Subgroups — #27592128

Order 13568.

1842 conjugacy classes of subgroups.

The subgroup lattice has 1536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20283066	C₂	1	1	yes	maximal, characteristic, complemented
2	#20283017	C₂	1	1	yes	maximal, characteristic, complemented
3	#20282621	C₂	1	1	yes	maximal, characteristic, complemented
4	#20282620	C₂	1	1	yes	maximal, characteristic, complemented
5	#20282549	C₂	1	1	yes	maximal, characteristic, complemented
6	#20282542	C₂	1	1	yes	maximal, characteristic, complemented
7	#20282254	C₂	1	1	yes	maximal, characteristic, complemented
8	#20282077	C₂	1	1	yes	maximal, characteristic, complemented
9	#20282075	C₂	1	1	yes	maximal, characteristic, complemented
10	#20282058	C₂	1	1	yes	maximal, characteristic, complemented
11	#20282057	C₂	1	1	yes	maximal, characteristic, complemented
12	#20281719	C₂	1	1	yes	maximal, characteristic, complemented
13	#20281716	C₂	1	1	yes	maximal, characteristic, complemented
14	#20281460	C₂	1	1	yes	maximal, characteristic, complemented
15	#20281458	C₂	1	1	yes	maximal, characteristic, complemented
16	#20281001	C₂	1	1	yes	maximal, characteristic, complemented
17	#20280999	C₂	1	1	yes	maximal, characteristic, complemented
18	#20280521	C₂	1	1	yes	maximal, characteristic, complemented
19	#20280450	C₂	1	1	yes	maximal, characteristic
20	#20279276	C₂	1	1	yes	maximal, characteristic, complemented
21	#20279272	C₂	1	1	yes	maximal, characteristic, complemented
22	#20278845	C₂	1	1	yes	maximal, characteristic, complemented
23	#20278834	C₂	1	1	yes	maximal, characteristic, complemented
24	#20278531	C₂	1	1	yes	maximal, characteristic, complemented
25	#20278519	C₂	1	1	yes	maximal, characteristic, complemented
26	#20278182	C₂	1	1	yes	maximal, characteristic, complemented
27	#20278180	C₂	1	1	yes	maximal, characteristic, complemented
28	#20277444	C₂	1	1	yes	maximal, characteristic, complemented
29	#20277414	C₂	1	1	yes	maximal, characteristic, complemented
30	#388×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2773	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#13133216	C₂²	1	1	yes	characteristic, complemented
33	C₂×#13133205	C₂²	1	1	yes	characteristic
34	C₂×#13133205	C₂²	1	1	yes	characteristic, complemented
35	C₂×#13133203	C₂²	1	1	yes	characteristic
36	C₂×#13133202	C₂²	1	1	yes	characteristic
37	C₂×#13133199	C₂²	1	1	yes	characteristic
38	C₂×#13133197	C₂²	1	1	yes	characteristic
39	C₂×#13133197	C₂²	1	1	yes	characteristic, complemented
40	C₂×#13133195	C₂²	1	1	yes	characteristic
41	C₂×#13133195	C₂²	1	1	yes	characteristic
42	C₂×#13133195	C₂²	1	1	yes	characteristic, complemented
43	C₂×#13133192	C₂²	1	1	yes	characteristic
44	C₂×#13133187	C₂²	1	1	yes	characteristic
45	C₂×#13133187	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic
47	C₂×#13133179	C₂²	1	1	yes	characteristic
48	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
50	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
52	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
53	C₅₃⋊#401	C₂²	1	1	yes	characteristic, complemented
54	C₅₃⋊#401	C₂²	1	1	yes	characteristic, complemented
55	#16810565	C₂²	1	1	yes	characteristic, complemented
56	#16810560	C₂²	1	1	yes	characteristic
57	#16810558	C₂²	1	1	yes	characteristic
58	#16810558	C₂²	1	1	yes	characteristic, complemented
59	#16810558	C₂²	1	1	yes	characteristic, complemented
60	#16810557	C₂²	1	1	yes	characteristic, complemented
61	#16810552	C₂²	1	1	yes	characteristic
62	#16810552	C₂²	1	1	yes	characteristic, complemented
63	#16810550	C₂²	1	1	yes	characteristic, complemented
64	#16810549	C₂²	1	1	yes	characteristic
65	#16810549	C₂²	1	1	yes	characteristic
66	#16810549	C₂²	1	1	yes	characteristic, complemented
67	#16810549	C₂²	1	1	yes	characteristic, complemented
68	#16810548	C₂²	1	1	yes	characteristic
69	#16810547	C₂²	1	1	yes	characteristic, complemented
70	#16810546	C₂²	1	1	yes	characteristic
71	#16810546	C₂²	1	1	yes	characteristic
72	#16810545	C₂²	1	1	yes	characteristic
73	#16810545	C₂²	1	1	yes	characteristic
74	#16810545	C₂²	1	1	yes	characteristic, complemented
75	#16810544	C₂²	1	1	yes	characteristic, complemented
76	#16810543	C₂²	1	1	yes	characteristic, complemented
77	#16810541	C₂²	1	1	yes	characteristic
78	#16810541	C₂²	1	1	yes	characteristic
79	#16810541	C₂²	1	1	yes	characteristic
80	#16810540	C₂²	1	1	yes	characteristic
81	#16810540	C₂²	1	1	yes	characteristic
82	#16810540	C₂²	1	1	yes	characteristic
83	#16810539	C₂²	1	1	yes	characteristic
84	#16810539	C₂²	1	1	yes	characteristic
85	#16810538	C₂²	1	1	yes	characteristic
86	#16810538	C₂²	1	1	yes	characteristic
87	#16810538	C₂²	1	1	yes	characteristic
88	#16810538	C₂²	1	1	yes	characteristic
89	#16810536	C₂²	1	1	yes	characteristic
90	#16810536	C₂²	1	1	yes	characteristic
91	#16810535	C₂²	1	1	yes	characteristic
92	#16810535	C₂²	1	1	yes	characteristic
93	#16810533	C₂²	1	1	yes	characteristic
94	#16810532	C₂²	1	1	yes	characteristic
95	#16810528	C₂²	1	1	yes	characteristic, complemented
96	#16810527	C₂²	1	1	yes	characteristic, complemented
97	#16810527	C₂²	1	1	yes	characteristic, complemented
98	#16810527	C₂²	1	1	yes	characteristic, complemented
99	#16810527	C₂²	1	1	yes	characteristic, complemented
100	#16810524	C₂²	1	1	yes	characteristic
101	#16810524	C₂²	1	1	yes	characteristic, complemented
102	#16810523	C₂²	1	1	yes	characteristic
103	#16810521	C₂²	1	1	yes	characteristic, complemented
104	#16810521	C₂²	1	1	yes	characteristic, complemented
105	#16810520	C₂²	1	1	yes	characteristic, complemented
106	#16810519	C₂²	1	1	yes	characteristic, complemented
107	#16810518	C₂²	1	1	yes	characteristic, complemented
108	#16810518	C₂²	1	1	yes	characteristic, complemented
109	#16810517	C₂²	1	1	yes	characteristic
110	#16810517	C₂²	1	1	yes	characteristic
111	#16810516	C₂²	1	1	yes	characteristic
112	#16810515	C₂²	1	1	yes	characteristic
113	#16810515	C₂²	1	1	yes	characteristic
114	#16810515	C₂²	1	1	yes	characteristic, complemented
115	#16810515	C₂²	1	1	yes	characteristic, complemented
116	#16810515	C₂²	1	1	yes	characteristic, complemented
117	#16810515	C₂²	1	1	yes	characteristic, complemented
118	#16810515	C₂²	1	1	yes	characteristic, complemented
119	#16810514	C₂²	1	1	yes	characteristic
120	#16810514	C₂²	1	1	yes	characteristic
121	#16810514	C₂²	1	1	yes	characteristic, complemented
122	#16810514	C₂²	1	1	yes	characteristic, complemented
123	#16810513	C₂²	1	1	yes	characteristic
124	#16810513	C₂²	1	1	yes	characteristic, complemented
125	#16810513	C₂²	1	1	yes	characteristic, complemented
