Subgroups — C₅₃×#62047 #27269559

Order 13568.

1860 conjugacy classes of subgroups.

The subgroup lattice has 1792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3558	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3521	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3401	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3394	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3370	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3326	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3323	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3318	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3313	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3296	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3280	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3275	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3273	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3269	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3264	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3262	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3258	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3251	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3224	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3222	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#3211	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#3125	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#3118	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#3045	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#3041	C₂	1	1	yes	maximal, characteristic, complemented
30	C₅₃×#3040	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2993	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×AGL(1,ℤ/8)×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	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
38	C₅₃×#562	—	2	1	no	—
39	C₅₃×H(3,𝔽₄)	—	2	1	no	—
40	C₅₃×#559	C₂²	1	1	yes	characteristic, complemented
41	C₅₃×#559	C₂²	1	1	yes	characteristic, complemented
42	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
43	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
44	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
45	C₅₃×#553	—	2	1	no	—
46	C₅₃×#553	C₂²	1	1	yes	characteristic, complemented
47	C₅₃×#552	—	2	1	no	—
48	C₅₃×#552	C₂²	1	1	yes	characteristic, complemented
49	C₅₃×#551	—	2	1	no	—
50	C₅₃×#551	—	2	1	no	—
51	C₅₃×#548	C₂²	1	1	yes	characteristic
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, complemented
59	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
60	D₄²×C₅₃	C₂²	1	1	yes	characteristic
61	D₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#542	C₂²	1	1	yes	characteristic
63	C₅₃×#542	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#542	C₂²	1	1	yes	characteristic, complemented
65	C₅₃×#541	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#539	—	2	1	no	—
67	C₅₃×#538	—	2	1	no	—
68	C₅₃×#538	—	2	1	no	—
69	C₅₃×#538	—	2	1	no	—
70	C₅₃×#538	—	2	1	no	—
71	C₅₃×#535	C₂²	1	1	yes	characteristic
72	C₅₃×#535	C₂²	1	1	yes	characteristic, complemented
73	C₅₃×#534	—	2	1	no	—
74	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#529	—	2	1	no	—
76	C₅₃×#529	C₂²	1	1	yes	characteristic
77	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
78	C₂×#126×C₅₃	—	2	1	no	—
79	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
80	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
81	C₅₃×#518	C₂²	1	1	yes	characteristic, complemented
82	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
83	C₅₃×#497	C₂²	1	1	yes	characteristic, complemented
84	C₅₃×#496	C₂²	1	1	yes	characteristic
85	C₅₃×#495	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#495	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×#488	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#488	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#482	C₂²	1	1	yes	characteristic
98	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
105	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
106	C₅₃×#477	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×#474	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#469	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#469	C₂²	1	1	yes	characteristic, complemented
114	C₅₃×#468	C₂²	1	1	yes	characteristic
115	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#466	C₂²	1	1	yes	characteristic
122	C₅₃×#465	C₂²	1	1	yes	characteristic
123	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#464	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×#464	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
135	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
136	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
137	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
138	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
139	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
140	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
141	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
142	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
143	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
144	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
145	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
146	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
147	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
148	C₅₃×#459	C₂²	1	1	yes	characteristic
149	C₅₃×#459	C₂²	1	1	yes	characteristic
150	C₅₃×#459	C₂²	1	1	yes	characteristic
151	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
152	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
153	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
154	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
155	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
156	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
157	C₅₃×#451	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×#450	C₂²	1	1	yes	characteristic, complemented
161	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
162	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
163	C₅₃×#449	C₂²	1	1	yes	characteristic
164	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
165	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
166	C₅₃×#449	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
170	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
171	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
172	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
173	C₅₃×#442	C₂²	1	1	yes	characteristic, complemented
174	C₅₃×#442	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×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×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
181	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
182	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
183	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
184	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
185	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
186	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
187	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
188	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
189	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
190	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
191	C₅₃×#433	C₂²	1	1	yes	characteristic, complemented
192	C₅₃×#433	C₂²	1	1	yes	characteristic, complemented
193	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
194	C₅₃×#424	C₂²	1	1	yes	characteristic, complemented
195	C₅₃×#424	C₂²	1	1	yes	characteristic, complemented
196	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
197	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
198	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
199	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
200	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
201	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
202	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
203	C₂×#41×C₅₃	—	2	1	no	—
204	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
205	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
206	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
207	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
208	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
209	C₂²×D₄×C₅₃	—	2	1	no	—
210	C₂²×D₄×C₅₃	—	2	1	no	—
211	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
212	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
213	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
214	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
215	#137×C₅₃	—	4	2	no	—
216	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
217	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
218	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
219	#135×C₅₃	—	4	2	no	—
220	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
221	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
222	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
223	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
224	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
225	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
226	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
