Subgroups — #27592686

Order 13568.

1736 conjugacy classes of subgroups.

The subgroup lattice has 1502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20283036	C₂	1	1	yes	maximal, characteristic, complemented
2	#20283012	C₂	1	1	yes	maximal, characteristic, complemented
3	#20282405	C₂	1	1	yes	maximal, characteristic, complemented
4	#20282341	C₂	1	1	yes	maximal, characteristic, complemented
5	#20282239	C₂	1	1	yes	maximal, characteristic, complemented
6	#20282053	C₂	1	1	yes	maximal, characteristic, complemented
7	#20281874	C₂	1	1	yes	maximal, characteristic, complemented
8	#20281769	C₂	1	1	yes	maximal, characteristic, complemented
9	#20281753	C₂	1	1	yes	maximal, characteristic, complemented
10	#20281722	C₂	1	1	yes	maximal, characteristic, complemented
11	#20281326	C₂	1	1	yes	maximal, characteristic, complemented
12	#20281221	C₂	1	1	yes	maximal, characteristic, complemented
13	#20281134	C₂	1	1	yes	maximal, characteristic, complemented
14	#20281094	C₂	1	1	yes	maximal, characteristic, complemented
15	#20281090	C₂	1	1	yes	maximal, characteristic, complemented
16	#20281042	C₂	1	1	yes	maximal, characteristic
17	#20280998	C₂	1	1	yes	maximal, characteristic, complemented
18	#20280749	C₂	1	1	yes	maximal, characteristic, complemented
19	#20280728	C₂	1	1	yes	maximal, characteristic, complemented
20	#20280324	C₂	1	1	yes	maximal, characteristic, complemented
21	#20280240	C₂	1	1	yes	maximal, characteristic, complemented
22	#20279807	C₂	1	1	yes	maximal, characteristic, complemented
23	#20279600	C₂	1	1	yes	maximal, characteristic, complemented
24	#20279575	C₂	1	1	yes	maximal, characteristic, complemented
25	#20279563	C₂	1	1	yes	maximal, characteristic, complemented
26	#20278409	C₂	1	1	yes	maximal, characteristic, complemented
27	#20278093	C₂	1	1	yes	maximal, characteristic, complemented
28	#20277512	C₂	1	1	yes	maximal, characteristic, complemented
29	#20277309	C₂	1	1	yes	maximal, characteristic, complemented
30	#20277151	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2753	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#13133216	C₂²	1	1	yes	characteristic, complemented
33	C₂×#13133204	C₂²	1	1	yes	characteristic
34	C₂×#13133203	C₂²	1	1	yes	characteristic
35	C₂×#13133199	C₂²	1	1	yes	characteristic
36	C₂×#13133199	C₂²	1	1	yes	characteristic
37	C₂×#13133198	C₂²	1	1	yes	characteristic
38	C₂×#13133198	C₂²	1	1	yes	characteristic, complemented
39	C₂×#13133194	C₂²	1	1	yes	characteristic, complemented
40	C₂×#13133189	C₂²	1	1	yes	characteristic
41	C₂×#13133185	C₂²	1	1	yes	characteristic
42	C₂×#13133185	C₂²	1	1	yes	characteristic
43	C₂×#13133177	C₂²	1	1	yes	characteristic
44	C₂×#13133175	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
46	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
47	#16810565	C₂²	1	1	yes	characteristic, complemented
48	#16810565	C₂²	1	1	yes	characteristic, complemented
49	#16810564	C₂²	1	1	yes	characteristic, complemented
50	#16810563	C₂²	1	1	yes	characteristic, complemented
51	#16810559	C₂²	1	1	yes	characteristic
52	#16810556	C₂²	1	1	yes	characteristic, complemented
53	#16810555	C₂²	1	1	yes	characteristic, complemented
54	#16810553	C₂²	1	1	yes	characteristic, complemented
55	#16810553	C₂²	1	1	yes	characteristic, complemented
56	#16810552	C₂²	1	1	yes	characteristic
57	#16810552	C₂²	1	1	yes	characteristic
58	#16810551	C₂²	1	1	yes	characteristic
59	#16810551	C₂²	1	1	yes	characteristic, complemented