126	#16810512	C₂²	1	1	yes	characteristic
127	#16810512	C₂²	1	1	yes	characteristic
128	#16810512	C₂²	1	1	yes	characteristic
129	#16810512	C₂²	1	1	yes	characteristic, complemented
130	#16810511	C₂²	1	1	yes	characteristic
131	#16810511	C₂²	1	1	yes	characteristic
132	#16810509	C₂²	1	1	yes	characteristic, complemented
133	#16810509	C₂²	1	1	yes	characteristic, complemented
134	#16810508	C₂²	1	1	yes	characteristic, complemented
135	#16810508	C₂²	1	1	yes	characteristic, complemented
136	#16810507	C₂²	1	1	yes	characteristic, complemented
137	#16810506	C₂²	1	1	yes	characteristic, complemented
138	#16810506	C₂²	1	1	yes	characteristic, complemented
139	#16810501	C₂²	1	1	yes	characteristic
140	#16810501	C₂²	1	1	yes	characteristic
141	#16810501	C₂²	1	1	yes	characteristic
142	#16810501	C₂²	1	1	yes	characteristic
143	#16810501	C₂²	1	1	yes	characteristic
144	#16810501	C₂²	1	1	yes	characteristic
145	#16810501	C₂²	1	1	yes	characteristic
146	#16810501	C₂²	1	1	yes	characteristic
147	#16810501	C₂²	1	1	yes	characteristic
148	#16810501	C₂²	1	1	yes	characteristic, complemented
149	#16810501	C₂²	1	1	yes	characteristic, complemented
150	#16810499	C₂²	1	1	yes	characteristic
151	#16810497	C₂²	1	1	yes	characteristic
152	#16810497	C₂²	1	1	yes	characteristic, complemented
153	#16810494	C₂²	1	1	yes	characteristic
154	#16810494	C₂²	1	1	yes	characteristic
155	#16810494	C₂²	1	1	yes	characteristic
156	#16810494	C₂²	1	1	yes	characteristic, complemented
157	#16810494	C₂²	1	1	yes	characteristic, complemented
158	#16810494	C₂²	1	1	yes	characteristic, complemented
159	#16810492	C₂²	1	1	yes	characteristic, complemented
160	#16810490	C₂²	1	1	yes	characteristic, complemented
161	#16810490	C₂²	1	1	yes	characteristic, complemented
162	#16810482	C₂²	1	1	yes	characteristic
163	#16810482	C₂²	1	1	yes	characteristic
164	#16810480	C₂²	1	1	yes	characteristic
165	#16810480	C₂²	1	1	yes	characteristic
166	#16810478	C₂²	1	1	yes	characteristic
167	#16810478	C₂²	1	1	yes	characteristic
168	C₄×#11719921	C₂²	1	1	yes	characteristic
169	#16810470	C₂²	1	1	yes	characteristic
170	#95×D₅₃	C₂²	1	1	yes	characteristic
171	#95×D₅₃	C₂²	1	1	yes	characteristic
172	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
173	C₅₃×#399	C₂²	1	1	yes	characteristic
174	C₅₃×#399	C₂²	1	1	yes	characteristic
175	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
176	C₅₃×#397	C₂²	1	1	yes	characteristic
177	C₅₃×#397	C₂²	1	1	yes	characteristic
178	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
179	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
180	C₅₃×#388	C₂²	1	1	yes	characteristic
181	C₅₃×#388	C₂²	1	1	yes	characteristic
182	C₅₃×#388	C₂²	1	1	yes	characteristic
183	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
184	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
185	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
186	C₅₃×#382	C₂²	1	1	yes	characteristic, complemented
187	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
188	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
189	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
190	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
191	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
192	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
193	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
194	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
195	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
196	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
197	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
198	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
199	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
200	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
201	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
202	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
203	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
204	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
205	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
206	#13133216	—	4	2	no	—
207	#13133205	—	4	2	no	—
208	#13133205	—	4	2	no	—
209	#13133203	—	4	2	no	—
210	#13133202	—	4	2	no	—
211	#13133199	—	4	2	no	—
212	#13133197	—	2	4	no	—
213	#13133197	—	4	2	no	—
214	#13133195	—	4	2	no	—
215	#13133195	—	4	2	no	—
216	#13133195	—	4	2	no	—
217	#13133192	—	2	4	no	—
218	#13133187	—	4	2	no	—
219	#13133187	—	4	2	no	—
220	C₄×D₂₁₂	—	4	2	no	—
221	#13133179	—	4	2	no	—
222	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
229	C₂×#11719919	C₂³	1	1	yes	characteristic
230	C₂×#11719919	C₂³	1	1	yes	characteristic
231	C₂×#11719919	C₂³	1	1	yes	characteristic
232	C₂×#11719919	C₂³	1	1	yes	characteristic
233	C₂×#11719919	C₂³	1	1	yes	characteristic
234	C₂×#11719919	C₂³	1	1	yes	characteristic
235	C₂×#11719919	C₂³	1	1	yes	characteristic
236	C₂×#11719919	C₂³	1	1	yes	characteristic
237	C₂×#11719919	C₂³	1	1	yes	characteristic
238	C₂×#11719919	C₂³	1	1	yes	characteristic
239	C₂×#11719919	C₂³	1	1	yes	characteristic
240	C₂×#11719919	C₂³	1	1	yes	characteristic
241	C₂×#11719919	C₂³	1	1	yes	characteristic
242	C₂×#11719919	C₂³	1	1	yes	characteristic
243	C₄⋊C₄×D₅₃	—	4	2	no	—
244	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
245	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
246	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
247	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
248	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
249	C₂×#11719921	C₂³	1	1	yes	characteristic
250	C₂×#11719921	C₂³	1	1	yes	characteristic
251	C₂×#11719921	C₂³	1	1	yes	characteristic
252	C₂×#11719921	C₂³	1	1	yes	characteristic
253	C₂×#11719921	C₂³	1	1	yes	characteristic
254	C₂×#11719921	C₂³	1	1	yes	characteristic
255	C₂×#11719921	C₂³	1	1	yes	characteristic
256	C₂×#11719921	C₂³	1	1	yes	characteristic
257	C₂×#11719921	C₂³	1	1	yes	characteristic
258	C₂×#11719921	C₂³	1	1	yes	characteristic
259	C₂×#11719921	C₂³	1	1	yes	characteristic
260	C₂×#11719921	C₂³	1	1	yes	characteristic
261	C₂×#11719921	C₂³	1	1	yes	characteristic
262	C₂×#11719921	C₂³	1	1	yes	characteristic
263	C₂×#11719921	C₂³	1	1	yes	characteristic
264	C₂×#11719921	C₂³	1	1	yes	characteristic
265	C₂×#11719921	C₂³	1	1	yes	characteristic
266	C₂×#11719921	C₂³	1	1	yes	characteristic
267	C₂×#11719921	C₂³	1	1	yes	characteristic
268	C₂×#11719921	C₂³	1	1	yes	characteristic
269	C₂×#11719921	C₂³	1	1	yes	characteristic
270	C₂×#11719921	C₂³	1	1	yes	characteristic
271	C₂×#11719921	C₂³	1	1	yes	characteristic
272	C₂×#11719921	C₂³	1	1	yes	characteristic