227	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
228	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
229	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
230	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
231	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
232	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
233	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
234	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
235	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
236	C₂×D₈×C₅₃	—	4	2	no	—
237	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
238	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
239	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
240	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
241	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
242	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
243	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
244	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
245	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
246	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
247	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
248	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
249	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
250	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
251	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
252	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
253	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
254	#127×C₅₃	C₂³	1	1	yes	characteristic
255	#127×C₅₃	C₂³	1	1	yes	characteristic
256	#127×C₅₃	C₂³	1	1	yes	characteristic
257	#126×C₅₃	—	2	1	no	—
258	#126×C₅₃	—	2	1	no	—
259	#126×C₅₃	—	2	1	no	—
260	#126×C₅₃	—	2	1	no	—
261	#126×C₅₃	—	2	1	no	—
262	#126×C₅₃	—	2	1	no	—
263	#126×C₅₃	—	2	1	no	—
264	#126×C₅₃	—	2	1	no	—
265	#126×C₅₃	—	2	1	no	—
266	#126×C₅₃	—	2	1	no	—
267	#126×C₅₃	—	2	1	no	—
268	#126×C₅₃	—	2	1	no	—
269	#126×C₅₃	D₄	1	1	yes	characteristic
270	#126×C₅₃	D₄	1	1	yes	characteristic
271	#125×C₅₃	—	2	1	no	—
272	#125×C₅₃	—	2	1	no	—
273	#125×C₅₃	—	2	1	no	—
274	#125×C₅₃	D₄	1	1	yes	characteristic
275	#125×C₅₃	C₂³	1	1	yes	characteristic
276	#125×C₅₃	C₂³	1	1	yes	characteristic
277	#124×C₅₃	—	2	1	no	—
278	#124×C₅₃	—	2	1	no	—
279	#124×C₅₃	—	2	1	no	—
280	#124×C₅₃	—	2	1	no	—
281	#124×C₅₃	—	2	1	no	—
282	#124×C₅₃	—	2	1	no	—
283	#124×C₅₃	—	2	1	no	—
284	#124×C₅₃	—	2	1	no	—
285	#124×C₅₃	—	2	1	no	—
286	#124×C₅₃	—	2	1	no	—
287	#124×C₅₃	—	2	1	no	—
288	#124×C₅₃	D₄	1	1	yes	characteristic
289	#124×C₅₃	C₂³	1	1	yes	characteristic
290	#124×C₅₃	C₂³	1	1	yes	characteristic
291	#124×C₅₃	C₂³	1	1	yes	characteristic
292	#124×C₅₃	C₂³	1	1	yes	characteristic
293	#124×C₅₃	C₂³	1	1	yes	characteristic
294	#124×C₅₃	C₂³	1	1	yes	characteristic
295	#124×C₅₃	C₂³	1	1	yes	characteristic
296	#124×C₅₃	C₂³	1	1	yes	characteristic
297	#123×C₅₃	—	2	1	no	—
298	#123×C₅₃	—	2	1	no	—
299	#123×C₅₃	—	2	1	no	—
300	#123×C₅₃	—	2	1	no	—
301	#123×C₅₃	—	2	1	no	—
302	#123×C₅₃	—	2	1	no	—
303	#123×C₅₃	—	2	1	no	—
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	D₄	1	1	yes	characteristic
314	#123×C₅₃	D₄	1	1	yes	characteristic
315	C₂²⋊Q₈×C₅₃	—	2	1	no	—
316	C₂²⋊Q₈×C₅₃	—	2	1	no	—
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	D₄	1	1	yes	characteristic
325	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
326	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
327	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
328	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
329	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
330	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
331	#121×C₅₃	—	2	1	no	—
332	#121×C₅₃	—	2	1	no	—
333	#121×C₅₃	—	2	1	no	—
334	#121×C₅₃	—	2	1	no	—
335	#121×C₅₃	—	2	1	no	—
336	#121×C₅₃	—	2	1	no	—
337	#121×C₅₃	—	2	1	no	—
338	#121×C₅₃	—	2	1	no	—
339	#121×C₅₃	—	2	1	no	—
340	#121×C₅₃	—	2	1	no	—
341	#121×C₅₃	—	2	1	no	—
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	D₄	1	1	yes	characteristic
347	#121×C₅₃	C₂³	1	1	yes	characteristic
348	#121×C₅₃	C₂³	1	1	yes	characteristic
349	#121×C₅₃	C₂³	1	1	yes	characteristic
350	#121×C₅₃	C₂³	1	1	yes	characteristic
351	#121×C₅₃	C₂³	1	1	yes	characteristic
352	#121×C₅₃	C₂³	1	1	yes	characteristic
353	#120×C₅₃	—	2	1	no	—
354	#120×C₅₃	—	2	1	no	—
355	#120×C₅₃	—	2	1	no	—
356	#120×C₅₃	—	2	1	no	—
357	#120×C₅₃	—	2	1	no	—
358	#120×C₅₃	—	2	1	no	—
359	#120×C₅₃	—	2	1	no	—
360	#120×C₅₃	—	2	1	no	—
361	#120×C₅₃	—	2	1	no	—
362	#120×C₅₃	—	2	1	no	—
363	#120×C₅₃	—	2	1	no	—
364	#120×C₅₃	—	2	1	no	—
365	C₄×Q₈×C₅₃	—	2	1	no	—
366	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
367	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
368	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
369	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
370	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
371	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
372	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
373	C₄×D₄×C₅₃	—	2	1	no	—
374	C₄×D₄×C₅₃	—	2	1	no	—
375	C₄×D₄×C₅₃	—	2	1	no	—
376	C₄×D₄×C₅₃	—	2	1	no	—
377	C₄×D₄×C₅₃	—	2	1	no	—
378	C₄×D₄×C₅₃	—	2	1	no	—
379	C₄×D₄×C₅₃	—	2	1	no	—
380	C₄×D₄×C₅₃	—	2	1	no	—
381	C₄×D₄×C₅₃	—	2	1	no	—
382	C₄×D₄×C₅₃	—	2	1	no	—
383	C₄×D₄×C₅₃	—	2	1	no	—
384	C₄×D₄×C₅₃	—	2	1	no	—
385	C₄×D₄×C₅₃	—	2	1	no	—
386	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
387	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
388	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
389	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
390	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
391	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
392	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
393	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
394	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
395	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
396	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
397	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
398	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
399	#117×C₅₃	—	2	1	no	—
400	#117×C₅₃	—	2	1	no	—
401	#117×C₅₃	—	2	1	no	—
402	#117×C₅₃	—	2	1	no	—
403	#117×C₅₃	—	2	1	no	—
404	#117×C₅₃	C₂³	1	1	yes	characteristic
405	#117×C₅₃	C₂³	1	1	yes	characteristic
406	#117×C₅₃	C₂³	1	1	yes	characteristic
407	#117×C₅₃	C₂³	1	1	yes	characteristic
408	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
409	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
410	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
411	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
412	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
413	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
414	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
415	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
416	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
417	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
418	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
419	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
420	C₂×C₄²×C₅₃	—	2	1	no	—
421	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
422	#107×C₅₃	C₂³	1	1	yes	characteristic
423	#107×C₅₃	C₂³	1	1	yes	characteristic
424	#107×C₅₃	C₂³	1	1	yes	characteristic
425	#107×C₅₃	C₂³	1	1	yes	characteristic
426	#106×C₅₃	C₂³	1	1	yes	characteristic
427	#106×C₅₃	C₂³	1	1	yes	characteristic
428	#106×C₅₃	C₂³	1	1	yes	characteristic
429	#106×C₅₃	C₂³	1	1	yes	characteristic
430	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
431	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
432	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
433	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
434	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
435	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
436	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
437	C₄⋊C₈×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	#103×C₅₃	C₂³	1	1	yes	characteristic
441	#103×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	#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
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	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
473	C₂²⋊C₈×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	#97×C₅₃	C₂³	1	1	yes	characteristic
479	#97×C₅₃	C₂³	1	1	yes	characteristic
480	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
481	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
482	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
483	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
484	C₂⁴×C₅₃	—	2	1	no	—
485	C₂⁴×C₅₃	—	2	1	no	—
486	C₂⁴×C₅₃	—	2	1	no	—
487	C₂⁴×C₅₃	—	2	1	no	—
488	#41×C₅₃	—	2	2	no	—
489	#41×C₅₃	—	2	2	no	—
490	#41×C₅₃	—	4	1	no	—
491	#41×C₅₃	—	4	1	no	—
492	#41×C₅₃	—	4	1	no	—
493	#41×C₅₃	—	4	1	no	—
494	#41×C₅₃	—	4	1	no	—
495	#41×C₅₃	—	4	1	no	—
496	#41×C₅₃	—	8	2	no	—
497	C₂×Q₈×C₅₃	—	2	1	no	—
498	C₂×Q₈×C₅₃	—	2	1	no	—
499	C₂×Q₈×C₅₃	—	2	1	no	—
500	C₂×Q₈×C₅₃	—	4	1	no	—
501	C₂×Q₈×C₅₃	—	4	1	no	—
502	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
503	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
504	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
