547	C₂²×C₅₃	semidirect
1017. #542	C₂²×C₅₃	semidirect
1018. #541	C₂²×C₅₃	semidirect
1024. #537	C₂²×C₅₃	semidirect
1025. #536	C₂²×C₅₃	semidirect
1030. #525	C₂²×C₅₃	semidirect
1031. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
1035. #497	C₂²×C₅₃	semidirect
1036. #496	C₂²×C₅₃	semidirect
1037. #495	C₂²×C₅₃	semidirect
1038. #492	C₂²×C₅₃	semidirect
1039. #490	C₂²×C₅₃	semidirect
1040. #489	C₂²×C₅₃	semidirect
1041. #488	C₂²×C₅₃	semidirect
1042. #486	C₂²×C₅₃	semidirect
1043. #485	C₂²×C₅₃	semidirect
1044. #484	C₂²×C₅₃	semidirect
1045. #483	C₂²×C₅₃	semidirect
1046. #483	C₂²×C₅₃	semidirect
1047. #483	C₂²×C₅₃	semidirect
1048. #482	C₂²×C₅₃	semidirect
1049. #482	C₂²×C₅₃	semidirect
1050. #482	C₂²×C₅₃	semidirect
1051. #481	C₂²×C₅₃	semidirect
1052. #481	C₂²×C₅₃	semidirect
1053. #481	C₂²×C₅₃	semidirect
1054. #481	C₂²×C₅₃	semidirect
1055. #479	C₂²×C₅₃	semidirect
1056. #478	C₂²×C₅₃	semidirect
1057. #476	C₂²×C₅₃	semidirect
1058. #475	C₂²×C₅₃	semidirect
1059. #470	C₂²×C₅₃	semidirect
1060. #470	C₂²×C₅₃	semidirect
1061. #469	C₂²×C₅₃	semidirect
1062. #468	C₂²×C₅₃	semidirect
1063. #467	C₂²×C₅₃	semidirect
1064. #466	C₂²×C₅₃	semidirect
1065. #466	C₂²×C₅₃	semidirect
1066. #465	C₂²×C₅₃	semidirect
1067. #465	C₂²×C₅₃	semidirect
1068. #465	C₂²×C₅₃	semidirect
1069. #465	C₂²×C₅₃	semidirect
1070. #465	C₂²×C₅₃	semidirect
1071. #465	C₂²×C₅₃	semidirect
1072. #465	C₂²×C₅₃	semidirect
1073. #465	C₂²×C₅₃	semidirect
1074. #465	C₂²×C₅₃	semidirect
1075. #464	C₂²×C₅₃	semidirect
1076. #464	C₂²×C₅₃	semidirect
1077. #464	C₂²×C₅₃	semidirect
1078. #464	C₂²×C₅₃	semidirect
1079. #463	C₂²×C₅₃	semidirect
1080. #463	C₂²×C₅₃	semidirect
1081. #462	C₂²×C₅₃	semidirect
1082. #461	C₂²×C₅₃	semidirect
1083. #460	C₂²×C₅₃	semidirect
1084. #460	C₂²×C₅₃	semidirect
1085. #460	C₂²×C₅₃	semidirect
1086. #459	C₂²×C₅₃	semidirect
1090. #452	C₂²×C₅₃	semidirect
1091. #452	C₂²×C₅₃	semidirect
1092. #452	C₂²×C₅₃	semidirect
1093. #452	C₂²×C₅₃	semidirect
1094. #452	C₂²×C₅₃	semidirect
1095. #452	C₂²×C₅₃	semidirect
1096. #452	C₂²×C₅₃	semidirect
1097. #452	C₂²×C₅₃	semidirect
1098. #452	C₂²×C₅₃	semidirect
1099. #452	C₂²×C₅₃	semidirect
1100. #452	C₂²×C₅₃	semidirect
1101. #451	C₂²×C₅₃	semidirect