273	C₂×#11719921	C₂³	1	1	yes	characteristic
274	C₂×#11719921	C₂³	1	1	yes	characteristic
275	C₂×#11719921	C₂³	1	1	yes	characteristic
276	C₂×#11719921	C₂³	1	1	yes	characteristic
277	C₂×#11719921	C₂³	1	1	yes	characteristic
278	C₂×#11719921	C₂³	1	1	yes	characteristic
279	C₂×#11719921	C₂³	1	1	yes	characteristic
280	C₂×#11719921	C₂³	1	1	yes	characteristic
281	C₂×#11719921	C₂³	1	1	yes	characteristic
282	C₂×#11719921	C₂³	1	1	yes	characteristic
283	C₂×#11719921	C₂³	1	1	yes	characteristic
284	C₂×#11719921	C₂³	1	1	yes	characteristic
285	C₂×#11719921	C₂³	1	1	yes	characteristic
286	C₂×#11719921	C₂³	1	1	yes	characteristic
287	C₂²⋊C₄×D₅₃	—	2	4	no	—
288	C₂²⋊C₄×D₅₃	—	4	2	no	—
289	C₂²⋊C₄×D₅₃	—	4	2	no	—
290	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
291	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
292	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
293	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
294	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
295	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
296	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
297	C₄²×D₅₃	—	4	2	no	—
298	#13133124	C₂³	1	1	yes	characteristic
299	#13133124	C₂³	1	1	yes	characteristic
300	#13133124	C₂³	1	1	yes	characteristic
301	#13133124	C₂³	1	1	yes	characteristic
302	#13133124	C₂³	1	1	yes	characteristic
303	#13133124	C₂³	1	1	yes	characteristic
304	#13133124	C₂³	1	1	yes	characteristic
305	#13133124	C₂³	1	1	yes	characteristic
306	#13133124	C₂³	1	1	yes	characteristic
307	#13133124	C₂³	1	1	yes	characteristic
308	#13133124	C₂³	1	1	yes	characteristic
309	#13133124	C₂³	1	1	yes	characteristic
310	#13133124	C₂³	1	1	yes	characteristic
311	#13133124	C₂³	1	1	yes	characteristic
312	#13133124	C₂³	1	1	yes	characteristic
313	#13133124	C₂³	1	1	yes	characteristic
314	#13133124	C₂³	1	1	yes	characteristic
315	#13133124	C₂³	1	1	yes	characteristic
316	#13133124	C₂³	1	1	yes	characteristic
317	#13133124	C₂³	1	1	yes	characteristic
318	#13133124	C₂³	1	1	yes	characteristic
319	#13133124	C₂³	1	1	yes	characteristic
320	#13133124	C₂³	1	1	yes	characteristic
321	#13133124	C₂³	1	1	yes	characteristic
322	#13133124	C₂³	1	1	yes	characteristic
323	#13133124	C₂³	1	1	yes	characteristic
324	#13133124	C₂³	1	1	yes	characteristic
325	#13133124	C₂³	1	1	yes	characteristic
326	#13133124	C₂³	1	1	yes	characteristic
327	#13133124	C₂³	1	1	yes	characteristic
328	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
329	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
330	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
331	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
332	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
333	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
334	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
335	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
336	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
337	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
338	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
339	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
340	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
341	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
342	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
343	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
344	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
345	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
346	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
347	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
348	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
349	#95×C₅₃	C₂³	1	1	yes	characteristic
350	#95×C₅₃	C₂³	1	1	yes	characteristic
351	#95×C₅₃	C₂³	1	1	yes	characteristic
352	#95×C₅₃	C₂³	1	1	yes	characteristic
353	#95×C₅₃	C₂³	1	1	yes	characteristic
354	#95×C₅₃	C₂³	1	1	yes	characteristic
355	#95×C₅₃	C₂³	1	1	yes	characteristic
356	#95×C₅₃	C₂³	1	1	yes	characteristic
357	#95×C₅₃	C₂³	1	1	yes	characteristic
358	#95×C₅₃	C₂³	1	1	yes	characteristic
359	#95×C₅₃	C₂³	1	1	yes	characteristic
360	#95×C₅₃	C₂³	1	1	yes	characteristic
361	#95×C₅₃	C₂³	1	1	yes	characteristic
362	#95×C₅₃	C₂³	1	1	yes	characteristic
363	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
364	C₂³×D₅₃	—	2	2	no	—
365	C₂³×D₅₃	—	2	2	no	—
366	C₂³×D₅₃	—	2	2	no	—
367	C₂³×D₅₃	—	4	1	no	—
368	C₂³×D₅₃	—	4	1	no	—
369	C₂³×D₅₃	—	4	1	no	—
370	C₂³×D₅₃	—	4	1	no	—
371	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
372	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
373	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
374	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
378	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
381	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
382	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
387	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
389	C₂×C₂²⋊D₅₃	—	4	1	no	—
390	C₂×C₂²⋊D₅₃	—	4	1	no	—
391	C₂×C₂²⋊D₅₃	—	4	1	no	—
392	C₂×C₂²⋊D₅₃	—	4	1	no	—
393	C₂×C₂²⋊D₅₃	—	4	1	no	—
394	C₂×C₂²⋊D₅₃	—	4	1	no	—
395	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
396	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
397	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
398	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
399	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
400	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
401	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
402	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
403	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
404	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
405	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
406	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
407	C₂×D₂₁₂	—	2	2	no	—
408	C₂×D₂₁₂	—	2	2	no	—
409	C₂×D₂₁₂	—	2	2	no	—
410	C₂×D₂₁₂	—	2	2	no	—
411	C₂×D₂₁₂	—	2	2	no	—
412	C₂×D₂₁₂	—	2	2	no	—
413	C₂×D₂₁₂	—	2	2	no	—
414	C₂×D₂₁₂	—	4	1	no	—
415	C₂×D₂₁₂	—	4	1	no	—
416	C₂×D₂₁₂	—	4	1	no	—
417	C₂×D₂₁₂	—	4	1	no	—
418	C₂×D₂₁₂	—	4	1	no	—
419	C₂×D₂₁₂	—	4	1	no	—
420	C₂×D₂₁₂	—	4	1	no	—
421	C₂×D₂₁₂	—	4	1	no	—
422	C₂×C₄×D₅₃	—	2	2	no	—
423	C₂×C₄×D₅₃	—	2	2	no	—
424	C₂×C₄×D₅₃	—	2	2	no	—
425	C₂×C₄×D₅₃	—	2	2	no	—
426	C₂×C₄×D₅₃	—	2	2	no	—
427	C₂×C₄×D₅₃	—	2	2	no	—
428	C₂×C₄×D₅₃	—	2	2	no	—
429	C₂×C₄×D₅₃	—	4	1	no	—
430	C₂×C₄×D₅₃	—	4	1	no	—
431	C₂×C₄×D₅₃	—	4	1	no	—
432	C₂×C₄×D₅₃	—	4	1	no	—
433	C₂×C₄×D₅₃	—	4	1	no	—
434	C₂×C₄×D₅₃	—	4	1	no	—
435	C₂×C₄×D₅₃	—	4	1	no	—
436	C₂×C₄×D₅₃	—	4	1	no	—