505	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
506	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
507	C₂×D₄×C₅₃	—	2	2	no	—
508	C₂×D₄×C₅₃	—	2	1	no	—
509	C₂×D₄×C₅₃	—	2	1	no	—
510	C₂×D₄×C₅₃	—	2	1	no	—
511	C₂×D₄×C₅₃	—	2	1	no	—
512	C₂×D₄×C₅₃	—	2	1	no	—
513	C₂×D₄×C₅₃	—	2	1	no	—
514	C₂×D₄×C₅₃	—	2	1	no	—
515	C₂×D₄×C₅₃	—	2	1	no	—
516	C₂×D₄×C₅₃	—	2	1	no	—
517	C₂×D₄×C₅₃	—	2	1	no	—
518	C₂×D₄×C₅₃	—	2	1	no	—
519	C₂×D₄×C₅₃	—	2	1	no	—
520	C₂×D₄×C₅₃	—	2	1	no	—
521	C₂×D₄×C₅₃	—	2	1	no	—
522	C₂×D₄×C₅₃	—	2	1	no	—
523	C₂×D₄×C₅₃	—	2	1	no	—
524	C₂×D₄×C₅₃	—	2	1	no	—
525	C₂×D₄×C₅₃	—	2	1	no	—
526	C₂×D₄×C₅₃	—	2	1	no	—
527	C₂×D₄×C₅₃	—	2	1	no	—
528	C₂×D₄×C₅₃	—	4	1	no	—
529	C₂×D₄×C₅₃	—	4	1	no	—
530	C₂×D₄×C₅₃	—	4	1	no	—
531	C₂×D₄×C₅₃	—	4	1	no	—
532	C₂×D₄×C₅₃	—	4	1	no	—
533	C₂×D₄×C₅₃	—	4	1	no	—
534	C₂×D₄×C₅₃	—	4	1	no	—
535	C₂×D₄×C₅₃	—	8	2	no	—
536	C₂×D₄×C₅₃	—	8	2	no	—
537	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
538	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
539	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
540	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
541	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
542	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
543	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
544	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
545	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
546	C₂²×C₄×C₅₃	—	2	1	no	—
547	C₂²×C₄×C₅₃	—	2	1	no	—
548	C₂²×C₄×C₅₃	—	2	1	no	—
549	C₂²×C₄×C₅₃	—	2	1	no	—
550	C₂²×C₄×C₅₃	—	2	1	no	—
551	C₂²×C₄×C₅₃	—	2	1	no	—
552	C₂²×C₄×C₅₃	—	2	1	no	—
553	C₂²×C₄×C₅₃	—	2	1	no	—
554	C₂²×C₄×C₅₃	—	2	1	no	—
555	C₂²×C₄×C₅₃	—	2	1	no	—
556	C₂²×C₄×C₅₃	—	2	1	no	—
557	C₂²×C₄×C₅₃	—	2	1	no	—
558	C₂²×C₄×C₅₃	—	2	1	no	—
559	C₂²×C₄×C₅₃	—	2	1	no	—
560	C₂²×C₄×C₅₃	—	2	1	no	—
561	C₂²×C₄×C₅₃	—	2	1	no	—
562	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
563	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
564	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
565	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
566	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
567	Q₁₆×C₅₃	—	4	1	no	—
568	Q₁₆×C₅₃	—	4	1	no	—
569	Q₁₆×C₅₃	—	4	1	no	—
570	Q₁₆×C₅₃	—	4	1	no	—
571	SD₁₆×C₅₃	—	2	2	no	—
572	SD₁₆×C₅₃	—	2	2	no	—
573	SD₁₆×C₅₃	—	4	1	no	—
574	SD₁₆×C₅₃	—	4	1	no	—
575	SD₁₆×C₅₃	—	4	1	no	—
576	SD₁₆×C₅₃	—	4	1	no	—
577	SD₁₆×C₅₃	—	4	1	no	—
578	SD₁₆×C₅₃	—	4	1	no	—
579	SD₁₆×C₅₃	—	4	1	no	—
580	SD₁₆×C₅₃	—	4	1	no	—
581	SD₁₆×C₅₃	—	4	1	no	—
582	SD₁₆×C₅₃	—	4	1	no	—
583	D₈×C₅₃	—	2	2	no	—
584	D₈×C₅₃	—	2	2	no	—
585	D₈×C₅₃	—	2	2	no	—
586	D₈×C₅₃	—	2	2	no	—
587	D₈×C₅₃	—	4	1	no	—
588	D₈×C₅₃	—	4	1	no	—
589	D₈×C₅₃	—	4	1	no	—
590	D₈×C₅₃	—	4	1	no	—
591	M₁₆×C₅₃	—	4	1	no	—
592	M₁₆×C₅₃	—	4	1	no	—
593	M₁₆×C₅₃	—	4	1	no	—
594	M₁₆×C₅₃	—	4	1	no	—
595	C₂×C₈×C₅₃	—	4	1	no	—
596	C₂×C₈×C₅₃	—	4	1	no	—
597	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
598	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
599	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
600	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
601	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
602	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
603	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
604	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
605	C₄⋊C₄×C₅₃	—	2	1	no	—
606	C₄⋊C₄×C₅₃	—	2	1	no	—
607	C₄⋊C₄×C₅₃	—	2	1	no	—
608	C₄⋊C₄×C₅₃	—	2	1	no	—
609	C₄⋊C₄×C₅₃	—	2	1	no	—
610	C₄⋊C₄×C₅₃	—	2	1	no	—
611	C₄⋊C₄×C₅₃	—	2	1	no	—
612	C₄⋊C₄×C₅₃	—	2	1	no	—
613	C₄⋊C₄×C₅₃	—	2	1	no	—
614	C₄⋊C₄×C₅₃	—	2	1	no	—
615	C₄⋊C₄×C₅₃	—	2	1	no	—
616	C₄⋊C₄×C₅₃	—	2	1	no	—
617	C₄⋊C₄×C₅₃	—	2	1	no	—
618	C₄⋊C₄×C₅₃	—	2	1	no	—
619	C₄⋊C₄×C₅₃	—	2	1	no	—
620	C₄⋊C₄×C₅₃	—	2	1	no	—
621	C₄⋊C₄×C₅₃	—	2	1	no	—
622	C₄⋊C₄×C₅₃	—	2	1	no	—
623	C₄⋊C₄×C₅₃	—	2	1	no	—
624	C₄⋊C₄×C₅₃	—	2	1	no	—
625	C₄⋊C₄×C₅₃	—	2	1	no	—
626	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
627	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
628	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
629	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
630	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
631	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
632	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
633	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
634	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
635	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
636	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
637	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
638	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
639	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
640	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
641	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
642	C₂²⋊C₄×C₅₃	—	2	1	no	—
643	C₂²⋊C₄×C₅₃	—	2	1	no	—
644	C₂²⋊C₄×C₅₃	—	2	1	no	—
645	C₂²⋊C₄×C₅₃	—	2	1	no	—
646	C₂²⋊C₄×C₅₃	—	2	1	no	—
647	C₂²⋊C₄×C₅₃	—	2	1	no	—
648	C₂²⋊C₄×C₅₃	—	2	1	no	—
649	C₂²⋊C₄×C₅₃	—	2	1	no	—
650	C₂²⋊C₄×C₅₃	—	2	1	no	—
651	C₂²⋊C₄×C₅₃	—	2	1	no	—
652	C₂²⋊C₄×C₅₃	—	2	1	no	—
653	C₂²⋊C₄×C₅₃	—	2	1	no	—
654	C₂²⋊C₄×C₅₃	—	2	1	no	—
655	C₂²⋊C₄×C₅₃	—	2	1	no	—
656	C₂²⋊C₄×C₅₃	—	2	1	no	—
657	C₂²⋊C₄×C₅₃	—	2	1	no	—
658	C₂²⋊C₄×C₅₃	—	2	1	no	—
659	C₂²⋊C₄×C₅₃	—	2	1	no	—
660	C₂²⋊C₄×C₅₃	—	2	1	no	—
661	C₂²⋊C₄×C₅₃	—	2	1	no	—
662	C₂²⋊C₄×C₅₃	—	2	1	no	—
663	C₂²⋊C₄×C₅₃	—	2	1	no	—
664	C₂²⋊C₄×C₅₃	—	2	1	no	—
665	C₂²⋊C₄×C₅₃	—	2	1	no	—
666	C₂²⋊C₄×C₅₃	—	2	1	no	—
667	C₂²⋊C₄×C₅₃	—	2	1	no	—
668	C₂²⋊C₄×C₅₃	—	2	1	no	—
669	C₂²⋊C₄×C₅₃	—	2	1	no	—
670	C₂²⋊C₄×C₅₃	—	2	1	no	—
671	C₂²⋊C₄×C₅₃	—	2	1	no	—
672	C₂²⋊C₄×C₅₃	—	2	1	no	—
673	C₂²⋊C₄×C₅₃	—	2	1	no	—
674	C₂²⋊C₄×C₅₃	—	2	1	no	—
675	C₂²⋊C₄×C₅₃	—	2	1	no	—
676	C₂²⋊C₄×C₅₃	—	2	1	no	—
677	C₂²⋊C₄×C₅₃	—	2	1	no	—
678	C₂²⋊C₄×C₅₃	—	2	1	no	—
679	C₂²⋊C₄×C₅₃	—	2	1	no	—
680	C₂²⋊C₄×C₅₃	—	2	1	no	—
681	C₂²⋊C₄×C₅₃	—	2	1	no	—
682	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
683	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
684	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
685	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
686	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
687	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
688	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
689	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
690	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
691	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
692	C₄²×C₅₃	—	2	1	no	—
693	C₄²×C₅₃	—	2	1	no	—
694	C₄²×C₅₃	—	2	1	no	—
695	C₄²×C₅₃	—	2	1	no	—
696	C₄²×C₅₃	—	2	1	no	—
697	C₄²×C₅₃	—	2	1	no	—
698	C₄²×C₅₃	—	2	1	no	—
699	C₄²×C₅₃	—	2	1	no	—
700	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
701	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
702	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
703	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
704	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
705	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
706	C₂³×C₅₃	—	2	1	no	—
707	C₂³×C₅₃	—	2	1	no	—
708	C₂³×C₅₃	—	2	1	no	—
709	C₂³×C₅₃	—	2	1	no	—
710	C₂³×C₅₃	—	2	1	no	—
711	C₂³×C₅₃	—	2	1	no	—
712	C₂³×C₅₃	—	4	2	no	—
713	C₂³×C₅₃	—	4	2	no	—
714	C₂³×C₅₃	—	8	1	no	—
715	C₂³×C₅₃	—	8	1	no	—
716	C₂³×C₅₃	—	8	1	no	—
717	C₂³×C₅₃	—	8	1	no	—
718	C₂³×C₅₃	—	8	1	no	—
719	C₂³×C₅₃	—	8	1	no	—
720	C₂³×C₅₃	—	8	1	no	—
721	C₂³×C₅₃	—	8	1	no	—
722	C₂³×C₅₃	—	8	1	no	—
723	C₂³×C₅₃	—	8	1	no	—
724	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
725	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
726	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
727	Q₈×C₅₃	—	2	1	no	—
728	Q₈×C₅₃	—	2	1	no	—
729	Q₈×C₅₃	—	2	1	no	—
730	Q₈×C₅₃	—	2	1	no	—
731	Q₈×C₅₃	—	2	1	no	—
732	Q₈×C₅₃	—	2	1	no	—
733	Q₈×C₅₃	—	2	1	no	—
734	Q₈×C₅₃	—	2	1	no	—
735	Q₈×C₅₃	—	4	1	no	—
736	Q₈×C₅₃	—	8	1	no	—
737	Q₈×C₅₃	—	8	1	no	—
738	Q₈×C₅₃	—	8	1	no	—
739	D₄×C₅₃	—	2	1	no	—
740	D₄×C₅₃	—	2	1	no	—
741	D₄×C₅₃	—	2	1	no	—
742	D₄×C₅₃	—	2	1	no	—
743	D₄×C₅₃	—	2	1	no	—
744	D₄×C₅₃	—	2	1	no	—
745	D₄×C₅₃	—	2	1	no	—
746	D₄×C₅₃	—	2	1	no	—
747	D₄×C₅₃	—	2	1	no	—
748	D₄×C₅₃	—	2	1	no	—
749	D₄×C₅₃	—	2	1	no	—
750	D₄×C₅₃	—	4	1	no	—
751	D₄×C₅₃	—	4	1	no	—
752	D₄×C₅₃	—	4	1	no	—
753	D₄×C₅₃	—	4	2	no	—
754	D₄×C₅₃	—	4	2	no	—
755	D₄×C₅₃	—	4	2	no	—
756	D₄×C₅₃	—	4	2	no	—
757	D₄×C₅₃	—	4	2	no	—
758	D₄×C₅₃	—	8	1	no	—
759	D₄×C₅₃	—	8	1	no	—
760	D₄×C₅₃	—	8	1	no	—
761	D₄×C₅₃	—	8	1	no	—
762	D₄×C₅₃	—	8	1	no	—
763	D₄×C₅₃	—	8	1	no	—
764	D₄×C₅₃	—	8	1	no	—
765	D₄×C₅₃	—	8	1	no	—
766	D₄×C₅₃	—	8	1	no	—
767	D₄×C₅₃	—	8	1	no	—
768	D₄×C₅₃	—	8	1	no	—
769	D₄×C₅₃	—	8	1	no	—
770	D₄×C₅₃	—	8	1	no	—
771	D₄×C₅₃	—	8	1	no	—
772	D₄×C₅₃	—	8	1	no	—
773	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
774	C₂×C₄×C₅₃	—	2	1	no	—
775	C₂×C₄×C₅₃	—	2	1	no	—
776	C₂×C₄×C₅₃	—	2	1	no	—
777	C₂×C₄×C₅₃	—	2	1	no	—
778	C₂×C₄×C₅₃	—	2	1	no	—
779	C₂×C₄×C₅₃	—	2	1	no	—
780	C₂×C₄×C₅₃	—	2	1	no	—
781	C₂×C₄×C₅₃	—	2	1	no	—
782	C₂×C₄×C₅₃	—	2	1	no	—
783	C₂×C₄×C₅₃	—	2	1	no	—
784	C₂×C₄×C₅₃	—	2	1	no	—
785	C₂×C₄×C₅₃	—	2	1	no	—
786	C₂×C₄×C₅₃	—	2	1	no	—
787	C₂×C₄×C₅₃	—	2	1	no	—
788	C₂×C₄×C₅₃	—	2	1	no	—
789	C₂×C₄×C₅₃	—	2	1	no	—
790	C₂×C₄×C₅₃	—	4	1	no	—
791	C₂×C₄×C₅₃	—	4	1	no	—
792	C₂×C₄×C₅₃	—	4	2	no	—
793	C₂×C₄×C₅₃	—	4	2	no	—
794	C₂×C₄×C₅₃	—	8	1	no	—
795	C₂×C₄×C₅₃	—	8	1	no	—
796	C₂×C₄×C₅₃	—	8	1	no	—
797	C₂×C₄×C₅₃	—	8	1	no	—