60	#16810550	C₂²	1	1	yes	characteristic
61	#16810549	C₂²	1	1	yes	characteristic
62	#16810549	C₂²	1	1	yes	characteristic
63	#16810548	C₂²	1	1	yes	characteristic
64	#16810548	C₂²	1	1	yes	characteristic
65	#16810548	C₂²	1	1	yes	characteristic, complemented
66	#16810548	C₂²	1	1	yes	characteristic, complemented
67	#16810547	C₂²	1	1	yes	characteristic
68	#16810547	C₂²	1	1	yes	characteristic
69	#16810546	C₂²	1	1	yes	characteristic
70	#16810546	C₂²	1	1	yes	characteristic
71	#16810546	C₂²	1	1	yes	characteristic, complemented
72	#16810545	C₂²	1	1	yes	characteristic
73	#16810545	C₂²	1	1	yes	characteristic
74	#16810545	C₂²	1	1	yes	characteristic
75	#16810544	C₂²	1	1	yes	characteristic, complemented
76	#16810539	C₂²	1	1	yes	characteristic
77	#16810539	C₂²	1	1	yes	characteristic
78	#16810539	C₂²	1	1	yes	characteristic
79	#16810539	C₂²	1	1	yes	characteristic
80	#16810539	C₂²	1	1	yes	characteristic
81	#16810538	C₂²	1	1	yes	characteristic
82	#16810537	C₂²	1	1	yes	characteristic
83	#16810536	C₂²	1	1	yes	characteristic
84	#16810536	C₂²	1	1	yes	characteristic
85	#16810536	C₂²	1	1	yes	characteristic
86	#16810535	C₂²	1	1	yes	characteristic
87	#16810535	C₂²	1	1	yes	characteristic, complemented
88	#16810531	C₂²	1	1	yes	characteristic
89	#16810529	C₂²	1	1	yes	characteristic, complemented
90	#16810527	C₂²	1	1	yes	characteristic, complemented
91	#16810527	C₂²	1	1	yes	characteristic, complemented
92	#16810526	C₂²	1	1	yes	characteristic
93	#16810523	C₂²	1	1	yes	characteristic
94	#16810523	C₂²	1	1	yes	characteristic
95	#16810523	C₂²	1	1	yes	characteristic
96	#16810521	C₂²	1	1	yes	characteristic, complemented
97	#16810521	C₂²	1	1	yes	characteristic, complemented
98	#16810519	C₂²	1	1	yes	characteristic, complemented
99	#16810518	C₂²	1	1	yes	characteristic, complemented
100	#16810517	C₂²	1	1	yes	characteristic
101	#16810517	C₂²	1	1	yes	characteristic
102	#16810517	C₂²	1	1	yes	characteristic, complemented
103	#16810517	C₂²	1	1	yes	characteristic, complemented
104	#16810516	C₂²	1	1	yes	characteristic
105	#16810516	C₂²	1	1	yes	characteristic
106	#16810516	C₂²	1	1	yes	characteristic
107	#16810516	C₂²	1	1	yes	characteristic
108	#16810516	C₂²	1	1	yes	characteristic, complemented
109	#16810516	C₂²	1	1	yes	characteristic, complemented
110	#16810515	C₂²	1	1	yes	characteristic
111	#16810515	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
115	#16810514	C₂²	1	1	yes	characteristic
116	#16810514	C₂²	1	1	yes	characteristic
117	#16810514	C₂²	1	1	yes	characteristic
118	#16810513	C₂²	1	1	yes	characteristic
119	#16810513	C₂²	1	1	yes	characteristic
120	#16810512	C₂²	1	1	yes	characteristic
121	#16810512	C₂²	1	1	yes	characteristic
122	#16810512	C₂²	1	1	yes	characteristic
123	#16810511	C₂²	1	1	yes	characteristic
124	#16810511	C₂²	1	1	yes	characteristic
125	#16810511	C₂²	1	1	yes	characteristic, complemented
126	#16810510	C₂²	1	1	yes	characteristic, complemented
127	#16810510	C₂²	1	1	yes	characteristic, complemented
128	#16810509	C₂²	1	1	yes	characteristic, complemented
129	#16810509	C₂²	1	1	yes	characteristic, complemented
130	#16810506	C₂²	1	1	yes	characteristic, complemented
131	#16810506	C₂²	1	1	yes	characteristic, complemented
132	#16810506	C₂²	1	1	yes	characteristic, complemented
133	#16810505	C₂²	1	1	yes	characteristic, complemented
134	#16810505	C₂²	1	1	yes	characteristic, complemented
135	#16810505	C₂²	1	1	yes	characteristic, complemented
136	#16810505	C₂²	1	1	yes	characteristic, complemented