437	C₂×C₄×D₅₃	—	4	1	no	—
438	C₂×C₄×D₅₃	—	4	1	no	—
439	C₂×C₄×D₅₃	—	4	1	no	—
440	C₂×C₄×D₅₃	—	4	1	no	—
441	C₂×C₄×D₅₃	—	4	1	no	—
442	C₂×C₄×D₅₃	—	4	1	no	—
443	C₂×C₄×D₅₃	—	4	1	no	—
444	C₂×C₄×D₅₃	—	4	1	no	—
445	C₂×C₄×D₅₃	#41	1	4	yes	—
446	C₂×Dic₁₀₆	—	2	2	no	—
447	C₂×Dic₁₀₆	—	2	2	no	—
448	C₂×Dic₁₀₆	—	2	2	no	—
449	C₂×Dic₁₀₆	—	4	1	no	—
450	C₂×Dic₁₀₆	—	4	1	no	—
451	C₂×Dic₁₀₆	—	4	1	no	—
452	C₂×Dic₁₀₆	—	4	1	no	—
453	C₂×Dic₁₀₆	—	4	1	no	—
454	C₂×Dic₁₀₆	—	4	1	no	—
455	C₄⋊C₄×C₅₃	—	2	2	no	—
456	C₄⋊C₄×C₅₃	—	2	2	no	—
457	C₄⋊C₄×C₅₃	—	2	2	no	—
458	C₄⋊C₄×C₅₃	—	4	1	no	—
459	C₄⋊C₄×C₅₃	—	4	1	no	—
460	C₄⋊C₄×C₅₃	—	4	1	no	—
461	C₄⋊C₄×C₅₃	—	4	1	no	—
462	C₄⋊C₄×C₅₃	—	4	1	no	—
463	C₄⋊C₄×C₅₃	—	4	1	no	—
464	C₄⋊C₄×C₅₃	—	4	1	no	—
465	C₄⋊C₄×C₅₃	—	4	1	no	—
466	C₂²⋊C₄×C₅₃	—	2	2	no	—
467	C₂²⋊C₄×C₅₃	—	2	2	no	—
468	C₂²⋊C₄×C₅₃	—	4	1	no	—
469	C₂²⋊C₄×C₅₃	—	4	1	no	—
470	C₂²⋊C₄×C₅₃	—	4	1	no	—
471	C₂²⋊C₄×C₅₃	—	4	1	no	—
472	C₂²⋊C₄×C₅₃	—	4	1	no	—
473	C₄²×C₅₃	—	2	2	no	—
474	C₄²×C₅₃	—	4	1	no	—
475	C₄²×C₅₃	—	4	1	no	—
476	C₂²⋊Dic₅₃	—	2	2	no	—
477	C₂²⋊Dic₅₃	—	2	2	no	—
478	C₂²⋊Dic₅₃	—	4	1	no	—
479	C₂²⋊Dic₅₃	—	4	1	no	—
480	C₂²⋊Dic₅₃	—	4	1	no	—
481	#11719921	—	2	2	no	—
482	#11719921	—	2	2	no	—
483	#11719921	—	2	2	no	—
484	#11719921	—	2	2	no	—
485	#11719921	—	2	2	no	—
486	#11719921	—	2	2	no	—
487	#11719921	—	2	2	no	—
488	#11719921	—	2	2	no	—
489	#11719921	—	2	2	no	—
490	#11719921	—	2	2	no	—
491	#11719921	—	2	2	no	—
492	#11719921	—	2	2	no	—
493	#11719921	—	2	2	no	—
494	#11719921	—	2	2	no	—
495	#11719921	—	2	2	no	—
496	#11719921	—	2	2	no	—
497	#11719921	—	4	1	no	—
498	#11719921	—	4	1	no	—
499	#11719921	—	4	1	no	—
500	#11719921	—	4	1	no	—
501	#11719921	—	4	1	no	—
502	#11719921	—	4	1	no	—
503	#11719921	—	4	1	no	—
504	#11719921	—	4	1	no	—
505	#11719921	—	4	1	no	—
506	#11719921	—	4	1	no	—
507	#11719921	—	4	1	no	—
508	#11719921	—	4	1	no	—
509	#11719921	—	4	1	no	—
510	#11719921	—	4	1	no	—
511	#11719921	—	4	1	no	—
512	#11719921	—	4	1	no	—
513	#11719921	—	4	1	no	—
514	#11719921	—	4	1	no	—
515	#11719921	—	4	1	no	—
516	#11719921	—	4	1	no	—
517	#11719921	—	4	1	no	—
518	#11719921	—	4	1	no	—
519	C₄⋊Dic₅₃	—	2	2	no	—
520	C₄⋊Dic₅₃	—	2	2	no	—
521	C₄⋊Dic₅₃	—	2	2	no	—
522	C₄⋊Dic₅₃	—	2	2	no	—
523	C₄⋊Dic₅₃	—	4	1	no	—
524	C₄⋊Dic₅₃	—	4	1	no	—
525	C₄⋊Dic₅₃	—	4	1	no	—
526	#11719919	—	2	2	no	—
527	#11719919	—	4	1	no	—
528	#11719919	—	4	1	no	—
529	#11719919	—	4	1	no	—
530	#11719919	—	4	1	no	—
531	#11719919	—	4	1	no	—
532	#11719919	—	4	1	no	—
533	#11719919	—	4	1	no	—
534	#11719919	—	4	1	no	—
535	#11719919	—	4	1	no	—
536	#11719919	—	4	1	no	—
537	#11719919	—	4	1	no	—
538	#11719919	—	4	1	no	—
539	#11719919	—	4	1	no	—
540	C₄×Dic₅₃	—	2	2	no	—
541	C₄×Dic₅₃	—	4	1	no	—
542	C₄×Dic₅₃	—	4	1	no	—
543	C₄×Dic₅₃	—	4	1	no	—
544	C₄×Dic₅₃	—	4	1	no	—
545	C₄×Dic₅₃	—	4	1	no	—
546	C₄×Dic₅₃	—	4	1	no	—
547	C₂³×C₅₃	—	2	1	no	—
548	C₂³×C₅₃	—	2	1	no	—
549	C₂³×C₅₃	—	2	1	no	—
550	C₂³×C₅₃	—	2	1	no	—
551	C₂³×C₅₃	—	2	1	no	—
552	C₂³×C₅₃	—	2	1	no	—
553	C₂³×C₅₃	—	2	1	no	—
554	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
555	C₂²×D₅₃	—	2	1	no	—
556	C₂²×D₅₃	—	2	1	no	—
557	C₂²×D₅₃	—	2	1	no	—
558	C₂²×D₅₃	—	2	1	no	—
559	C₂²×D₅₃	—	2	1	no	—
560	C₂²×D₅₃	—	2	1	no	—
561	C₂²×D₅₃	—	2	1	no	—
562	C₂²×D₅₃	—	2	1	no	—
563	C₂²×D₅₃	—	2	1	no	—
564	C₂²×D₅₃	—	2	1	no	—
565	C₂²×D₅₃	—	2	1	no	—
566	C₂²×D₅₃	—	2	1	no	—
567	C₂²×D₅₃	—	2	1	no	—
568	C₂²×D₅₃	—	2	1	no	—
569	C₂²×D₅₃	—	2	1	no	—
570	C₂²×D₅₃	—	2	1	no	—
571	C₂²×D₅₃	—	2	1	no	—
572	C₂²×D₅₃	—	2	1	no	—
573	C₂²×D₅₃	—	2	1	no	—
574	C₂²×D₅₃	—	2	1	no	—
575	C₂²×D₅₃	—	2	1	no	—
576	C₂²×D₅₃	—	2	1	no	—
577	C₂²×D₅₃	—	2	1	no	—
578	C₂²×D₅₃	—	2	1	no	—
579	C₂²×D₅₃	—	2	1	no	—
580	C₂²×D₅₃	—	4	4	no	—
581	C₂²×D₅₃	—	4	4	no	—
582	C₂²×D₅₃	—	4	4	no	—
583	C₂²×D₅₃	—	8	2	no	—
584	C₂²×D₅₃	—	8	2	no	—
585	C₂²×D₅₃	—	8	2	no	—
586	C₂²×D₅₃	—	8	2	no	—
587	C₂²×D₅₃	C₂×#41	1	2	yes	—
588	C₂²×D₅₃	H(5,𝔽₂)	1	2	yes	—
589	C₂²×D₅₃	2₋¹⁺⁴	1	2	yes	—
590	C₂×C₄×C₅₃	—	2	1	no	—
591	C₂×C₄×C₅₃	—	2	1	no	—
592	C₂×C₄×C₅₃	—	2	1	no	—
593	C₂×C₄×C₅₃	—	2	1	no	—
594	C₂×C₄×C₅₃	—	2	1	no	—
595	C₂×C₄×C₅₃	—	2	1	no	—
596	C₂×C₄×C₅₃	—	2	1	no	—
597	C₂×C₄×C₅₃	—	2	1	no	—
598	C₂×C₄×C₅₃	—	2	1	no	—
599	C₂×C₄×C₅₃	—	2	1	no	—
600	C₂×C₄×C₅₃	—	2	1	no	—
601	C₂×C₄×C₅₃	—	2	1	no	—
602	C₂×C₄×C₅₃	—	2	1	no	—
603	C₂×C₄×C₅₃	—	2	1	no	—
604	C₂×C₄×C₅₃	—	2	1	no	—
605	C₂×C₄×C₅₃	—	2	1	no	—
606	C₂×C₄×C₅₃	—	2	1	no	—
607	C₂×C₄×C₅₃	—	2	1	no	—
608	C₂×C₄×C₅₃	—	2	1	no	—
609	C₂×C₄×C₅₃	—	2	1	no	—
610	C₂×C₄×C₅₃	—	2	1	no	—
611	C₂×C₄×C₅₃	—	2	1	no	—
612	C₂×C₄×C₅₃	—	2	1	no	—
613	C₂×C₄×C₅₃	—	2	1	no	—
614	C₂×C₄×C₅₃	—	2	1	no	—
615	C₂×C₄×C₅₃	—	2	1	no	—
616	C₂×C₄×C₅₃	—	2	1	no	—
617	C₂×C₄×C₅₃	—	2	1	no	—
618	C₂×C₄×C₅₃	—	2	1	no	—
619	C₂×C₄×C₅₃	—	2	1	no	—
620	C₂×C₄×C₅₃	—	2	1	no	—
621	C₂×C₄×C₅₃	—	2	1	no	—
622	C₂×C₄×C₅₃	—	2	1	no	—
623	C₂×C₄×C₅₃	—	2	1	no	—
624	C₂×C₄×C₅₃	—	2	1	no	—
625	C₂×C₄×C₅₃	—	2	1	no	—
626	C₂×C₄×C₅₃	—	2	1	no	—
627	C₂×C₄×C₅₃	—	2	1	no	—
628	C₂×C₄×C₅₃	—	2	1	no	—
629	C₂×C₄×C₅₃	—	2	1	no	—
630	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
631	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
632	C₂²⋊D₅₃	—	8	2	no	—
633	C₂²⋊D₅₃	—	8	2	no	—
634	C₂×Dic₅₃	—	2	1	no	—
635	C₂×Dic₅₃	—	2	1	no	—
636	C₂×Dic₅₃	—	2	1	no	—
637	C₂×Dic₅₃	—	2	1	no	—
638	C₂×Dic₅₃	—	2	1	no	—
639	C₂×Dic₅₃	—	2	1	no	—
640	C₂×Dic₅₃	—	2	1	no	—
641	C₂×Dic₅₃	—	2	1	no	—
642	C₂×Dic₅₃	—	2	1	no	—
643	C₂×Dic₅₃	—	2	1	no	—
644	C₂×Dic₅₃	—	2	1	no	—
645	C₂×Dic₅₃	—	2	1	no	—
646	C₂×Dic₅₃	—	2	1	no	—
647	C₂×Dic₅₃	—	2	1	no	—
648	C₂×Dic₅₃	—	2	1	no	—
649	C₂×Dic₅₃	—	2	1	no	—
650	C₂×Dic₅₃	—	2	1	no	—
651	C₂×Dic₅₃	—	2	1	no	—
652	C₂×Dic₅₃	—	2	1	no	—
653	C₂×Dic₅₃	—	2	1	no	—
654	C₂×Dic₅₃	—	2	1	no	—
655	C₂×Dic₅₃	—	2	1	no	—
656	C₂×Dic₅₃	—	2	1	no	—
657	C₂×Dic₅₃	—	2	1	no	—
658	C₂×Dic₅₃	—	2	1	no	—
659	C₂×Dic₅₃	—	2	1	no	—
660	C₂×Dic₅₃	—	2	1	no	—
661	C₂×Dic₅₃	—	2	1	no	—
662	C₂×Dic₅₃	—	2	1	no	—
663	C₂×Dic₅₃	—	2	1	no	—
664	C₂×Dic₅₃	—	2	1	no	—
665	C₂×Dic₅₃	—	2	1	no	—
666	C₂×Dic₅₃	—	2	1	no	—
667	C₂×Dic₅₃	—	2	1	no	—
668	C₂×Dic₅₃	C₂×#41	1	2	yes	—
669	C₂×Dic₅₃	H(5,𝔽₂)	1	2	yes	—
670	D₂₁₂	—	4	4	no	—
671	D₂₁₂	—	4	4	no	—
672	D₂₁₂	—	8	2	no	—
673	D₂₁₂	—	8	2	no	—
674	D₂₁₂	—	8	2	no	—
675	C₄×D₅₃	—	4	4	no	—
676	C₄×D₅₃	—	4	4	no	—
677	C₄×D₅₃	—	4	4	no	—
678	C₄×D₅₃	—	4	4	no	—
679	C₄×D₅₃	—	8	2	no	—
680	C₄×D₅₃	—	8	2	no	—
681	C₄×D₅₃	—	8	2	no	—
682	C₄×D₅₃	—	8	2	no	—
683	Dic₁₀₆	—	8	2	no	—
684	Dic₁₀₆	—	8	2	no	—
685	Dic₁₀₆	—	8	2	no	—
686	#36766	—	53	1	no	maximal, Sylow
687	C₂²×C₅₃	—	4	1	no	—
688	C₂²×C₅₃	—	4	1	no	—
689	C₂²×C₅₃	—	4	1	no	—
690	C₂²×C₅₃	—	4	1	no	—
691	C₂²×C₅₃	—	4	1	no	—
692	C₂²×C₅₃	—	4	1	no	—
693	C₂²×C₅₃	—	4	1	no	—
694	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