798	C₂×C₄×C₅₃	—	8	1	no	—
799	C₂×C₄×C₅₃	—	8	1	no	—
800	C₂×C₄×C₅₃	—	8	1	no	—
801	C₂×C₄×C₅₃	—	8	1	no	—
802	C₂×C₄×C₅₃	—	8	1	no	—
803	C₂×C₄×C₅₃	—	8	1	no	—
804	C₂×C₄×C₅₃	—	8	1	no	—
805	C₂×C₄×C₅₃	—	8	1	no	—
806	C₂×C₄×C₅₃	—	8	1	no	—
807	C₂×C₄×C₅₃	—	8	1	no	—
808	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
809	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
810	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
811	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
812	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
813	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
814	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
815	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
816	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
817	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
818	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
819	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
820	C₈×C₅₃	—	2	1	no	—
821	C₈×C₅₃	—	2	1	no	—
822	C₈×C₅₃	—	2	1	no	—
823	C₈×C₅₃	—	2	1	no	—
824	C₈×C₅₃	—	2	1	no	—
825	C₈×C₅₃	—	2	1	no	—
826	C₈×C₅₃	—	2	1	no	—
827	C₈×C₅₃	—	2	1	no	—
828	#62047	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
829	C₂²×C₅₃	—	2	1	no	—
830	C₂²×C₅₃	—	2	1	no	—
831	C₂²×C₅₃	—	2	1	no	—
832	C₂²×C₅₃	—	2	1	no	—
833	C₂²×C₅₃	—	2	1	no	—
834	C₂²×C₅₃	—	2	1	no	—
835	C₂²×C₅₃	—	2	1	no	—
836	C₂²×C₅₃	—	2	1	no	—
837	C₂²×C₅₃	—	2	1	no	—
838	C₂²×C₅₃	—	2	2	no	—
839	C₂²×C₅₃	—	4	1	no	—
840	C₂²×C₅₃	—	4	1	no	—
841	C₂²×C₅₃	—	4	1	no	—
842	C₂²×C₅₃	—	4	1	no	—
843	C₂²×C₅₃	—	4	1	no	—
844	C₂²×C₅₃	—	4	1	no	—
845	C₂²×C₅₃	—	4	1	no	—
846	C₂²×C₅₃	—	4	1	no	—
847	C₂²×C₅₃	—	4	1	no	—
848	C₂²×C₅₃	—	4	1	no	—
849	C₂²×C₅₃	—	4	1	no	—
850	C₂²×C₅₃	—	4	1	no	—
851	C₂²×C₅₃	—	4	1	no	—
852	C₂²×C₅₃	—	4	1	no	—
853	C₂²×C₅₃	—	4	1	no	—
854	C₂²×C₅₃	—	4	1	no	—
855	C₂²×C₅₃	—	4	1	no	—
856	C₂²×C₅₃	—	16	2	no	—
857	C₂²×C₅₃	—	16	2	no	—
858	C₂²×C₅₃	—	16	2	no	—
859	C₂²×C₅₃	—	16	2	no	—
860	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
861	C₄×C₅₃	—	2	1	no	—
862	C₄×C₅₃	—	2	1	no	—
863	C₄×C₅₃	—	2	1	no	—
864	C₄×C₅₃	—	2	1	no	—
865	C₄×C₅₃	—	2	1	no	—
866	C₄×C₅₃	—	2	1	no	—
867	C₄×C₅₃	—	2	1	no	—
868	C₄×C₅₃	—	2	1	no	—
869	C₄×C₅₃	—	2	1	no	—
870	C₄×C₅₃	—	2	1	no	—
871	C₄×C₅₃	—	2	1	no	—
872	C₄×C₅₃	—	4	1	no	—
873	C₄×C₅₃	—	4	1	no	—
874	C₄×C₅₃	—	4	1	no	—
875	C₄×C₅₃	—	4	1	no	—
876	C₄×C₅₃	—	4	1	no	—
877	C₄×C₅₃	—	4	1	no	—
878	C₄×C₅₃	—	4	1	no	—
879	C₄×C₅₃	—	4	1	no	—
880	C₄×C₅₃	—	4	1	no	—
881	C₄×C₅₃	—	4	1	no	—
882	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
883	C₄×C₅₃	#585	1	1	yes	characteristic
884	#3558	C₂×C₅₃	1	1	yes	characteristic, complemented
885	#3521	C₂×C₅₃	1	1	yes	characteristic, complemented
886	#3401	C₂×C₅₃	1	1	yes	characteristic, complemented
887	#3394	C₂×C₅₃	1	1	yes	characteristic, complemented
888	#3370	C₂×C₅₃	1	1	yes	characteristic, complemented
889	#3361	C₂×C₅₃	1	1	yes	characteristic, complemented
890	#3326	C₂×C₅₃	1	1	yes	characteristic, complemented
891	#3324	C₂×C₅₃	1	1	yes	characteristic, complemented
892	#3323	C₂×C₅₃	1	1	yes	characteristic, complemented
893	#3318	C₂×C₅₃	1	1	yes	characteristic, complemented
894	#3313	C₂×C₅₃	1	1	yes	characteristic, complemented
895	#3296	C₂×C₅₃	1	1	yes	characteristic, complemented
896	#3280	C₂×C₅₃	1	1	yes	characteristic, complemented
897	#3275	C₂×C₅₃	1	1	yes	characteristic, complemented
898	#3273	C₂×C₅₃	1	1	yes	characteristic, complemented
899	#3272	C₂×C₅₃	1	1	yes	characteristic, complemented
900	#3269	C₂×C₅₃	1	1	yes	characteristic, complemented
901	#3264	C₂×C₅₃	1	1	yes	characteristic, complemented
902	#3262	C₂×C₅₃	1	1	yes	characteristic, complemented
903	#3258	C₂×C₅₃	1	1	yes	characteristic, complemented
904	#3251	C₂×C₅₃	1	1	yes	characteristic, complemented
905	#3224	C₂×C₅₃	1	1	yes	characteristic, complemented
906	#3222	C₂×C₅₃	1	1	yes	characteristic, complemented
907	#3211	C₂×C₅₃	1	1	yes	characteristic, complemented
908	#3125	C₂×C₅₃	1	1	yes	characteristic, complemented
909	#3118	C₂×C₅₃	1	1	yes	characteristic, complemented
910	#3106	C₂×C₅₃	1	1	yes	characteristic, complemented
911	#3045	C₂×C₅₃	1	1	yes	characteristic, complemented
912	#3041	C₂×C₅₃	1	1	yes	characteristic, complemented
913	#3040	C₂×C₅₃	1	1	yes	characteristic, complemented
914	#2993	C₂×C₅₃	1	1	yes	characteristic, complemented
915	C₂×C₅₃	—	4	1	no	—
916	C₂×C₅₃	—	4	1	no	—
917	C₂×C₅₃	—	4	1	no	—
918	C₂×C₅₃	—	4	2	no	—
919	C₂×C₅₃	—	8	1	no	—
920	C₂×C₅₃	—	8	1	no	—
921	C₂×C₅₃	—	8	1	no	—
922	C₂×C₅₃	—	8	1	no	—
923	C₂×C₅₃	—	8	1	no	—
924	C₂×C₅₃	#3488	1	1	yes	characteristic
925	C₂×C₅₃	#3584	1	1	yes	characteristic
926	C₂×C₅₃	#3585	1	1	yes	characteristic
927	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
928	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
929	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
930	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
931	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic, complemented
932	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
933	#562	—	2	1	no	—
934	H(3,𝔽₄)	—	2	1	no	—
935	#559	C₂²×C₅₃	1	1	yes	characteristic, complemented
936	#559	C₂²×C₅₃	1	1	yes	characteristic, complemented
937	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
938	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
939	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
940	#553	—	2	1	no	—
941	#553	C₂²×C₅₃	1	1	yes	characteristic, complemented
942	#552	—	2	1	no	—
943	#552	C₂²×C₅₃	1	1	yes	characteristic, complemented
944	#551	—	2	1	no	—
945	#551	—	2	1	no	—
946	#548	C₂²×C₅₃	1	1	yes	characteristic
947	#548	C₂²×C₅₃	1	1	yes	characteristic, complemented
948	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
949	#546	—	2	1	no	—
950	#546	—	2	1	no	—
951	#546	C₂²×C₅₃	1	1	yes	characteristic
952	#546	C₂²×C₅₃	1	1	yes	characteristic
953	#546	C₂²×C₅₃	1	1	yes	characteristic, complemented
954	#546	C₂²×C₅₃	1	1	yes	characteristic, complemented
955	D₄²	C₂²×C₅₃	1	1	yes	characteristic
956	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
957	#542	C₂²×C₅₃	1	1	yes	characteristic
958	#542	C₂²×C₅₃	1	1	yes	characteristic, complemented
959	#542	C₂²×C₅₃	1	1	yes	characteristic, complemented
960	#541	C₂²×C₅₃	1	1	yes	characteristic, complemented
961	#539	—	2	1	no	—
962	#538	—	2	1	no	—
963	#538	—	2	1	no	—
964	#538	—	2	1	no	—
965	#538	—	2	1	no	—
966	#535	C₂²×C₅₃	1	1	yes	characteristic
967	#535	C₂²×C₅₃	1	1	yes	characteristic, complemented
968	#534	—	2	1	no	—
969	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
970	#529	—	2	1	no	—
971	#529	C₂²×C₅₃	1	1	yes	characteristic
972	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
973	C₂×#126	—	2	1	no	—
974	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic, complemented
975	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
976	#518	C₂²×C₅₃	1	1	yes	characteristic, complemented
977	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
978	#497	C₂²×C₅₃	1	1	yes	characteristic, complemented
979	#496	C₂²×C₅₃	1	1	yes	characteristic
980	#495	C₂²×C₅₃	1	1	yes	characteristic, complemented
981	#495	C₂²×C₅₃	1	1	yes	characteristic, complemented
982	#495	C₂²×C₅₃	1	1	yes	characteristic, complemented
983	#492	C₂²×C₅₃	1	1	yes	characteristic, complemented
984	#490	C₂²×C₅₃	1	1	yes	characteristic, complemented
985	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
986	#488	C₂²×C₅₃	1	1	yes	characteristic, complemented
987	#488	C₂²×C₅₃	1	1	yes	characteristic, complemented
988	#488	C₂²×C₅₃	1	1	yes	characteristic, complemented
989	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
990	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
991	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
992	#482	C₂²×C₅₃	1	1	yes	characteristic
993	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
994	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
995	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
996	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
997	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
998	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
999	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
1000	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
1001	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
1002	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
1003	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
1004	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
1005	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
1006	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
1007	#469	C₂²×C₅₃	1	1	yes	characteristic, complemented
1008	#469	C₂²×C₅₃	1	1	yes	characteristic, complemented
1009	#468	C₂²×C₅₃	1	1	yes	characteristic
1010	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1011	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1012	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1013	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1014	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
1015	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
1016	#466	C₂²×C₅₃	1	1	yes	characteristic
1017	#465	C₂²×C₅₃	1	1	yes	characteristic