137	#16810504	C₂²	1	1	yes	characteristic, complemented
138	#16810503	C₂²	1	1	yes	characteristic
139	#16810503	C₂²	1	1	yes	characteristic
140	#16810503	C₂²	1	1	yes	characteristic, complemented
141	#16810502	C₂²	1	1	yes	characteristic
142	#16810502	C₂²	1	1	yes	characteristic
143	#16810500	C₂²	1	1	yes	characteristic
144	#16810500	C₂²	1	1	yes	characteristic
145	#16810500	C₂²	1	1	yes	characteristic
146	#16810500	C₂²	1	1	yes	characteristic
147	#16810499	C₂²	1	1	yes	characteristic
148	#16810498	C₂²	1	1	yes	characteristic, complemented
149	#16810498	C₂²	1	1	yes	characteristic, complemented
150	#16810498	C₂²	1	1	yes	characteristic, complemented
151	#16810497	C₂²	1	1	yes	characteristic
152	#16810496	C₂²	1	1	yes	characteristic, complemented
153	#16810490	C₂²	1	1	yes	characteristic, complemented
154	#16810487	C₂²	1	1	yes	characteristic, complemented
155	#16810485	C₂²	1	1	yes	characteristic
156	#16810484	C₂²	1	1	yes	characteristic, complemented
157	#16810482	C₂²	1	1	yes	characteristic
158	#16810481	C₂²	1	1	yes	characteristic, complemented
159	#16810480	C₂²	1	1	yes	characteristic
160	#16810480	C₂²	1	1	yes	characteristic
161	#16810478	C₂²	1	1	yes	characteristic
162	#16810478	C₂²	1	1	yes	characteristic
163	#16810478	C₂²	1	1	yes	characteristic
164	#16810478	C₂²	1	1	yes	characteristic
165	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
166	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
167	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
168	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
169	C₄×#11719921	C₂²	1	1	yes	characteristic
170	#16810470	C₂²	1	1	yes	characteristic
171	#16810468	C₂²	1	1	yes	characteristic, complemented
172	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
173	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
174	C₅₃×#394	C₂²	1	1	yes	characteristic
175	C₅₃×#394	C₂²	1	1	yes	characteristic
176	C₅₃×#394	C₂²	1	1	yes	characteristic
177	C₅₃×#392	C₂²	1	1	yes	characteristic
178	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
179	C₅₃×#388	C₂²	1	1	yes	characteristic
180	C₅₃×#388	C₂²	1	1	yes	characteristic
181	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
182	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
183	C₅₃×#386	C₂²	1	1	yes	characteristic
184	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
185	C₅₃×#385	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×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
191	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
192	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
193	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
194	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
195	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
196	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
197	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
198	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
199	#13133216	—	4	2	no	—
200	#13133204	—	4	2	no	—
201	#13133203	—	4	2	no	—
202	#13133199	—	2	4	no	—
203	#13133199	—	4	2	no	—
204	#13133198	—	4	2	no	—
205	#13133198	—	4	2	no	—
206	#13133194	—	4	2	no	—
207	#13133189	—	4	2	no	—
208	#13133185	—	4	2	no	—
209	#13133185	—	4	2	no	—
210	#13133177	—	2	4	no	—
211	#13133175	—	4	2	no	—
212	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
213	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
214	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