695	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
696	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
697	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
698	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
699	C₂²×C₅₃	#585	1	1	yes	characteristic
700	C₂²×C₅₃	#585	1	1	yes	characteristic
701	C₂×D₅₃	—	2	2	no	—
702	C₂×D₅₃	—	2	2	no	—
703	C₂×D₅₃	—	2	2	no	—
704	C₂×D₅₃	—	2	2	no	—
705	C₂×D₅₃	—	2	2	no	—
706	C₂×D₅₃	—	2	2	no	—
707	C₂×D₅₃	—	4	1	no	—
708	C₂×D₅₃	—	4	1	no	—
709	C₂×D₅₃	—	4	1	no	—
710	C₂×D₅₃	—	4	1	no	—
711	C₂×D₅₃	—	4	1	no	—
712	C₂×D₅₃	—	4	1	no	—
713	C₂×D₅₃	—	4	1	no	—
714	C₂×D₅₃	—	4	1	no	—
715	C₂×D₅₃	—	4	1	no	—
716	C₂×D₅₃	—	4	1	no	—
717	C₂×D₅₃	—	4	1	no	—
718	C₂×D₅₃	—	4	1	no	—
719	C₂×D₅₃	—	4	1	no	—
720	C₂×D₅₃	—	4	1	no	—
721	C₂×D₅₃	—	4	1	no	—
722	C₂×D₅₃	—	4	1	no	—
723	C₂×D₅₃	—	4	1	no	—
724	C₂×D₅₃	—	4	1	no	—
725	C₂×D₅₃	—	4	1	no	—
726	C₂×D₅₃	—	4	1	no	—
727	C₂×D₅₃	—	4	1	no	—
728	C₂×D₅₃	—	8	8	no	—
729	C₂×D₅₃	#542	1	4	yes	—
730	C₄×C₅₃	—	2	2	no	—
731	C₄×C₅₃	—	2	2	no	—
732	C₄×C₅₃	—	4	1	no	—
733	C₄×C₅₃	—	4	1	no	—
734	C₄×C₅₃	—	4	1	no	—
735	C₄×C₅₃	—	4	1	no	—
736	C₄×C₅₃	—	4	1	no	—
737	C₄×C₅₃	—	4	1	no	—
738	C₄×C₅₃	—	4	1	no	—
739	C₄×C₅₃	—	4	1	no	—
740	C₄×C₅₃	—	4	1	no	—
741	C₄×C₅₃	—	4	1	no	—
742	C₄×C₅₃	—	4	1	no	—
743	C₄×C₅₃	—	4	1	no	—
744	Dic₅₃	—	2	2	no	—
745	Dic₅₃	—	2	2	no	—
746	Dic₅₃	—	4	1	no	—
747	Dic₅₃	—	4	1	no	—
748	Dic₅₃	—	4	1	no	—
749	Dic₅₃	—	4	1	no	—
750	Dic₅₃	—	4	1	no	—
751	Dic₅₃	—	4	1	no	—
752	Dic₅₃	—	4	1	no	—
753	Dic₅₃	—	4	1	no	—
754	Dic₅₃	—	4	1	no	—
755	Dic₅₃	—	4	1	no	—
756	#2857	—	53	1	no	—
757	#2850	—	53	1	no	—
758	#2801	—	53	1	no	—
759	#2801	—	53	1	no	—
760	#2795	—	53	1	no	—
761	#2795	—	53	1	no	—
762	#2773	—	53	1	no	—
763	#2773	D₅₃	1	1	yes	characteristic, complemented
764	#2759	—	53	1	no	—
765	#2759	—	53	1	no	—
766	#2757	—	53	1	no	—
767	#2757	—	53	1	no	—
768	#2730	—	53	1	no	—
769	#2730	—	53	1	no	—
770	#2710	—	53	1	no	—
771	#2710	—	53	1	no	—
772	#2674	—	53	1	no	—
773	#2674	—	53	1	no	—
774	#2626	—	53	1	no	—
775	#2617	—	53	1	no	—
776	#2510	—	53	1	no	—
777	#2510	—	53	1	no	—
778	#2472	—	53	1	no	—
779	#2472	—	53	1	no	—
780	#2449	—	53	1	no	—
781	#2449	—	53	1	no	—
782	#2418	—	53	1	no	—
783	#2418	—	53	1	no	—
784	#2329	—	53	1	no	—
785	#2325	—	53	1	no	—
786	C₂×#388	—	53	1	no	—
787	C₂×C₅₃	—	8	1	no	—
788	C₂×C₅₃	C₂×#542	1	1	yes	characteristic
789	C₂×C₅₃	#3505	1	1	yes	characteristic
790	C₂×C₅₃	#3506	1	1	yes	characteristic
791	C₂×C₅₃	#3535	1	1	yes	characteristic
792	C₂×C₅₃	#3537	1	1	yes	characteristic
793	C₂×C₅₃	#3560	1	1	yes	characteristic
794	C₂×C₅₃	#3561	1	1	yes	characteristic
795	D₅₃	—	2	4	no	—
796	D₅₃	—	8	1	no	—
797	D₅₃	—	8	1	no	—
798	D₅₃	—	8	1	no	—
799	C₂×C₄⋊Q₈	—	53	1	no	—
800	C₂×#124	—	53	1	no	—
801	C₂×#124	—	53	1	no	—
802	C₂×#124	—	53	1	no	—
803	C₂×#123	—	53	1	no	—
804	C₂×#123	—	53	1	no	—
805	C₂×C₂²⋊Q₈	—	53	1	no	—
806	C₂×C₂²⋊Q₈	—	53	1	no	—
807	C₂×C₂²⋊Q₈	—	53	1	no	—
808	C₂×C₂²⋊Q₈	—	53	1	no	—
809	C₂×C₂²⋊Q₈	—	53	1	no	—
810	C₂×#121	—	53	1	no	—
811	C₂×#120	—	53	1	no	—
812	C₂×#120	—	53	1	no	—
813	C₂×C₄×D₄	—	53	1	no	—
814	C₂×C₄×D₄	—	53	1	no	—
815	C₂²×C₄⋊C₄	—	53	1	no	—
816	C₂²×C₂²⋊C₄	—	53	1	no	—
817	C₂²×C₂²⋊C₄	—	53	1	no	—
818	C₂²×C₂²⋊C₄	—	53	1	no	—
819	C₂²×C₄²	—	53	1	no	—
820	#401	—	53	1	no	—
821	#401	—	53	1	no	—
822	#400	—	53	1	no	—
823	#400	C₂×D₅₃	1	1	yes	characteristic, complemented
824	#399	—	53	1	no	—
825	#399	—	53	1	no	—
826	#399	—	53	1	no	—
827	#399	—	53	1	no	—
828	#399	C₂×D₅₃	1	1	yes	characteristic
829	#399	C₂×D₅₃	1	1	yes	characteristic
830	#398	—	53	1	no	—
831	#398	C₂×D₅₃	1	1	yes	characteristic, complemented
832	#397	—	53	1	no	—
833	#397	—	53	1	no	—
834	#397	—	53	1	no	—
835	#397	—	53	1	no	—
836	#397	—	53	1	no	—
837	#397	—	53	1	no	—
838	#397	—	53	1	no	—
839	#397	—	53	1	no	—
840	#397	C₂×D₅₃	1	1	yes	characteristic
841	#397	C₂×D₅₃	1	1	yes	characteristic
842	#396	—	53	1	no	—
843	#396	—	53	1	no	—
844	#396	—	53	1	no	—
845	#396	—	53	1	no	—
846	#396	—	53	1	no	—
847	#396	—	53	1	no	—
848	#395	—	53	1	no	—
849	#395	—	53	1	no	—
850	#394	—	53	1	no	—
851	#394	—	53	1	no	—
852	#394	—	53	1	no	—
853	#394	—	53	1	no	—
854	#394	—	53	1	no	—
855	#394	—	53	1	no	—
856	#394	—	53	1	no	—
857	#394	—	53	1	no	—
858	#394	—	53	1	no	—
859	#394	—	53	1	no	—
860	#394	—	53	1	no	—
861	#394	—	53	1	no	—
862	#393	—	53	1	no	—
863	#393	—	53	1	no	—
864	#393	—	53	1	no	—
865	#393	—	53	1	no	—
866	#392	—	53	1	no	—
867	#392	—	53	1	no	—
868	#391	—	53	1	no	—
869	#391	—	53	1	no	—
870	#391	—	53	1	no	—
871	#391	—	53	1	no	—
872	#391	—	53	1	no	—
873	#390	—	53	1	no	—
874	#390	—	53	1	no	—
875	#390	—	53	1	no	—
876	#389	—	53	1	no	—
877	#389	—	53	1	no	—
878	#389	—	53	1	no	—
879	#389	—	53	1	no	—
880	#389	—	53	1	no	—
881	#389	—	53	1	no	—
882	#389	C₂×D₅₃	1	1	yes	characteristic, complemented
883	#389	C₂×D₅₃	1	1	yes	characteristic, complemented
884	#388	—	53	1	no	—
885	#388	—	53	1	no	—
886	#388	—	53	1	no	—
887	#388	—	53	1	no	—
888	#388	—	53	1	no	—
889	#388	—	53	1	no	—
890	#388	—	53	1	no	—
891	#388	—	53	1	no	—
892	#388	—	53	1	no	—
893	#388	—	53	1	no	—
894	#388	—	53	1	no	—
895	#388	—	53	1	no	—
896	#388	—	53	1	no	—
897	#388	—	53	1	no	—
898	#388	—	53	1	no	—
899	#388	—	53	1	no	—
900	#388	—	53	1	no	—
901	#388	—	53	1	no	—
902	#388	—	53	1	no	—
903	#388	—	53	1	no	—
904	#388	—	53	1	no	—
905	#388	—	53	1	no	—
906	#388	—	53	1	no	—
907	#388	C₂×D₅₃	1	1	yes	characteristic
908	#388	C₂×D₅₃	1	1	yes	characteristic
909	#388	C₂×D₅₃	1	1	yes	characteristic
910	#387	—	53	1	no	—
911	#387	—	53	1	no	—
912	#387	—	53	1	no	—
913	#387	—	53	1	no	—
914	#387	—	53	1	no	—
915	#387	—	53	1	no	—
916	#387	—	53	1	no	—
917	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
918	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
919	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
920	#386	—	53	1	no	—
921	#386	—	53	1	no	—
922	#386	—	53	1	no	—
923	#386	—	53	1	no	—
924	#386	—	53	1	no	—
925	#386	—	53	1	no	—
926	#386	—	53	1	no	—
927	#386	—	53	1	no	—
928	#386	—	53	1	no	—
929	#386	—	53	1	no	—
930	#386	—	53	1	no	—
931	#386	—	53	1	no	—
932	#385	—	53	1	no	—
933	#385	—	53	1	no	—
934	#385	—	53	1	no	—
935	#385	—	53	1	no	—
936	#385	—	53	1	no	—
937	#385	—	53	1	no	—
938	#385	—	53	1	no	—
939	#385	—	53	1	no	—
940	#384	—	53	1	no	—
941	#383	—	53	1	no	—
942	#383	—	53	1	no	—
943	#382	C₂×D₅₃	1	1	yes	characteristic, complemented
944	#380	—	53	1	no	—
945	#380	—	53	1	no	—
946	#380	—	53	1	no	—
947	#380	—	53	1	no	—
948	#379	—	53	1	no	—
949	#379	—	53	1	no	—
950	C₄×C₂²⋊C₄	—	53	1	no	—
951	C₄×C₂²⋊C₄	—	53	1	no	—
952	C₂×#95	—	53	1	no	—
953	C₂×#95	—	53	1	no	—