1018	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1019	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1020	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1021	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1022	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1023	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1024	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1025	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1026	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1027	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1028	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1029	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1030	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1031	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1032	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1033	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1034	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1035	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1036	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1037	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1038	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
1039	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1040	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1041	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1042	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1043	#459	C₂²×C₅₃	1	1	yes	characteristic
1044	#459	C₂²×C₅₃	1	1	yes	characteristic
1045	#459	C₂²×C₅₃	1	1	yes	characteristic
1046	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1047	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1048	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1049	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1050	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1051	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1052	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1053	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1054	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1055	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1056	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1057	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1058	#449	C₂²×C₅₃	1	1	yes	characteristic
1059	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1060	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1061	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1062	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1063	#447	C₂²×C₅₃	1	1	yes	characteristic
1064	#447	C₂²×C₅₃	1	1	yes	characteristic
1065	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1066	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
1067	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1068	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1069	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1070	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1071	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1072	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1073	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1074	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1075	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1076	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1077	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1078	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1079	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1080	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
1081	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
1082	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
1083	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1084	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1085	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1086	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1087	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1088	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
1089	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
1090	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
1091	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
1092	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
1093	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
1094	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
1095	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
1096	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1097	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
1098	C₅₃	#62047	1	1	yes	characteristic, direct product factor, Sylow
1099	C₂×#41	—	2	1	no	—
1100	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1101	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1102	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1103	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1104	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1105	C₂²×D₄	—	2	1	no	—
1106	C₂²×D₄	—	2	1	no	—
1107	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1108	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1109	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1110	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1111	#137	—	4	2	no	—
1112	AGL(1,ℤ/8)	—	4	2	no	—
1113	AGL(1,ℤ/8)	—	4	2	no	—
1114	AGL(1,ℤ/8)	—	4	2	no	—
1115	#135	—	4	2	no	—
1116	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1117	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1118	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1119	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1120	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1121	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1122	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1123	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1124	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1125	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1126	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1127	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1128	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1129	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1130	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1131	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1132	C₂×D₈	—	4	2	no	—
1133	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1134	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1135	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1136	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1137	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1138	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1139	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1140	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1141	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1142	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1143	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1144	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1145	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1146	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1147	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1148	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1149	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1150	#127	C₂³×C₅₃	1	1	yes	characteristic
1151	#127	C₂³×C₅₃	1	1	yes	characteristic
1152	#127	C₂³×C₅₃	1	1	yes	characteristic
1153	#126	—	2	1	no	—
1154	#126	—	2	1	no	—
1155	#126	—	2	1	no	—
1156	#126	—	2	1	no	—
1157	#126	—	2	1	no	—
1158	#126	—	2	1	no	—
1159	#126	—	2	1	no	—
1160	#126	—	2	1	no	—
1161	#126	—	2	1	no	—
1162	#126	—	2	1	no	—
1163	#126	—	2	1	no	—
1164	#126	—	2	1	no	—
1165	#126	D₄×C₅₃	1	1	yes	characteristic
1166	#126	D₄×C₅₃	1	1	yes	characteristic
1167	#125	—	2	1	no	—
1168	#125	—	2	1	no	—
1169	#125	—	2	1	no	—
1170	#125	D₄×C₅₃	1	1	yes	characteristic
1171	#125	C₂³×C₅₃	1	1	yes	characteristic
1172	#125	C₂³×C₅₃	1	1	yes	characteristic
1173	#124	—	2	1	no	—
1174	#124	—	2	1	no	—
1175	#124	—	2	1	no	—
1176	#124	—	2	1	no	—
1177	#124	—	2	1	no	—
1178	#124	—	2	1	no	—
1179	#124	—	2	1	no	—
1180	#124	—	2	1	no	—
1181	#124	—	2	1	no	—
1182	#124	—	2	1	no	—
1183	#124	—	2	1	no	—
1184	#124	D₄×C₅₃	1	1	yes	characteristic
1185	#124	C₂³×C₅₃	1	1	yes	characteristic
1186	#124	C₂³×C₅₃	1	1	yes	characteristic
1187	#124	C₂³×C₅₃	1	1	yes	characteristic
1188	#124	C₂³×C₅₃	1	1	yes	characteristic
1189	#124	C₂³×C₅₃	1	1	yes	characteristic
1190	#124	C₂³×C₅₃	1	1	yes	characteristic
1191	#124	C₂³×C₅₃	1	1	yes	characteristic
1192	#124	C₂³×C₅₃	1	1	yes	characteristic
1193	#123	—	2	1	no	—
1194	#123	—	2	1	no	—
1195	#123	—	2	1	no	—
1196	#123	—	2	1	no	—
1197	#123	—	2	1	no	—
1198	#123	—	2	1	no	—
1199	#123	—	2	1	no	—
1200	#123	—	2	1	no	—
1201	#123	—	2	1	no	—
1202	#123	—	2	1	no	—
1203	#123	—	2	1	no	—
1204	#123	—	2	1	no	—
1205	#123	—	2	1	no	—
1206	#123	—	2	1	no	—
1207	#123	—	2	1	no	—
1208	#123	—	2	1	no	—
1209	#123	D₄×C₅₃	1	1	yes	characteristic
1210	#123	D₄×C₅₃	1	1	yes	characteristic
1211	C₂²⋊Q₈	—	2	1	no	—
1212	C₂²⋊Q₈	—	2	1	no	—
1213	C₂²⋊Q₈	—	2	1	no	—
1214	C₂²⋊Q₈	—	2	1	no	—
1215	C₂²⋊Q₈	—	2	1	no	—
1216	C₂²⋊Q₈	—	2	1	no	—
1217	C₂²⋊Q₈	—	2	1	no	—
1218	C₂²⋊Q₈	—	2	1	no	—
1219	C₂²⋊Q₈	—	2	1	no	—
1220	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