215	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
216	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
222	C₂×#11719919	C₂³	1	1	yes	characteristic
223	C₂×#11719919	C₂³	1	1	yes	characteristic
224	C₂×#11719919	C₂³	1	1	yes	characteristic
225	C₂×#11719919	C₂³	1	1	yes	characteristic
226	C₂×#11719919	C₂³	1	1	yes	characteristic
227	C₂×#11719919	C₂³	1	1	yes	characteristic
228	C₂×#11719919	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×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
237	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
238	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
239	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
240	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
241	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
242	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
243	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
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×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
250	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
251	C₂×C₂²⋊Dic₅₃	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	C₂²⋊C₄×D₅₃	—	2	4	no	—
275	C₂×C₄×Dic₅₃	—	4	2	no	—
276	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
277	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
278	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
279	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
280	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
281	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
282	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
283	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
284	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
285	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
286	#13133124	C₂³	1	1	yes	characteristic
287	#13133124	C₂³	1	1	yes	characteristic
288	#13133124	C₂³	1	1	yes	characteristic
289	#13133124	C₂³	1	1	yes	characteristic
290	#13133124	C₂³	1	1	yes	characteristic
291	#13133124	C₂³	1	1	yes	characteristic
292	#13133124	C₂³	1	1	yes	characteristic
293	#13133124	C₂³	1	1	yes	characteristic
294	#13133124	C₂³	1	1	yes	characteristic
295	#13133124	C₂³	1	1	yes	characteristic
296	#13133124	C₂³	1	1	yes	characteristic
297	#13133124	C₂³	1	1	yes	characteristic
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	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
323	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
324	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
325	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
326	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
327	C₂×C₄⋊C₄×C₅₃	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×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
332	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
333	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
334	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
335	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
336	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
337	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
338	C₂×C₂²⋊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×C₄²×C₅₃	C₂³	1	1	yes	characteristic
346	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
347	#95×C₅₃	C₂³	1	1	yes	characteristic
348	#95×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	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