954	C₅₃	#36766	1	1	yes	characteristic, complemented, Sylow
955	C₂⁵	—	53	1	no	—
956	C₂²×Q₈	—	53	1	no	—
957	C₂²×Q₈	—	53	1	no	—
958	C₂²×Q₈	—	53	1	no	—
959	C₂²×D₄	—	53	1	no	—
960	C₂²×D₄	—	53	1	no	—
961	C₂²×D₄	—	53	1	no	—
962	C₂²×D₄	—	53	1	no	—
963	C₂²×D₄	—	53	1	no	—
964	C₂²×D₄	—	53	1	no	—
965	C₂²×D₄	—	53	1	no	—
966	C₂³×C₄	—	53	1	no	—
967	C₂³×C₄	—	53	1	no	—
968	C₂³×C₄	—	53	1	no	—
969	C₂³×C₄	—	53	1	no	—
970	C₂³×C₄	—	53	1	no	—
971	C₂³×C₄	—	53	1	no	—
972	C₂³×C₄	—	53	1	no	—
973	C₂³×C₄	—	53	1	no	—
974	C₄⋊Q₈	—	212	2	no	—
975	#124	—	212	2	no	—
976	#124	—	212	2	no	—
977	#124	—	212	2	no	—
978	#123	—	212	2	no	—
979	#123	—	212	2	no	—
980	C₂²⋊Q₈	—	106	4	no	—
981	C₂²⋊Q₈	—	212	2	no	—
982	C₂²⋊Q₈	—	212	2	no	—
983	C₂²⋊Q₈	—	212	2	no	—
984	C₂²⋊Q₈	—	212	2	no	—
985	#121	—	106	4	no	—
986	#120	—	212	2	no	—
987	#120	—	212	2	no	—
988	C₄×D₄	—	212	2	no	—
989	C₄×D₄	—	212	2	no	—
990	C₂×C₄⋊C₄	—	53	1	no	—
991	C₂×C₄⋊C₄	—	53	1	no	—
992	C₂×C₄⋊C₄	—	53	1	no	—
993	C₂×C₄⋊C₄	—	53	1	no	—
994	C₂×C₄⋊C₄	—	53	1	no	—
995	C₂×C₄⋊C₄	—	53	1	no	—
996	C₂×C₄⋊C₄	—	53	1	no	—
997	C₂×C₄⋊C₄	—	53	1	no	—
998	C₂×C₄⋊C₄	—	53	1	no	—
999	C₂×C₄⋊C₄	—	53	1	no	—
1000	C₂×C₄⋊C₄	—	53	1	no	—
1001	C₂×C₄⋊C₄	—	53	1	no	—
1002	C₂×C₄⋊C₄	—	53	1	no	—
1003	C₂×C₄⋊C₄	—	53	1	no	—
1004	C₂×C₄⋊C₄	—	53	1	no	—
1005	C₂×C₄⋊C₄	—	53	1	no	—
1006	C₂×C₄⋊C₄	—	53	1	no	—
1007	C₂×C₄⋊C₄	—	53	1	no	—
1008	C₂×C₄⋊C₄	—	53	1	no	—
1009	C₂×C₄⋊C₄	—	53	1	no	—
1010	C₂×C₄⋊C₄	—	53	1	no	—
1011	C₂×C₄⋊C₄	—	212	2	no	—
1012	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1013	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1014	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1015	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1016	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1017	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1018	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1019	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1020	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1021	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1022	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1023	C₂×C₂²⋊C₄	—	53	1	no	—
1024	C₂×C₂²⋊C₄	—	53	1	no	—
1025	C₂×C₂²⋊C₄	—	53	1	no	—
1026	C₂×C₂²⋊C₄	—	53	1	no	—
1027	C₂×C₂²⋊C₄	—	53	1	no	—
1028	C₂×C₂²⋊C₄	—	53	1	no	—
1029	C₂×C₂²⋊C₄	—	53	1	no	—
1030	C₂×C₂²⋊C₄	—	53	1	no	—
1031	C₂×C₂²⋊C₄	—	53	1	no	—
1032	C₂×C₂²⋊C₄	—	53	1	no	—
1033	C₂×C₂²⋊C₄	—	53	1	no	—
1034	C₂×C₂²⋊C₄	—	53	1	no	—
1035	C₂×C₂²⋊C₄	—	53	1	no	—
1036	C₂×C₂²⋊C₄	—	53	1	no	—
1037	C₂×C₂²⋊C₄	—	53	1	no	—
1038	C₂×C₂²⋊C₄	—	53	1	no	—
1039	C₂×C₂²⋊C₄	—	53	1	no	—
1040	C₂×C₂²⋊C₄	—	53	1	no	—
1041	C₂×C₂²⋊C₄	—	53	1	no	—
1042	C₂×C₂²⋊C₄	—	53	1	no	—
1043	C₂×C₂²⋊C₄	—	53	1	no	—
1044	C₂×C₂²⋊C₄	—	53	1	no	—
1045	C₂×C₂²⋊C₄	—	53	1	no	—
1046	C₂×C₂²⋊C₄	—	53	1	no	—
1047	C₂×C₂²⋊C₄	—	53	1	no	—
1048	C₂×C₂²⋊C₄	—	53	1	no	—
1049	C₂×C₂²⋊C₄	—	53	1	no	—
1050	C₂×C₂²⋊C₄	—	53	1	no	—
1051	C₂×C₂²⋊C₄	—	53	1	no	—
1052	C₂×C₂²⋊C₄	—	53	1	no	—
1053	C₂×C₂²⋊C₄	—	53	1	no	—
1054	C₂×C₂²⋊C₄	—	53	1	no	—
1055	C₂×C₂²⋊C₄	—	53	1	no	—
1056	C₂×C₂²⋊C₄	—	53	1	no	—
1057	C₂×C₂²⋊C₄	—	53	1	no	—
1058	C₂×C₂²⋊C₄	—	53	1	no	—
1059	C₂×C₂²⋊C₄	—	53	1	no	—
1060	C₂×C₂²⋊C₄	—	53	1	no	—
1061	C₂×C₂²⋊C₄	—	53	1	no	—
1062	C₂×C₂²⋊C₄	—	53	1	no	—
1063	C₂×C₂²⋊C₄	—	53	1	no	—
1064	C₂×C₂²⋊C₄	—	53	1	no	—
1065	C₂×C₂²⋊C₄	—	53	1	no	—
1066	C₂×C₂²⋊C₄	—	106	4	no	—
1067	C₂×C₂²⋊C₄	—	212	2	no	—
1068	C₂×C₂²⋊C₄	—	212	2	no	—
1069	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1070	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1071	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1072	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1073	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1074	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1075	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1076	C₂×C₄²	—	53	1	no	—
1077	C₂×C₄²	—	53	1	no	—
1078	C₂×C₄²	—	53	1	no	—
1079	C₂×C₄²	—	53	1	no	—
1080	C₂×C₄²	—	53	1	no	—
1081	C₂×C₄²	—	53	1	no	—
1082	C₂×C₄²	—	53	1	no	—
1083	C₂×C₄²	—	212	2	no	—
1084	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1085	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1086	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1087	#95	—	53	1	no	—
1088	#95	—	53	1	no	—
1089	#95	—	53	1	no	—
1090	#95	—	53	1	no	—
1091	#95	—	53	1	no	—
1092	#95	—	53	1	no	—
1093	#95	—	53	1	no	—
1094	#95	—	53	1	no	—
1095	#95	—	53	1	no	—
1096	#95	—	53	1	no	—
1097	#95	—	53	1	no	—
1098	#95	—	53	1	no	—
1099	#95	—	53	1	no	—
1100	#95	—	53	1	no	—
1101	#95	—	53	1	no	—
1102	#95	—	53	1	no	—
1103	#95	—	53	1	no	—
1104	#95	—	53	1	no	—
1105	#95	—	53	1	no	—
1106	#95	—	53	1	no	—
1107	#95	—	53	1	no	—
1108	#95	—	53	1	no	—
1109	#95	—	53	1	no	—
1110	#95	—	53	1	no	—
1111	#95	—	53	1	no	—
1112	#95	—	53	1	no	—
1113	#95	—	53	1	no	—
1114	#95	—	53	1	no	—
1115	#95	—	53	1	no	—
1116	#95	—	53	1	no	—
1117	#95	C₂²×D₅₃	1	1	yes	characteristic
1118	#95	C₂²×D₅₃	1	1	yes	characteristic
1119	#95	C₂²×D₅₃	1	1	yes	characteristic
1120	#95	C₂²×D₅₃	1	1	yes	characteristic
1121	#95	C₂²×D₅₃	1	1	yes	characteristic
1122	#95	C₂²×D₅₃	1	1	yes	characteristic
1123	#95	C₂²×D₅₃	1	1	yes	characteristic
1124	#95	C₂²×D₅₃	1	1	yes	characteristic
1125	#95	C₂²×D₅₃	1	1	yes	characteristic
1126	#95	C₂²×D₅₃	1	1	yes	characteristic
1127	#95	C₂²×D₅₃	1	1	yes	characteristic
1128	#95	C₂²×D₅₃	1	1	yes	characteristic
1129	#95	C₂²×D₅₃	1	1	yes	characteristic
1130	#95	C₂²×D₅₃	1	1	yes	characteristic
1131	C₂⁴	—	53	1	no	—
1132	C₂⁴	—	53	1	no	—
1133	C₂⁴	—	53	1	no	—
1134	C₂⁴	—	53	1	no	—
1135	C₂⁴	—	106	2	no	—
1136	C₂⁴	—	106	2	no	—
1137	C₂⁴	—	106	2	no	—
1138	C₂⁴	—	212	1	no	—
1139	C₂⁴	—	212	1	no	—
1140	C₂⁴	—	212	1	no	—
1141	C₂⁴	—	212	1	no	—
1142	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1143	C₂×Q₈	—	106	2	no	—
1144	C₂×Q₈	—	106	2	no	—
1145	C₂×Q₈	—	106	2	no	—
1146	C₂×Q₈	—	212	1	no	—
1147	C₂×Q₈	—	212	1	no	—
1148	C₂×Q₈	—	212	1	no	—
1149	C₂×Q₈	—	212	1	no	—
1150	C₂×Q₈	—	212	1	no	—
1151	C₂×Q₈	—	212	1	no	—
1152	C₂×D₄	—	106	2	no	—
1153	C₂×D₄	—	106	2	no	—
1154	C₂×D₄	—	106	2	no	—
1155	C₂×D₄	—	106	2	no	—
1156	C₂×D₄	—	106	2	no	—
1157	C₂×D₄	—	106	2	no	—
1158	C₂×D₄	—	106	2	no	—
1159	C₂×D₄	—	212	1	no	—
1160	C₂×D₄	—	212	1	no	—
1161	C₂×D₄	—	212	1	no	—
1162	C₂×D₄	—	212	1	no	—
1163	C₂×D₄	—	212	1	no	—
1164	C₂×D₄	—	212	1	no	—
1165	C₂×D₄	—	212	1	no	—
1166	C₂×D₄	—	212	1	no	—
1167	C₂×D₄	—	212	1	no	—
1168	C₂×D₄	—	212	1	no	—
1169	C₂×D₄	—	212	1	no	—
1170	C₂×D₄	—	212	1	no	—
1171	C₂×D₄	—	212	1	no	—
1172	C₂×D₄	—	212	1	no	—
1173	C₂²×C₄	—	53	1	no	—
1174	C₂²×C₄	—	53	1	no	—
1175	C₂²×C₄	—	53	4	no	—
1176	C₂²×C₄	—	53	1	no	—
1177	C₂²×C₄	—	53	1	no	—