1221	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1222	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1223	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1224	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1225	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1226	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1227	#121	—	2	1	no	—
1228	#121	—	2	1	no	—
1229	#121	—	2	1	no	—
1230	#121	—	2	1	no	—
1231	#121	—	2	1	no	—
1232	#121	—	2	1	no	—
1233	#121	—	2	1	no	—
1234	#121	—	2	1	no	—
1235	#121	—	2	1	no	—
1236	#121	—	2	1	no	—
1237	#121	—	2	1	no	—
1238	#121	—	2	1	no	—
1239	#121	—	2	1	no	—
1240	#121	—	2	1	no	—
1241	#121	—	2	1	no	—
1242	#121	D₄×C₅₃	1	1	yes	characteristic
1243	#121	C₂³×C₅₃	1	1	yes	characteristic
1244	#121	C₂³×C₅₃	1	1	yes	characteristic
1245	#121	C₂³×C₅₃	1	1	yes	characteristic
1246	#121	C₂³×C₅₃	1	1	yes	characteristic
1247	#121	C₂³×C₅₃	1	1	yes	characteristic
1248	#121	C₂³×C₅₃	1	1	yes	characteristic
1249	#120	—	2	1	no	—
1250	#120	—	2	1	no	—
1251	#120	—	2	1	no	—
1252	#120	—	2	1	no	—
1253	#120	—	2	1	no	—
1254	#120	—	2	1	no	—
1255	#120	—	2	1	no	—
1256	#120	—	2	1	no	—
1257	#120	—	2	1	no	—
1258	#120	—	2	1	no	—
1259	#120	—	2	1	no	—
1260	#120	—	2	1	no	—
1261	C₄×Q₈	—	2	1	no	—
1262	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1263	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1264	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1265	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1266	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1267	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1268	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1269	C₄×D₄	—	2	1	no	—
1270	C₄×D₄	—	2	1	no	—
1271	C₄×D₄	—	2	1	no	—
1272	C₄×D₄	—	2	1	no	—
1273	C₄×D₄	—	2	1	no	—
1274	C₄×D₄	—	2	1	no	—
1275	C₄×D₄	—	2	1	no	—
1276	C₄×D₄	—	2	1	no	—
1277	C₄×D₄	—	2	1	no	—
1278	C₄×D₄	—	2	1	no	—
1279	C₄×D₄	—	2	1	no	—
1280	C₄×D₄	—	2	1	no	—
1281	C₄×D₄	—	2	1	no	—
1282	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1283	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1284	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1285	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1286	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1287	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1288	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1289	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1290	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1291	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1292	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1293	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1294	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1295	#117	—	2	1	no	—
1296	#117	—	2	1	no	—
1297	#117	—	2	1	no	—
1298	#117	—	2	1	no	—
1299	#117	—	2	1	no	—
1300	#117	C₂³×C₅₃	1	1	yes	characteristic
1301	#117	C₂³×C₅₃	1	1	yes	characteristic
1302	#117	C₂³×C₅₃	1	1	yes	characteristic
1303	#117	C₂³×C₅₃	1	1	yes	characteristic
1304	C₂×C₄⋊C₄	—	2	1	no	—
1305	C₂×C₄⋊C₄	—	2	1	no	—
1306	C₂×C₄⋊C₄	—	2	1	no	—
1307	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1308	C₂×C₂²⋊C₄	—	2	1	no	—
1309	C₂×C₂²⋊C₄	—	2	1	no	—
1310	C₂×C₂²⋊C₄	—	2	1	no	—
1311	C₂×C₂²⋊C₄	—	2	1	no	—
1312	C₂×C₂²⋊C₄	—	2	1	no	—
1313	C₂×C₂²⋊C₄	—	2	1	no	—
1314	C₂×C₂²⋊C₄	—	2	1	no	—
1315	C₂×C₂²⋊C₄	—	2	1	no	—
1316	C₂×C₄²	—	2	1	no	—
1317	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1318	#107	C₂³×C₅₃	1	1	yes	characteristic
1319	#107	C₂³×C₅₃	1	1	yes	characteristic
1320	#107	C₂³×C₅₃	1	1	yes	characteristic
1321	#107	C₂³×C₅₃	1	1	yes	characteristic
1322	#106	C₂³×C₅₃	1	1	yes	characteristic
1323	#106	C₂³×C₅₃	1	1	yes	characteristic
1324	#106	C₂³×C₅₃	1	1	yes	characteristic
1325	#106	C₂³×C₅₃	1	1	yes	characteristic
1326	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1327	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1328	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1329	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1330	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1331	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1332	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1333	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1334	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1335	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1336	#103	C₂³×C₅₃	1	1	yes	characteristic
1337	#103	C₂³×C₅₃	1	1	yes	characteristic
1338	#103	C₂³×C₅₃	1	1	yes	characteristic
1339	#103	C₂³×C₅₃	1	1	yes	characteristic
1340	#103	C₂³×C₅₃	1	1	yes	characteristic
1341	#103	C₂³×C₅₃	1	1	yes	characteristic
1342	#103	C₂³×C₅₃	1	1	yes	characteristic
1343	#103	C₂³×C₅₃	1	1	yes	characteristic
1344	#103	C₂³×C₅₃	1	1	yes	characteristic
1345	#103	C₂³×C₅₃	1	1	yes	characteristic
1346	#103	C₂³×C₅₃	1	1	yes	characteristic
1347	#103	C₂³×C₅₃	1	1	yes	characteristic
1348	#102	C₂³×C₅₃	1	1	yes	characteristic
1349	#102	C₂³×C₅₃	1	1	yes	characteristic
1350	#102	C₂³×C₅₃	1	1	yes	characteristic
1351	#102	C₂³×C₅₃	1	1	yes	characteristic
1352	#102	C₂³×C₅₃	1	1	yes	characteristic
1353	#102	C₂³×C₅₃	1	1	yes	characteristic
1354	#102	C₂³×C₅₃	1	1	yes	characteristic
1355	#102	C₂³×C₅₃	1	1	yes	characteristic
1356	#102	C₂³×C₅₃	1	1	yes	characteristic
1357	#102	C₂³×C₅₃	1	1	yes	characteristic
1358	#102	C₂³×C₅₃	1	1	yes	characteristic
1359	#102	C₂³×C₅₃	1	1	yes	characteristic
1360	#102	C₂³×C₅₃	1	1	yes	characteristic
1361	#102	C₂³×C₅₃	1	1	yes	characteristic
1362	#102	C₂³×C₅₃	1	1	yes	characteristic
1363	#102	C₂³×C₅₃	1	1	yes	characteristic
1364	#102	C₂³×C₅₃	1	1	yes	characteristic
1365	#102	C₂³×C₅₃	1	1	yes	characteristic
1366	#102	C₂³×C₅₃	1	1	yes	characteristic
1367	#102	C₂³×C₅₃	1	1	yes	characteristic
1368	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1369	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1370	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1371	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1372	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1373	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1374	#97	C₂³×C₅₃	1	1	yes	characteristic
1375	#97	C₂³×C₅₃	1	1	yes	characteristic
1376	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1377	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1378	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1379	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1380	C₂⁴	—	2	1	no	—
1381	C₂⁴	—	2	1	no	—
1382	C₂⁴	—	2	1	no	—
1383	C₂⁴	—	2	1	no	—
1384	#41	—	2	2	no	—
1385	#41	—	2	2	no	—
1386	#41	—	4	1	no	—
1387	#41	—	4	1	no	—
1388	#41	—	4	1	no	—
1389	#41	—	4	1	no	—
1390	#41	—	4	1	no	—
1391	#41	—	4	1	no	—
1392	#41	—	8	2	no	—
1393	C₂×Q₈	—	2	1	no	—
1394	C₂×Q₈	—	2	1	no	—
1395	C₂×Q₈	—	2	1	no	—
1396	C₂×Q₈	—	4	1	no	—
1397	C₂×Q₈	—	4	1	no	—
1398	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1399	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1400	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1401	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1402	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1403	C₂×D₄	—	2	2	no	—
1404	C₂×D₄	—	2	1	no	—
1405	C₂×D₄	—	2	1	no	—
1406	C₂×D₄	—	2	1	no	—
1407	C₂×D₄	—	2	1	no	—
1408	C₂×D₄	—	2	1	no	—
1409	C₂×D₄	—	2	1	no	—
1410	C₂×D₄	—	2	1	no	—
1411	C₂×D₄	—	2	1	no	—
1412	C₂×D₄	—	2	1	no	—
1413	C₂×D₄	—	2	1	no	—
1414	C₂×D₄	—	2	1	no	—
1415	C₂×D₄	—	2	1	no	—
1416	C₂×D₄	—	2	1	no	—
1417	C₂×D₄	—	2	1	no	—
1418	C₂×D₄	—	2	1	no	—
1419	C₂×D₄	—	2	1	no	—
1420	C₂×D₄	—	2	1	no	—
1421	C₂×D₄	—	2	1	no	—
1422	C₂×D₄	—	2	1	no	—
1423	C₂×D₄	—	2	1	no	—
1424	C₂×D₄	—	4	1	no	—
1425	C₂×D₄	—	4	1	no	—
1426	C₂×D₄	—	4	1	no	—
1427	C₂×D₄	—	4	1	no	—
1428	C₂×D₄	—	4	1	no	—
1429	C₂×D₄	—	4	1	no	—
1430	C₂×D₄	—	4	1	no	—
1431	C₂×D₄	—	8	2	no	—
1432	C₂×D₄	—	8	2	no	—
1433	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1434	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1435	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1436	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1437	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1438	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1439	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1440	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1441	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1442	C₂²×C₄	—	2	1	no	—
1443	C₂²×C₄	—	2	1	no	—
1444	C₂²×C₄	—	2	1	no	—
1445	C₂²×C₄	—	2	1	no	—
1446	C₂²×C₄	—	2	1	no	—
1447	C₂²×C₄	—	2	1	no	—
1448	C₂²×C₄	—	2	1	no	—
1449	C₂²×C₄	—	2	1	no	—
1450	C₂²×C₄	—	2	1	no	—
1451	C₂²×C₄	—	2	1	no	—
1452	C₂²×C₄	—	2	1	no	—
1453	C₂²×C₄	—	2	1	no	—
1454	C₂²×C₄	—	2	1	no	—
1455	C₂²×C₄	—	2	1	no	—
1456	C₂²×C₄	—	2	1	no	—
1457	C₂²×C₄	—	2	1	no	—
1458	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1459	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1460	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1461	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1462	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1463	Q₁₆	—	4	1	no	—
1464	Q₁₆	—	4	1	no	—
1465	Q₁₆	—	4	1	no	—
1466	Q₁₆	—	4	1	no	—
1467	SD₁₆	—	2	2	no	—
1468	SD₁₆	—	2	2	no	—
1469	SD₁₆	—	4	1	no	—
1470	SD₁₆	—	4	1	no	—
1471	SD₁₆	—	4	1	no	—
1472	SD₁₆	—	4	1	no	—
1473	SD₁₆	—	4	1	no	—
1474	SD₁₆	—	4	1	no	—
1475	SD₁₆	—	4	1	no	—
1476	SD₁₆	—	4	1	no	—
1477	SD₁₆	—	4	1	no	—
1478	SD₁₆	—	4	1	no	—
1479	D₈	—	2	2	no	—
1480	D₈	—	2	2	no	—
1481	D₈	—	2	2	no	—
1482	D₈	—	2	2	no	—
1483	D₈	—	4	1	no	—