1102. #451	C₂²×C₅₃	semidirect
1103. #450	C₂²×C₅₃	semidirect
1104. #450	C₂²×C₅₃	semidirect
1105. #450	C₂²×C₅₃	semidirect
1106. #450	C₂²×C₅₃	semidirect
1107. #450	C₂²×C₅₃	semidirect
1108. #450	C₂²×C₅₃	semidirect
1109. #450	C₂²×C₅₃	semidirect
1111. #449	C₂²×C₅₃	semidirect
1112. #449	C₂²×C₅₃	semidirect
1113. #449	C₂²×C₅₃	semidirect
1114. #449	C₂²×C₅₃	semidirect
1115. #449	C₂²×C₅₃	semidirect
1116. #448	C₂²×C₅₃	semidirect
1117. #448	C₂²×C₅₃	semidirect
1118. #448	C₂²×C₅₃	semidirect
1119. #448	C₂²×C₅₃	semidirect
1120. #447	C₂²×C₅₃	semidirect
1121. #447	C₂²×C₅₃	semidirect
1122. #447	C₂²×C₅₃	semidirect
1123. #442	C₂²×C₅₃	semidirect
1124. #441	C₂²×C₅₃	semidirect
1125. #441	C₂²×C₅₃	semidirect
1126. #440	C₂²×C₅₃	semidirect
1127. C₄×Q₁₆	C₂²×C₅₃	semidirect
1128. C₄×SD₁₆	C₂²×C₅₃	semidirect
1129. C₄×SD₁₆	C₂²×C₅₃	semidirect
1130. C₄×SD₁₆	C₂²×C₅₃	semidirect
1131. #435	C₂²×C₅₃	semidirect
1132. #435	C₂²×C₅₃	semidirect
1133. #435	C₂²×C₅₃	semidirect
1134. #435	C₂²×C₅₃	semidirect
1135. C₈×D₄	C₂²×C₅₃	semidirect
1136. C₈×D₄	C₂²×C₅₃	semidirect
1137. C₈×D₄	C₂²×C₅₃	semidirect
1138. C₈×D₄	C₂²×C₅₃	semidirect
1139. #433	C₂²×C₅₃	semidirect
1140. #433	C₂²×C₅₃	semidirect
1141. #418	C₂²×C₅₃	semidirect
1142. #417	C₂²×C₅₃	semidirect
1143. #416	C₂²×C₅₃	semidirect
1144. #416	C₂²×C₅₃	semidirect
1145. #416	C₂²×C₅₃	semidirect
1146. C₂×#103	C₂²×C₅₃	semidirect
1147. C₂×#102	C₂²×C₅₃	semidirect
1148. C₂×#102	C₂²×C₅₃	semidirect
1149. #408	C₂²×C₅₃	semidirect
1150. #408	C₂²×C₅₃	semidirect
1151. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
1152. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
1153. C₅₃	#61640	direct (N × H)

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×#3488	2
C₅₃×#3318	2
C₅₃×#3317	2
C₅₃×#3316	2
C₅₃×#3311	2
C₅₃×#3304	2
C₅₃×#3301	2
C₅₃×#3296	2
C₅₃×#3295	2
C₅₃×#3285	2
C₅₃×#3284	2
C₅₃×#3282	2
D₄×SD₁₆×C₅₃	2
C₅₃×#3271	2
C₅₃×#3270	2
C₅₃×#3267	2
C₅₃×#3265	2
C₅₃×#3224	2
C₅₃×#3222	2
C₅₃×#3204	2
C₅₃×#3201	2
C₅₃×#3188	2
C₅₃×#3187	2
C₅₃×#3125	2
C₅₃×#3120	2
C₅₃×#3012	2
C₅₃×#3009	2
C₅₃×#3002	2
C₂×C₅₃×#452	2
C₅₃×#2977	2
#61640	53

Subgroups — C53×#61640 #27269152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61640 #27269152