1178	C₂²×C₄	—	53	1	no	—
1179	C₂²×C₄	—	53	1	no	—
1180	C₂²×C₄	—	53	1	no	—
1181	C₂²×C₄	—	53	1	no	—
1182	C₂²×C₄	—	53	1	no	—
1183	C₂²×C₄	—	53	1	no	—
1184	C₂²×C₄	—	53	1	no	—
1185	C₂²×C₄	—	53	1	no	—
1186	C₂²×C₄	—	106	2	no	—
1187	C₂²×C₄	—	106	2	no	—
1188	C₂²×C₄	—	106	2	no	—
1189	C₂²×C₄	—	106	2	no	—
1190	C₂²×C₄	—	106	2	no	—
1191	C₂²×C₄	—	106	2	no	—
1192	C₂²×C₄	—	106	2	no	—
1193	C₂²×C₄	—	212	1	no	—
1194	C₂²×C₄	—	212	1	no	—
1195	C₂²×C₄	—	212	1	no	—
1196	C₂²×C₄	—	212	1	no	—
1197	C₂²×C₄	—	212	1	no	—
1198	C₂²×C₄	—	212	1	no	—
1199	C₂²×C₄	—	212	1	no	—
1200	C₂²×C₄	—	212	1	no	—
1201	C₂²×C₄	—	212	1	no	—
1202	C₂²×C₄	—	212	1	no	—
1203	C₂²×C₄	—	212	1	no	—
1204	C₂²×C₄	—	212	1	no	—
1205	C₂²×C₄	—	212	1	no	—
1206	C₂²×C₄	—	212	1	no	—
1207	C₂²×C₄	—	212	1	no	—
1208	C₂²×C₄	—	212	1	no	—
1209	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1210	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1211	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1212	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1213	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1214	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1215	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1216	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1217	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1218	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1219	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1220	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1221	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1222	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1223	C₄⋊C₄	—	2	2	no	—
1224	C₄⋊C₄	—	2	2	no	—
1225	C₄⋊C₄	—	2	2	no	—
1226	C₄⋊C₄	—	4	1	no	—
1227	C₄⋊C₄	—	4	1	no	—
1228	C₄⋊C₄	—	4	1	no	—
1229	C₄⋊C₄	—	4	1	no	—
1230	C₄⋊C₄	—	4	1	no	—
1231	C₄⋊C₄	—	4	1	no	—
1232	C₄⋊C₄	—	4	1	no	—
1233	C₄⋊C₄	—	4	1	no	—
1234	C₄⋊C₄	—	106	2	no	—
1235	C₄⋊C₄	—	106	2	no	—
1236	C₄⋊C₄	—	106	2	no	—
1237	C₄⋊C₄	—	106	2	no	—
1238	C₄⋊C₄	—	106	2	no	—
1239	C₄⋊C₄	—	212	1	no	—
1240	C₄⋊C₄	—	212	1	no	—
1241	C₄⋊C₄	—	212	1	no	—
1242	C₄⋊C₄	—	212	1	no	—
1243	C₄⋊C₄	—	212	1	no	—
1244	C₄⋊C₄	—	212	1	no	—
1245	C₄⋊C₄	—	212	1	no	—
1246	C₄⋊C₄	—	212	1	no	—
1247	C₄⋊C₄	—	212	1	no	—
1248	C₄⋊C₄	—	212	1	no	—
1249	C₄⋊C₄	—	212	1	no	—
1250	C₄⋊C₄	—	212	1	no	—
1251	C₄⋊C₄	—	212	1	no	—
1252	C₄⋊C₄	—	212	1	no	—
1253	C₄⋊C₄	—	212	1	no	—
1254	C₄⋊C₄	—	212	1	no	—
1255	C₂²⋊C₄	—	2	2	no	—
1256	C₂²⋊C₄	—	2	2	no	—
1257	C₂²⋊C₄	—	4	1	no	—
1258	C₂²⋊C₄	—	4	1	no	—
1259	C₂²⋊C₄	—	4	1	no	—
1260	C₂²⋊C₄	—	4	1	no	—
1261	C₂²⋊C₄	—	4	1	no	—
1262	C₂²⋊C₄	—	106	2	no	—
1263	C₂²⋊C₄	—	106	2	no	—
1264	C₂²⋊C₄	—	106	2	no	—
1265	C₂²⋊C₄	—	106	2	no	—
1266	C₂²⋊C₄	—	106	2	no	—
1267	C₂²⋊C₄	—	106	2	no	—
1268	C₂²⋊C₄	—	106	2	no	—
1269	C₂²⋊C₄	—	106	2	no	—
1270	C₂²⋊C₄	—	106	2	no	—
1271	C₂²⋊C₄	—	106	2	no	—
1272	C₂²⋊C₄	—	106	2	no	—
1273	C₂²⋊C₄	—	106	2	no	—
1274	C₂²⋊C₄	—	106	2	no	—
1275	C₂²⋊C₄	—	106	2	no	—
1276	C₂²⋊C₄	—	106	2	no	—
1277	C₂²⋊C₄	—	106	2	no	—
1278	C₂²⋊C₄	—	106	2	no	—
1279	C₂²⋊C₄	—	106	2	no	—
1280	C₂²⋊C₄	—	212	1	no	—
1281	C₂²⋊C₄	—	212	1	no	—
1282	C₂²⋊C₄	—	212	1	no	—
1283	C₂²⋊C₄	—	212	1	no	—
1284	C₂²⋊C₄	—	212	1	no	—
1285	C₂²⋊C₄	—	212	1	no	—
1286	C₂²⋊C₄	—	212	1	no	—
1287	C₂²⋊C₄	—	212	1	no	—
1288	C₂²⋊C₄	—	212	1	no	—
1289	C₂²⋊C₄	—	212	1	no	—
1290	C₂²⋊C₄	—	212	1	no	—
1291	C₂²⋊C₄	—	212	1	no	—
1292	C₂²⋊C₄	—	212	1	no	—
1293	C₂²⋊C₄	—	212	1	no	—
1294	C₂²⋊C₄	—	212	1	no	—
1295	C₂²⋊C₄	—	212	1	no	—
1296	C₂²⋊C₄	—	212	1	no	—
1297	C₂²⋊C₄	—	212	1	no	—
1298	C₂²⋊C₄	—	212	1	no	—
1299	C₂²⋊C₄	—	212	1	no	—
1300	C₂²⋊C₄	—	212	1	no	—
1301	C₂²⋊C₄	—	212	1	no	—
1302	C₂²⋊C₄	—	212	1	no	—
1303	C₂²⋊C₄	—	212	1	no	—
1304	C₂²⋊C₄	—	212	1	no	—
1305	C₄²	—	2	2	no	—
1306	C₄²	—	4	1	no	—
1307	C₄²	—	4	1	no	—
1308	C₄²	—	106	2	no	—
1309	C₄²	—	212	1	no	—
1310	C₄²	—	212	1	no	—
1311	C₄²	—	212	1	no	—
1312	C₄²	—	212	1	no	—
1313	C₄²	—	212	1	no	—
1314	C₄²	—	212	1	no	—
1315	C₂³	—	2	1	no	—
1316	C₂³	—	2	1	no	—
1317	C₂³	—	2	1	no	—
1318	C₂³	—	2	1	no	—
1319	C₂³	—	2	1	no	—
1320	C₂³	—	2	1	no	—
1321	C₂³	—	2	1	no	—
1322	C₂³	—	53	2	no	—
1323	C₂³	—	53	2	no	—
1324	C₂³	—	53	2	no	—
1325	C₂³	—	106	1	no	—
1326	C₂³	—	106	1	no	—
1327	C₂³	—	106	1	no	—
1328	C₂³	—	106	1	no	—
1329	C₂³	—	106	1	no	—
1330	C₂³	—	106	1	no	—
1331	C₂³	—	106	1	no	—
1332	C₂³	—	106	1	no	—
1333	C₂³	—	106	1	no	—
1334	C₂³	—	106	1	no	—
1335	C₂³	—	106	1	no	—
1336	C₂³	—	106	1	no	—
1337	C₂³	—	106	1	no	—
1338	C₂³	—	106	1	no	—
1339	C₂³	—	106	1	no	—
1340	C₂³	—	106	1	no	—
1341	C₂³	—	106	1	no	—
1342	C₂³	—	106	1	no	—
1343	C₂³	—	106	1	no	—
1344	C₂³	—	106	1	no	—
1345	C₂³	—	106	1	no	—
1346	C₂³	—	106	1	no	—
1347	C₂³	—	106	1	no	—
1348	C₂³	—	106	1	no	—
1349	C₂³	—	106	1	no	—
1350	C₂³	—	424	2	no	—
1351	C₂³	—	424	2	no	—
1352	C₂³	—	424	2	no	—
1353	C₂³	—	424	2	no	—
1354	C₂³	—	212	4	no	—
1355	C₂³	—	212	4	no	—
1356	C₂³	—	212	4	no	—
1357	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1358	Q₈	—	424	2	no	—
1359	Q₈	—	424	2	no	—
1360	Q₈	—	424	2	no	—
1361	D₄	—	424	2	no	—
1362	D₄	—	424	2	no	—
1363	D₄	—	424	2	no	—
1364	D₄	—	424	2	no	—
1365	D₄	—	424	2	no	—
1366	D₄	—	212	4	no	—
1367	D₄	—	212	4	no	—
1368	C₂×C₄	—	2	1	no	—
1369	C₂×C₄	—	2	1	no	—
1370	C₂×C₄	—	2	1	no	—
1371	C₂×C₄	—	2	1	no	—
1372	C₂×C₄	—	2	1	no	—
1373	C₂×C₄	—	2	1	no	—
1374	C₂×C₄	—	2	1	no	—
1375	C₂×C₄	—	2	1	no	—
1376	C₂×C₄	—	2	1	no	—
1377	C₂×C₄	—	2	1	no	—
1378	C₂×C₄	—	2	1	no	—
1379	C₂×C₄	—	2	1	no	—
1380	C₂×C₄	—	2	1	no	—
1381	C₂×C₄	—	2	1	no	—
1382	C₂×C₄	—	2	1	no	—
1383	C₂×C₄	—	2	1	no	—
1384	C₂×C₄	—	2	1	no	—
1385	C₂×C₄	—	2	1	no	—
1386	C₂×C₄	—	2	1	no	—
1387	C₂×C₄	—	2	1	no	—
1388	C₂×C₄	—	2	1	no	—
1389	C₂×C₄	—	2	1	no	—
1390	C₂×C₄	—	2	1	no	—
1391	C₂×C₄	—	2	1	no	—
1392	C₂×C₄	—	2	1	no	—
1393	C₂×C₄	—	2	1	no	—
1394	C₂×C₄	—	2	1	no	—
1395	C₂×C₄	—	2	1	no	—
1396	C₂×C₄	—	2	1	no	—
1397	C₂×C₄	—	2	1	no	—
1398	C₂×C₄	—	2	1	no	—
1399	C₂×C₄	—	2	1	no	—
1400	C₂×C₄	—	2	1	no	—
1401	C₂×C₄	—	2	1	no	—
1402	C₂×C₄	—	2	1	no	—
1403	C₂×C₄	—	2	1	no	—
1404	C₂×C₄	—	2	1	no	—
1405	C₂×C₄	—	2	1	no	—
1406	C₂×C₄	—	2	1	no	—
1407	C₂×C₄	—	2	1	no	—
1408	C₂×C₄	—	53	2	no	—
1409	C₂×C₄	—	53	2	no	—
1410	C₂×C₄	—	106	1	no	—
1411	C₂×C₄	—	106	1	no	—
1412	C₂×C₄	—	106	1	no	—
1413	C₂×C₄	—	106	1	no	—
1414	C₂×C₄	—	106	1	no	—
1415	C₂×C₄	—	106	1	no	—
1416	C₂×C₄	—	106	1	no	—
1417	C₂×C₄	—	106	1	no	—
1418	C₂×C₄	—	106	1	no	—
1419	C₂×C₄	—	106	1	no	—
1420	C₂×C₄	—	106	1	no	—
1421	C₂×C₄	—	106	1	no	—
1422	C₂×C₄	—	106	1	no	—
1423	C₂×C₄	—	106	1	no	—
1424	C₂×C₄	—	106	1	no	—
1425	C₂×C₄	—	106	1	no	—
1426	C₂×C₄	—	106	1	no	—
1427	C₂×C₄	—	106	1	no	—
1428	C₂×C₄	—	106	1	no	—
1429	C₂×C₄	—	106	1	no	—
1430	C₂×C₄	—	106	1	no	—