1484	D₈	—	4	1	no	—
1485	D₈	—	4	1	no	—
1486	D₈	—	4	1	no	—
1487	M₁₆	—	4	1	no	—
1488	M₁₆	—	4	1	no	—
1489	M₁₆	—	4	1	no	—
1490	M₁₆	—	4	1	no	—
1491	C₂×C₈	—	4	1	no	—
1492	C₂×C₈	—	4	1	no	—
1493	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1494	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1495	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1496	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1497	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1498	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1499	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1500	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1501	C₄⋊C₄	—	2	1	no	—
1502	C₄⋊C₄	—	2	1	no	—
1503	C₄⋊C₄	—	2	1	no	—
1504	C₄⋊C₄	—	2	1	no	—
1505	C₄⋊C₄	—	2	1	no	—
1506	C₄⋊C₄	—	2	1	no	—
1507	C₄⋊C₄	—	2	1	no	—
1508	C₄⋊C₄	—	2	1	no	—
1509	C₄⋊C₄	—	2	1	no	—
1510	C₄⋊C₄	—	2	1	no	—
1511	C₄⋊C₄	—	2	1	no	—
1512	C₄⋊C₄	—	2	1	no	—
1513	C₄⋊C₄	—	2	1	no	—
1514	C₄⋊C₄	—	2	1	no	—
1515	C₄⋊C₄	—	2	1	no	—
1516	C₄⋊C₄	—	2	1	no	—
1517	C₄⋊C₄	—	2	1	no	—
1518	C₄⋊C₄	—	2	1	no	—
1519	C₄⋊C₄	—	2	1	no	—
1520	C₄⋊C₄	—	2	1	no	—
1521	C₄⋊C₄	—	2	1	no	—
1522	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1523	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1524	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1525	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1526	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1527	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1528	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1529	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1530	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1531	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1532	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1533	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1534	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1535	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1536	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1537	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
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	—	2	1	no	—
1553	C₂²⋊C₄	—	2	1	no	—
1554	C₂²⋊C₄	—	2	1	no	—
1555	C₂²⋊C₄	—	2	1	no	—
1556	C₂²⋊C₄	—	2	1	no	—
1557	C₂²⋊C₄	—	2	1	no	—
1558	C₂²⋊C₄	—	2	1	no	—
1559	C₂²⋊C₄	—	2	1	no	—
1560	C₂²⋊C₄	—	2	1	no	—
1561	C₂²⋊C₄	—	2	1	no	—
1562	C₂²⋊C₄	—	2	1	no	—
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	—	2	1	no	—
1578	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
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	C₂×D₄×C₅₃	1	1	yes	characteristic
1583	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1584	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1585	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1586	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1587	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1588	C₄²	—	2	1	no	—
1589	C₄²	—	2	1	no	—
1590	C₄²	—	2	1	no	—
1591	C₄²	—	2	1	no	—
1592	C₄²	—	2	1	no	—
1593	C₄²	—	2	1	no	—
1594	C₄²	—	2	1	no	—
1595	C₄²	—	2	1	no	—
1596	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1597	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1598	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1599	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1600	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1601	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1602	C₂³	—	2	1	no	—
1603	C₂³	—	2	1	no	—
1604	C₂³	—	2	1	no	—
1605	C₂³	—	2	1	no	—
1606	C₂³	—	2	1	no	—
1607	C₂³	—	2	1	no	—
1608	C₂³	—	4	2	no	—
1609	C₂³	—	4	2	no	—
1610	C₂³	—	8	1	no	—
1611	C₂³	—	8	1	no	—
1612	C₂³	—	8	1	no	—
1613	C₂³	—	8	1	no	—
1614	C₂³	—	8	1	no	—
1615	C₂³	—	8	1	no	—
1616	C₂³	—	8	1	no	—
1617	C₂³	—	8	1	no	—
1618	C₂³	—	8	1	no	—
1619	C₂³	—	8	1	no	—
1620	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1621	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1622	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1623	Q₈	—	2	1	no	—
1624	Q₈	—	2	1	no	—
1625	Q₈	—	2	1	no	—
1626	Q₈	—	2	1	no	—
1627	Q₈	—	2	1	no	—
1628	Q₈	—	2	1	no	—
1629	Q₈	—	2	1	no	—
1630	Q₈	—	2	1	no	—
1631	Q₈	—	4	1	no	—
1632	Q₈	—	8	1	no	—
1633	Q₈	—	8	1	no	—
1634	Q₈	—	8	1	no	—
1635	D₄	—	2	1	no	—
1636	D₄	—	2	1	no	—
1637	D₄	—	2	1	no	—
1638	D₄	—	2	1	no	—
1639	D₄	—	2	1	no	—
1640	D₄	—	2	1	no	—
1641	D₄	—	2	1	no	—
1642	D₄	—	2	1	no	—
1643	D₄	—	2	1	no	—
1644	D₄	—	2	1	no	—
1645	D₄	—	2	1	no	—
1646	D₄	—	4	1	no	—
1647	D₄	—	4	1	no	—
1648	D₄	—	4	1	no	—
1649	D₄	—	4	2	no	—
1650	D₄	—	4	2	no	—
1651	D₄	—	4	2	no	—
1652	D₄	—	4	2	no	—
1653	D₄	—	4	2	no	—
1654	D₄	—	8	1	no	—
1655	D₄	—	8	1	no	—
1656	D₄	—	8	1	no	—
1657	D₄	—	8	1	no	—
1658	D₄	—	8	1	no	—
1659	D₄	—	8	1	no	—
1660	D₄	—	8	1	no	—
1661	D₄	—	8	1	no	—
1662	D₄	—	8	1	no	—
1663	D₄	—	8	1	no	—
1664	D₄	—	8	1	no	—
1665	D₄	—	8	1	no	—
1666	D₄	—	8	1	no	—
1667	D₄	—	8	1	no	—
1668	D₄	—	8	1	no	—
1669	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1670	C₂×C₄	—	2	1	no	—
1671	C₂×C₄	—	2	1	no	—
1672	C₂×C₄	—	2	1	no	—
1673	C₂×C₄	—	2	1	no	—
1674	C₂×C₄	—	2	1	no	—
1675	C₂×C₄	—	2	1	no	—
1676	C₂×C₄	—	2	1	no	—
1677	C₂×C₄	—	2	1	no	—
1678	C₂×C₄	—	2	1	no	—
1679	C₂×C₄	—	2	1	no	—
1680	C₂×C₄	—	2	1	no	—
1681	C₂×C₄	—	2	1	no	—
1682	C₂×C₄	—	2	1	no	—
1683	C₂×C₄	—	2	1	no	—
1684	C₂×C₄	—	2	1	no	—
1685	C₂×C₄	—	2	1	no	—
1686	C₂×C₄	—	4	1	no	—
1687	C₂×C₄	—	4	1	no	—
1688	C₂×C₄	—	4	2	no	—
1689	C₂×C₄	—	4	2	no	—
1690	C₂×C₄	—	8	1	no	—
1691	C₂×C₄	—	8	1	no	—
1692	C₂×C₄	—	8	1	no	—
1693	C₂×C₄	—	8	1	no	—
1694	C₂×C₄	—	8	1	no	—
1695	C₂×C₄	—	8	1	no	—
1696	C₂×C₄	—	8	1	no	—
1697	C₂×C₄	—	8	1	no	—
1698	C₂×C₄	—	8	1	no	—
1699	C₂×C₄	—	8	1	no	—
1700	C₂×C₄	—	8	1	no	—
1701	C₂×C₄	—	8	1	no	—
1702	C₂×C₄	—	8	1	no	—
1703	C₂×C₄	—	8	1	no	—
1704	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1705	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1706	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1707	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1708	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1709	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1710	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1711	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1712	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1713	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1714	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1715	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1716	C₈	—	2	1	no	—
1717	C₈	—	2	1	no	—
1718	C₈	—	2	1	no	—
1719	C₈	—	2	1	no	—
1720	C₈	—	2	1	no	—
1721	C₈	—	2	1	no	—
1722	C₈	—	2	1	no	—
1723	C₈	—	2	1	no	—
1724	C₂²	—	2	1	no	—
1725	C₂²	—	2	1	no	—
1726	C₂²	—	2	1	no	—
1727	C₂²	—	2	2	no	—
1728	C₂²	—	2	1	no	—
1729	C₂²	—	2	1	no	—
1730	C₂²	—	2	1	no	—
1731	C₂²	—	2	1	no	—
1732	C₂²	—	2	1	no	—
1733	C₂²	—	2	1	no	—
1734	C₂²	—	4	1	no	—
1735	C₂²	—	4	1	no	—
1736	C₂²	—	4	1	no	—
1737	C₂²	—	4	1	no	—
1738	C₂²	—	4	1	no	—
1739	C₂²	—	4	1	no	—
1740	C₂²	—	4	1	no	—
1741	C₂²	—	4	1	no	—
1742	C₂²	—	4	1	no	—
1743	C₂²	—	4	1	no	—
1744	C₂²	—	4	1	no	—
1745	C₂²	—	4	1	no	—
1746	C₂²	—	4	1	no	—
1747	C₂²	—	4	1	no	—
1748	C₂²	—	4	1	no	—
1749	C₂²	—	4	1	no	—
1750	C₂²	—	4	1	no	—
1751	C₂²	—	16	2	no	—
1752	C₂²	—	16	2	no	—
1753	C₂²	—	16	2	no	—
1754	C₂²	—	16	2	no	—
1755	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1756	C₄	—	2	1	no	—
1757	C₄	—	2	1	no	—
1758	C₄	—	2	1	no	—
1759	C₄	—	2	1	no	—
1760	C₄	—	2	1	no	—
1761	C₄	—	2	1	no	—
1762	C₄	—	2	1	no	—
1763	C₄	—	2	1	no	—
1764	C₄	—	2	1	no	—
1765	C₄	—	2	1	no	—
1766	C₄	—	2	1	no	—
1767	C₄	—	4	1	no	—
1768	C₄	—	4	1	no	—
1769	C₄	—	4	1	no	—
1770	C₄	—	4	1	no	—
1771	C₄	—	4	1	no	—
1772	C₄	—	4	1	no	—
1773	C₄	—	4	1	no	—
1774	C₄	—	4	1	no	—
1775	C₄	—	4	1	no	—
1776	C₄	—	4	1	no	—
1777	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1778	C₄	C₅₃×#585	1	1	yes	characteristic
1779	C₂	—	4	1	no	—
1780	C₂	—	4	1	no	—
1781	C₂	—	4	1	no	—
1782	C₂	—	4	2	no	—
1783	C₂	—	8	1	no	—
1784	C₂	—	8	1	no	—
1785	C₂	—	8	1	no	—
1786	C₂	—	8	1	no	—
1787	C₂	—	8	1	no	—
1788	C₂	C₅₃×#3488	1	1	yes	characteristic
1789	C₂	C₅₃×#3584	1	1	yes	characteristic
1790	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×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3558	C₂	semidirect
2. C₅₃×#3521	C₂	semidirect
3. C₅₃×#3401	C₂	semidirect
4. C₅₃×#3394	C₂	semidirect
5. C₅₃×#3370	C₂	semidirect
6. C₅₃×#3361	C₂	semidirect
7. C₅₃×#3326	C₂	semidirect
8. C₅₃×#3324	C₂	semidirect
9. C₅₃×#3323	C₂	semidirect
10. C₅₃×#3318	C₂	semidirect
11. C₅₃×#3313	C₂	semidirect
12. C₅₃×#3296	C₂	semidirect
13. C₅₃×#3280	C₂	semidirect
14. C₅₃×#3275	C₂	semidirect
15. C₅₃×#3273	C₂	semidirect
16. C₅₃×#3272	C₂	semidirect
17. C₅₃×#3269	C₂	semidirect
18. C₅₃×#3264	C₂	semidirect
19. C₅₃×#3262	C₂	semidirect
20. C₅₃×#3258	C₂	semidirect
21. C₅₃×#3251	C₂	semidirect
22. C₅₃×#3224	C₂	semidirect
23. C₅₃×#3222	C₂	semidirect
24. C₅₃×#3211	C₂	semidirect
25. C₅₃×#3125	C₂	semidirect
26. C₅₃×#3118	C₂	semidirect
27. C₅₃×#3106	C₂	semidirect
28. C₅₃×#3045	C₂	semidirect
29. C₅₃×#3041	C₂	semidirect
30. C₅₃×#3040	C₂	semidirect
31. C₅₃×#2993	C₂	semidirect
32. C₂×#137×C₅₃	C₂²	semidirect
34. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
35. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
36. C₂×#135×C₅₃	C₂²	semidirect
37. C₂²×D₈×C₅₃	C₂²	semidirect
40. C₅₃×#559	C₂²	semidirect
41. C₅₃×#559	C₂²	semidirect
42. C₅₃×#556	C₂²	semidirect