1431	C₂×C₄	—	106	1	no	—
1432	C₂×C₄	—	106	1	no	—
1433	C₂×C₄	—	106	1	no	—
1434	C₂×C₄	—	106	1	no	—
1435	C₂×C₄	—	106	1	no	—
1436	C₂×C₄	—	106	1	no	—
1437	C₂×C₄	—	106	1	no	—
1438	C₂×C₄	—	106	1	no	—
1439	C₂×C₄	—	106	1	no	—
1440	C₂×C₄	—	106	1	no	—
1441	C₂×C₄	—	106	1	no	—
1442	C₂×C₄	—	106	1	no	—
1443	C₂×C₄	—	106	1	no	—
1444	C₂×C₄	—	424	2	no	—
1445	C₂×C₄	—	424	2	no	—
1446	C₂×C₄	—	424	2	no	—
1447	C₂×C₄	—	424	2	no	—
1448	C₂×C₄	—	212	4	no	—
1449	C₂×C₄	—	212	4	no	—
1450	C₂×C₄	—	212	4	no	—
1451	C₂×C₄	—	212	4	no	—
1452	C₂×C₄	#41×D₅₃	1	2	yes	—
1453	C₂×C₄	#13133263	1	2	yes	—
1454	C₂²	—	4	1	no	—
1455	C₂²	—	4	1	no	—
1456	C₂²	—	4	1	no	—
1457	C₂²	—	4	1	no	—
1458	C₂²	—	4	1	no	—
1459	C₂²	—	4	1	no	—
1460	C₂²	—	4	1	no	—
1461	C₂²	—	53	4	no	—
1462	C₂²	—	106	2	no	—
1463	C₂²	—	106	2	no	—
1464	C₂²	—	106	2	no	—
1465	C₂²	—	106	2	no	—
1466	C₂²	—	106	2	no	—
1467	C₂²	—	106	2	no	—
1468	C₂²	—	424	8	no	—
1469	C₂²	—	212	1	no	—
1470	C₂²	—	212	1	no	—
1471	C₂²	—	212	1	no	—
1472	C₂²	—	212	1	no	—
1473	C₂²	—	212	1	no	—
1474	C₂²	—	212	1	no	—
1475	C₂²	—	212	1	no	—
1476	C₂²	—	212	1	no	—
1477	C₂²	—	212	1	no	—
1478	C₂²	—	212	1	no	—
1479	C₂²	—	212	1	no	—
1480	C₂²	—	212	1	no	—
1481	C₂²	—	212	1	no	—
1482	C₂²	—	212	1	no	—
1483	C₂²	—	212	1	no	—
1484	C₂²	—	212	1	no	—
1485	C₂²	—	212	1	no	—
1486	C₂²	—	212	1	no	—
1487	C₂²	—	212	1	no	—
1488	C₂²	—	212	1	no	—
1489	C₂²	—	212	1	no	—
1490	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1491	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1492	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1493	C₂²	C₂×#13133263	1	1	yes	characteristic
1494	C₂²	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1495	C₂²	#16811459	1	1	yes	characteristic
1496	C₂²	#16811460	1	1	yes	characteristic
1497	C₄	—	2	2	no	—
1498	C₄	—	2	2	no	—
1499	C₄	—	4	1	no	—
1500	C₄	—	4	1	no	—
1501	C₄	—	4	1	no	—
1502	C₄	—	4	1	no	—
1503	C₄	—	4	1	no	—
1504	C₄	—	4	1	no	—
1505	C₄	—	4	1	no	—
1506	C₄	—	4	1	no	—
1507	C₄	—	4	1	no	—
1508	C₄	—	4	1	no	—
1509	C₄	—	4	1	no	—
1510	C₄	—	4	1	no	—
1511	C₄	—	106	2	no	—
1512	C₄	—	106	2	no	—
1513	C₄	—	212	1	no	—
1514	C₄	—	212	1	no	—
1515	C₄	—	212	1	no	—
1516	C₄	—	212	1	no	—
1517	C₄	—	212	1	no	—
1518	C₄	—	212	1	no	—
1519	C₄	—	212	1	no	—
1520	C₄	—	212	1	no	—
1521	C₄	—	212	1	no	—
1522	C₄	—	212	1	no	—
1523	C₂	—	8	1	no	—
1524	C₂	—	106	4	no	—
1525	C₂	—	424	1	no	—
1526	C₂	—	424	1	no	—
1527	C₂	—	424	1	no	—
1528	C₂	#542×D₅₃	1	1	yes	characteristic
1529	C₂	#20288555	1	1	yes	characteristic
1530	C₂	#20288563	1	1	yes	characteristic
1531	C₂	#20288927	1	1	yes	characteristic
1532	C₂	#20288953	1	1	yes	characteristic
1533	C₂	#20289268	1	1	yes	characteristic
1534	C₂	#20289283	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator, socle, cosocle	C₂³×C₅₃	C₂⁵
Fitting	C₅₃×#2773	C₂
prime radical	#20280450	C₂
hypercenter	#2773	D₅₃
hypocenter	C₅₃	#36766
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #2773

Complements

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

N	H ≅ G/N	type
1. #20283066	C₂	semidirect
2. #20283017	C₂	semidirect
3. #20282621	C₂	semidirect
4. #20282620	C₂	semidirect
5. #20282549	C₂	semidirect
6. #20282542	C₂	semidirect
7. #20282254	C₂	semidirect
8. #20282077	C₂	semidirect
9. #20282075	C₂	semidirect
10. #20282058	C₂	semidirect
11. #20282057	C₂	semidirect
12. #20281719	C₂	semidirect
13. #20281716	C₂	semidirect
14. #20281460	C₂	semidirect
15. #20281458	C₂	semidirect
16. #20281001	C₂	semidirect
17. #20280999	C₂	semidirect
18. #20280521	C₂	semidirect
20. #20279276	C₂	semidirect
21. #20279272	C₂	semidirect
22. #20278845	C₂	semidirect
23. #20278834	C₂	semidirect
24. #20278531	C₂	semidirect
25. #20278519	C₂	semidirect
26. #20278182	C₂	semidirect
27. #20278180	C₂	semidirect
28. #20277444	C₂	semidirect
29. #20277414	C₂	semidirect
30. #388×D₅₃	C₂	semidirect
31. C₅₃×#2773	C₂	semidirect
32. C₂×#13133216	C₂²	semidirect
34. C₂×#13133205	C₂²	semidirect
39. C₂×#13133197	C₂²	semidirect
42. C₂×#13133195	C₂²	semidirect
53. C₅₃⋊#401	C₂²	semidirect
54. C₅₃⋊#401	C₂²	semidirect
55. #16810565	C₂²	semidirect
58. #16810558	C₂²	semidirect
59. #16810558	C₂²	semidirect
60. #16810557	C₂²	semidirect
62. #16810552	C₂²	semidirect
63. #16810550	C₂²	semidirect
66. #16810549	C₂²	semidirect
67. #16810549	C₂²	semidirect
69. #16810547	C₂²	semidirect
74. #16810545	C₂²	semidirect
75. #16810544	C₂²	semidirect
76. #16810543	C₂²	semidirect
95. #16810528	C₂²	semidirect
96. #16810527	C₂²	semidirect
97. #16810527	C₂²	semidirect
98. #16810527	C₂²	semidirect
99. #16810527	C₂²	semidirect
101. #16810524	C₂²	semidirect
103. #16810521	C₂²	semidirect
104. #16810521	C₂²	semidirect
105. #16810520	C₂²	semidirect
106. #16810519	C₂²	semidirect
107. #16810518	C₂²	semidirect
108. #16810518	C₂²	semidirect
114. #16810515	C₂²	semidirect
115. #16810515	C₂²	semidirect
116. #16810515	C₂²	semidirect
117. #16810515	C₂²	semidirect
118. #16810515	C₂²	semidirect
121. #16810514	C₂²	semidirect
122. #16810514	C₂²	semidirect
124. #16810513	C₂²	semidirect
125. #16810513	C₂²	semidirect
129. #16810512	C₂²	semidirect
132. #16810509	C₂²	semidirect
133. #16810509	C₂²	semidirect
134. #16810508	C₂²	semidirect
135. #16810508	C₂²	semidirect
136. #16810507	C₂²	semidirect
137. #16810506	C₂²	semidirect
138. #16810506	C₂²	semidirect
148. #16810501	C₂²	semidirect
149. #16810501	C₂²	semidirect
152. #16810497	C₂²	semidirect
156. #16810494	C₂²	semidirect
157. #16810494	C₂²	semidirect
158. #16810494	C₂²	semidirect
159. #16810492	C₂²	semidirect
160. #16810490	C₂²	semidirect
161. #16810490	C₂²	semidirect
172. C₅₃×#400	C₂²	semidirect
175. C₅₃×#398	C₂²	semidirect
178. C₅₃×#389	C₂²	semidirect
179. C₅₃×#389	C₂²	semidirect
183. C₅₃×#387	C₂²	semidirect
184. C₅₃×#387	C₂²	semidirect
185. C₅₃×#387	C₂²	semidirect
186. C₅₃×#382	C₂²	semidirect
763. #2773	D₅₃	semidirect
823. #400	C₂×D₅₃	semidirect
831. #398	C₂×D₅₃	semidirect
882. #389	C₂×D₅₃	semidirect
883. #389	C₂×D₅₃	semidirect
917. #387	C₂×D₅₃	semidirect
918. #387	C₂×D₅₃	semidirect
919. #387	C₂×D₅₃	semidirect
943. #382	C₂×D₅₃	semidirect
954. C₅₃	#36766	semidirect

Maximal subgroups

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

subgroup	index
#20283066	2
#20283017	2
#20282621	2
#20282620	2
#20282549	2
#20282542	2
#20282254	2
#20282077	2
#20282075	2
#20282058	2
#20282057	2
#20281719	2
#20281716	2
#20281460	2
#20281458	2
#20281001	2
#20280999	2
#20280521	2
#20280450	2
#20279276	2
#20279272	2
#20278845	2
#20278834	2
#20278531	2
#20278519	2
#20278182	2
#20278180	2
#20277444	2
#20277414	2
#388×D₅₃	2
C₅₃×#2773	2
#36766	53