43. C₅₃×#556	C₂²	semidirect
44. C₅₃×#554	C₂²	semidirect
46. C₅₃×#553	C₂²	semidirect
48. C₅₃×#552	C₂²	semidirect
52. C₅₃×#548	C₂²	semidirect
53. C₅₃×#547	C₂²	semidirect
58. C₅₃×#546	C₂²	semidirect
59. C₅₃×#546	C₂²	semidirect
61. D₄²×C₅₃	C₂²	semidirect
63. C₅₃×#542	C₂²	semidirect
64. C₅₃×#542	C₂²	semidirect
65. C₅₃×#541	C₂²	semidirect
72. C₅₃×#535	C₂²	semidirect
74. C₅₃×#532	C₂²	semidirect
77. C₅₃×#529	C₂²	semidirect
79. C₂×#124×C₅₃	C₂²	semidirect
80. C₅₃×#520	C₂²	semidirect
81. C₅₃×#518	C₂²	semidirect
82. C₄×#41×C₅₃	C₂²	semidirect
83. C₅₃×#497	C₂²	semidirect
85. C₅₃×#495	C₂²	semidirect
86. C₅₃×#495	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×#488	C₂²	semidirect
93. C₅₃×#488	C₂²	semidirect
94. C₅₃×#486	C₂²	semidirect
95. C₅₃×#485	C₂²	semidirect
96. C₅₃×#483	C₂²	semidirect
98. C₅₃×#482	C₂²	semidirect
99. C₅₃×#482	C₂²	semidirect
100. C₅₃×#481	C₂²	semidirect
101. C₅₃×#479	C₂²	semidirect
102. C₅₃×#478	C₂²	semidirect
103. C₅₃×#478	C₂²	semidirect
104. C₅₃×#478	C₂²	semidirect
105. C₅₃×#477	C₂²	semidirect
106. C₅₃×#477	C₂²	semidirect
107. C₅₃×#476	C₂²	semidirect
108. C₅₃×#475	C₂²	semidirect
109. C₅₃×#474	C₂²	semidirect
110. C₅₃×#474	C₂²	semidirect
111. C₅₃×#470	C₂²	semidirect
112. C₅₃×#469	C₂²	semidirect
113. C₅₃×#469	C₂²	semidirect
115. C₅₃×#468	C₂²	semidirect
116. C₅₃×#468	C₂²	semidirect
117. C₅₃×#468	C₂²	semidirect
118. C₅₃×#468	C₂²	semidirect
119. C₅₃×#467	C₂²	semidirect
120. C₅₃×#467	C₂²	semidirect
123. C₅₃×#464	C₂²	semidirect
124. C₅₃×#464	C₂²	semidirect
125. C₅₃×#464	C₂²	semidirect
126. C₅₃×#464	C₂²	semidirect
127. C₅₃×#464	C₂²	semidirect
128. C₅₃×#464	C₂²	semidirect
129. C₅₃×#464	C₂²	semidirect
130. C₅₃×#464	C₂²	semidirect
131. C₅₃×#463	C₂²	semidirect
132. C₅₃×#463	C₂²	semidirect
133. C₅₃×#463	C₂²	semidirect
134. C₅₃×#463	C₂²	semidirect
135. C₅₃×#463	C₂²	semidirect
136. C₅₃×#463	C₂²	semidirect
137. C₅₃×#463	C₂²	semidirect
138. C₅₃×#463	C₂²	semidirect
139. C₅₃×#463	C₂²	semidirect
140. C₅₃×#463	C₂²	semidirect
141. C₅₃×#463	C₂²	semidirect
142. C₅₃×#463	C₂²	semidirect
143. C₅₃×#462	C₂²	semidirect
144. C₅₃×#461	C₂²	semidirect
145. C₅₃×#460	C₂²	semidirect
146. C₅₃×#460	C₂²	semidirect
147. C₅₃×#460	C₂²	semidirect
151. C₅₃×#459	C₂²	semidirect
152. C₅₃×#459	C₂²	semidirect
153. C₅₃×#452	C₂²	semidirect
154. C₅₃×#452	C₂²	semidirect
155. C₅₃×#452	C₂²	semidirect
156. C₅₃×#452	C₂²	semidirect
157. C₅₃×#451	C₂²	semidirect
158. C₅₃×#450	C₂²	semidirect
159. C₅₃×#450	C₂²	semidirect
160. C₅₃×#450	C₂²	semidirect
161. C₅₃×#450	C₂²	semidirect
162. C₅₃×#450	C₂²	semidirect
164. C₅₃×#449	C₂²	semidirect
165. C₅₃×#449	C₂²	semidirect
166. C₅₃×#449	C₂²	semidirect
167. C₅₃×#448	C₂²	semidirect
170. C₅₃×#447	C₂²	semidirect
171. C₅₃×#446	C₂²	semidirect
172. C₈×Q₈×C₅₃	C₂²	semidirect
173. C₅₃×#442	C₂²	semidirect
174. C₅₃×#442	C₂²	semidirect
175. C₅₃×#441	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×SD₁₆×C₅₃	C₂²	semidirect
181. C₄×SD₁₆×C₅₃	C₂²	semidirect
182. C₄×D₈×C₅₃	C₂²	semidirect
183. C₄×D₈×C₅₃	C₂²	semidirect
184. C₄×D₈×C₅₃	C₂²	semidirect
185. C₅₃×#436	C₂²	semidirect
186. C₅₃×#436	C₂²	semidirect
187. C₅₃×#436	C₂²	semidirect
188. C₅₃×#435	C₂²	semidirect
189. C₅₃×#435	C₂²	semidirect
190. C₈×D₄×C₅₃	C₂²	semidirect
191. C₅₃×#433	C₂²	semidirect
192. C₅₃×#433	C₂²	semidirect
193. C₅₃×#431	C₂²	semidirect
194. C₅₃×#424	C₂²	semidirect
195. C₅₃×#424	C₂²	semidirect
196. C₅₃×#423	C₂²	semidirect
197. C₅₃×#419	C₂²	semidirect
198. C₅₃×#418	C₂²	semidirect
199. C₅₃×#418	C₂²	semidirect
200. C₅₃×#417	C₂²	semidirect
201. C₅₃×#416	C₂²	semidirect
202. C₂×#102×C₅₃	C₂²	semidirect
828. #62047	C₅₃	direct (N × H)
884. #3558	C₂×C₅₃	semidirect
885. #3521	C₂×C₅₃	semidirect
886. #3401	C₂×C₅₃	semidirect
887. #3394	C₂×C₅₃	semidirect
888. #3370	C₂×C₅₃	semidirect
889. #3361	C₂×C₅₃	semidirect
890. #3326	C₂×C₅₃	semidirect
891. #3324	C₂×C₅₃	semidirect
892. #3323	C₂×C₅₃	semidirect
893. #3318	C₂×C₅₃	semidirect
894. #3313	C₂×C₅₃	semidirect
895. #3296	C₂×C₅₃	semidirect
896. #3280	C₂×C₅₃	semidirect
897. #3275	C₂×C₅₃	semidirect
898. #3273	C₂×C₅₃	semidirect
899. #3272	C₂×C₅₃	semidirect
900. #3269	C₂×C₅₃	semidirect
901. #3264	C₂×C₅₃	semidirect
902. #3262	C₂×C₅₃	semidirect
903. #3258	C₂×C₅₃	semidirect
904. #3251	C₂×C₅₃	semidirect
905. #3224	C₂×C₅₃	semidirect
906. #3222	C₂×C₅₃	semidirect
907. #3211	C₂×C₅₃	semidirect
908. #3125	C₂×C₅₃	semidirect
909. #3118	C₂×C₅₃	semidirect
910. #3106	C₂×C₅₃	semidirect
911. #3045	C₂×C₅₃	semidirect
912. #3041	C₂×C₅₃	semidirect
913. #3040	C₂×C₅₃	semidirect
914. #2993	C₂×C₅₃	semidirect
927. C₂×#137	C₂²×C₅₃	semidirect
929. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
930. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
931. C₂×#135	C₂²×C₅₃	semidirect
932. C₂²×D₈	C₂²×C₅₃	semidirect
935. #559	C₂²×C₅₃	semidirect
936. #559	C₂²×C₅₃	semidirect
937. #556	C₂²×C₅₃	semidirect
938. #556	C₂²×C₅₃	semidirect
939. #554	C₂²×C₅₃	semidirect
941. #553	C₂²×C₅₃	semidirect
943. #552	C₂²×C₅₃	semidirect
947. #548	C₂²×C₅₃	semidirect
948. #547	C₂²×C₅₃	semidirect
953. #546	C₂²×C₅₃	semidirect
954. #546	C₂²×C₅₃	semidirect
956. D₄²	C₂²×C₅₃	semidirect
958. #542	C₂²×C₅₃	semidirect
959. #542	C₂²×C₅₃	semidirect
960. #541	C₂²×C₅₃	semidirect
967. #535	C₂²×C₅₃	semidirect
969. #532	C₂²×C₅₃	semidirect
972. #529	C₂²×C₅₃	semidirect
974. C₂×#124	C₂²×C₅₃	semidirect
975. #520	C₂²×C₅₃	semidirect
976. #518	C₂²×C₅₃	semidirect
977. C₄×#41	C₂²×C₅₃	semidirect
978. #497	C₂²×C₅₃	semidirect
980. #495	C₂²×C₅₃	semidirect
981. #495	C₂²×C₅₃	semidirect
982. #495	C₂²×C₅₃	semidirect
983. #492	C₂²×C₅₃	semidirect
984. #490	C₂²×C₅₃	semidirect
985. #489	C₂²×C₅₃	semidirect
986. #488	C₂²×C₅₃	semidirect
987. #488	C₂²×C₅₃	semidirect
988. #488	C₂²×C₅₃	semidirect
989. #486	C₂²×C₅₃	semidirect
990. #485	C₂²×C₅₃	semidirect
991. #483	C₂²×C₅₃	semidirect
993. #482	C₂²×C₅₃	semidirect
994. #482	C₂²×C₅₃	semidirect
995. #481	C₂²×C₅₃	semidirect
996. #479	C₂²×C₅₃	semidirect
997. #478	C₂²×C₅₃	semidirect
998. #478	C₂²×C₅₃	semidirect
999. #478	C₂²×C₅₃	semidirect
1000. #477	C₂²×C₅₃	semidirect
1001. #477	C₂²×C₅₃	semidirect
1002. #476	C₂²×C₅₃	semidirect
1003. #475	C₂²×C₅₃	semidirect
1004. #474	C₂²×C₅₃	semidirect
1005. #474	C₂²×C₅₃	semidirect
1006. #470	C₂²×C₅₃	semidirect
1007. #469	C₂²×C₅₃	semidirect
1008. #469	C₂²×C₅₃	semidirect
1010. #468	C₂²×C₅₃	semidirect
1011. #468	C₂²×C₅₃	semidirect
1012. #468	C₂²×C₅₃	semidirect
1013. #468	C₂²×C₅₃	semidirect
1014. #467	C₂²×C₅₃	semidirect
1015. #467	C₂²×C₅₃	semidirect
1018. #464	C₂²×C₅₃	semidirect
1019. #464	C₂²×C₅₃	semidirect
1020. #464	C₂²×C₅₃	semidirect
1021. #464	C₂²×C₅₃	semidirect
1022. #464	C₂²×C₅₃	semidirect
1023. #464	C₂²×C₅₃	semidirect
1024. #464	C₂²×C₅₃	semidirect
1025. #464	C₂²×C₅₃	semidirect
1026. #463	C₂²×C₅₃	semidirect
1027. #463	C₂²×C₅₃	semidirect
1028. #463	C₂²×C₅₃	semidirect
1029. #463	C₂²×C₅₃	semidirect
1030. #463	C₂²×C₅₃	semidirect
1031. #463	C₂²×C₅₃	semidirect
1032. #463	C₂²×C₅₃	semidirect
1033. #463	C₂²×C₅₃	semidirect
1034. #463	C₂²×C₅₃	semidirect
1035. #463	C₂²×C₅₃	semidirect
1036. #463	C₂²×C₅₃	semidirect
1037. #463	C₂²×C₅₃	semidirect
1038. #462	C₂²×C₅₃	semidirect
1039. #461	C₂²×C₅₃	semidirect
1040. #460	C₂²×C₅₃	semidirect
1041. #460	C₂²×C₅₃	semidirect
1042. #460	C₂²×C₅₃	semidirect
1046. #459	C₂²×C₅₃	semidirect
1047. #459	C₂²×C₅₃	semidirect
1048. #452	C₂²×C₅₃	semidirect
1049. #452	C₂²×C₅₃	semidirect
1050. #452	C₂²×C₅₃	semidirect
1051. #452	C₂²×C₅₃	semidirect
1052. #451	C₂²×C₅₃	semidirect
1053. #450	C₂²×C₅₃	semidirect
1054. #450	C₂²×C₅₃	semidirect
1055. #450	C₂²×C₅₃	semidirect
1056. #450	C₂²×C₅₃	semidirect
1057. #450	C₂²×C₅₃	semidirect
1059. #449	C₂²×C₅₃	semidirect
1060. #449	C₂²×C₅₃	semidirect
1061. #449	C₂²×C₅₃	semidirect
1062. #448	C₂²×C₅₃	semidirect
1065. #447	C₂²×C₅₃	semidirect
1066. #446	C₂²×C₅₃	semidirect
1067. C₈×Q₈	C₂²×C₅₃	semidirect
1068. #442	C₂²×C₅₃	semidirect
1069. #442	C₂²×C₅₃	semidirect
1070. #441	C₂²×C₅₃	semidirect
1071. #440	C₂²×C₅₃	semidirect
1072. C₄×SD₁₆	C₂²×C₅₃	semidirect
1073. C₄×SD₁₆	C₂²×C₅₃	semidirect
1074. C₄×SD₁₆	C₂²×C₅₃	semidirect
1075. C₄×SD₁₆	C₂²×C₅₃	semidirect
1076. C₄×SD₁₆	C₂²×C₅₃	semidirect
1077. C₄×D₈	C₂²×C₅₃	semidirect
1078. C₄×D₈	C₂²×C₅₃	semidirect
1079. C₄×D₈	C₂²×C₅₃	semidirect
1080. #436	C₂²×C₅₃	semidirect
1081. #436	C₂²×C₅₃	semidirect
1082. #436	C₂²×C₅₃	semidirect
1083. #435	C₂²×C₅₃	semidirect
1084. #435	C₂²×C₅₃	semidirect
1085. C₈×D₄	C₂²×C₅₃	semidirect
1086. #433	C₂²×C₅₃	semidirect
1087. #433	C₂²×C₅₃	semidirect
1088. #431	C₂²×C₅₃	semidirect
1089. #424	C₂²×C₅₃	semidirect
1090. #424	C₂²×C₅₃	semidirect
1091. #423	C₂²×C₅₃	semidirect
1092. #419	C₂²×C₅₃	semidirect
1093. #418	C₂²×C₅₃	semidirect
1094. #418	C₂²×C₅₃	semidirect
1095. #417	C₂²×C₅₃	semidirect
1096. #416	C₂²×C₅₃	semidirect
1097. C₂×#102	C₂²×C₅₃	semidirect
1098. C₅₃	#62047	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×#3558	2
C₅₃×#3521	2
C₅₃×#3401	2
C₅₃×#3394	2
C₅₃×#3370	2
C₅₃×#3361	2
C₅₃×#3326	2
C₅₃×#3324	2
C₅₃×#3323	2
C₅₃×#3318	2
C₅₃×#3313	2
C₅₃×#3296	2
C₅₃×#3280	2
C₅₃×#3275	2
C₅₃×#3273	2
C₅₃×#3272	2
C₅₃×#3269	2
C₅₃×#3264	2
C₅₃×#3262	2
C₅₃×#3258	2
C₅₃×#3251	2
C₅₃×#3224	2
C₅₃×#3222	2
C₅₃×#3211	2
C₅₃×#3125	2
C₅₃×#3118	2
C₅₃×#3106	2
C₅₃×#3045	2
C₅₃×#3041	2
C₅₃×#3040	2
C₅₃×#2993	2
#62047	53

Subgroups — C53×#62047 #27269559

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62047 #27269559