358	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
359	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
360	C₂³×D₅₃	—	2	2	no	—
361	C₂³×D₅₃	—	4	1	no	—
362	C₂³×D₅₃	—	4	1	no	—
363	C₂³×D₅₃	—	4	1	no	—
364	C₂³×D₅₃	—	4	1	no	—
365	C₂³×D₅₃	—	4	1	no	—
366	C₂³×D₅₃	—	4	1	no	—
367	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
368	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
369	C₂×D₄×C₅₃	—	2	2	no	—
370	C₂×D₄×C₅₃	—	2	2	no	—
371	C₂×D₄×C₅₃	—	4	1	no	—
372	C₂×D₄×C₅₃	—	4	1	no	—
373	C₂×D₄×C₅₃	—	4	1	no	—
374	C₂×D₄×C₅₃	—	4	1	no	—
375	C₂×D₄×C₅₃	—	4	1	no	—
376	C₂×D₄×C₅₃	—	4	1	no	—
377	C₂×D₄×C₅₃	—	4	1	no	—
378	C₂²×C₄×C₅₃	—	4	1	no	—
379	C₂²×C₄×C₅₃	—	4	1	no	—
380	C₂²×C₄×C₅₃	—	4	1	no	—
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	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
391	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
393	C₂×C₂²⋊D₅₃	—	2	2	no	—
394	C₂×C₂²⋊D₅₃	—	2	2	no	—
395	C₂×C₂²⋊D₅₃	—	2	2	no	—
396	C₂×C₂²⋊D₅₃	—	2	2	no	—
397	C₂×C₂²⋊D₅₃	—	2	2	no	—
398	C₂×C₂²⋊D₅₃	—	4	1	no	—
399	C₂×C₂²⋊D₅₃	—	4	1	no	—
400	C₂×C₂²⋊D₅₃	—	4	1	no	—
401	C₂×C₂²⋊D₅₃	—	4	1	no	—
402	C₂×C₂²⋊D₅₃	—	4	1	no	—
403	C₂×C₂²⋊D₅₃	—	4	1	no	—
404	C₂×C₂²⋊D₅₃	—	4	1	no	—
405	C₂²×Dic₅₃	—	2	2	no	—
406	C₂²×Dic₅₃	—	2	2	no	—
407	C₂²×Dic₅₃	—	2	2	no	—
408	C₂²×Dic₅₃	—	4	1	no	—
409	C₂²×Dic₅₃	—	4	1	no	—
410	C₂²×Dic₅₃	—	4	1	no	—
411	C₂²×Dic₅₃	—	4	1	no	—
412	C₂²×Dic₅₃	—	4	1	no	—
413	C₂²×Dic₅₃	—	4	1	no	—
414	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
415	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
416	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
417	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
418	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
419	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
420	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
421	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
422	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
423	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
424	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
425	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
426	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
427	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
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	#41	1	4	yes	—
434	C₂×Dic₁₀₆	—	2	2	no	—
435	C₂×Dic₁₀₆	—	4	1	no	—
436	C₂×Dic₁₀₆	—	4	1	no	—
437	C₂×Dic₁₀₆	—	4	1	no	—
438	C₂×Dic₁₀₆	—	4	1	no	—
439	C₂×Dic₁₀₆	—	4	1	no	—
440	C₄⋊C₄×C₅₃	—	4	1	no	—
441	C₄⋊C₄×C₅₃	—	4	1	no	—
442	C₄⋊C₄×C₅₃	—	4	1	no	—
443	C₄⋊C₄×C₅₃	—	4	1	no	—
444	C₄⋊C₄×C₅₃	—	4	1	no	—
445	C₂²⋊C₄×C₅₃	—	2	2	no	—
446	C₂²⋊C₄×C₅₃	—	2	2	no	—
447	C₂²⋊C₄×C₅₃	—	2	2	no	—
448	C₂²⋊C₄×C₅₃	—	2	2	no	—
449	C₂²⋊C₄×C₅₃	—	4	1	no	—
450	C₂²⋊C₄×C₅₃	—	4	1	no	—
451	C₂²⋊C₄×C₅₃	—	4	1	no	—
452	C₂²⋊C₄×C₅₃	—	4	1	no	—
453	C₂²⋊C₄×C₅₃	—	4	1	no	—
454	C₂²⋊C₄×C₅₃	—	4	1	no	—
455	C₂²⋊C₄×C₅₃	—	4	1	no	—
456	C₂²⋊C₄×C₅₃	—	4	1	no	—
457	C₂²⋊C₄×C₅₃	—	4	1	no	—
458	C₂²⋊C₄×C₅₃	—	4	1	no	—
459	C₄²×C₅₃	—	4	1	no	—
460	C₄²×C₅₃	—	4	1	no	—
461	C₂²⋊Dic₅₃	—	2	2	no	—
462	C₂²⋊Dic₅₃	—	2	2	no	—
463	C₂²⋊Dic₅₃	—	2	2	no	—
464	C₂²⋊Dic₅₃	—	2	2	no	—
465	C₂²⋊Dic₅₃	—	2	2	no	—
466	C₂²⋊Dic₅₃	—	2	2	no	—
467	C₂²⋊Dic₅₃	—	4	1	no	—
468	C₂²⋊Dic₅₃	—	4	1	no	—
469	C₂²⋊Dic₅₃	—	4	1	no	—
470	C₂²⋊Dic₅₃	—	4	1	no	—
471	C₂²⋊Dic₅₃	—	4	1	no	—
472	C₂²⋊Dic₅₃	—	4	1	no	—
473	C₂²⋊Dic₅₃	—	4	1	no	—
474	C₂²⋊Dic₅₃	—	4	1	no	—
475	C₂²⋊Dic₅₃	—	4	1	no	—
476	C₂²⋊Dic₅₃	—	4	1	no	—
477	#11719921	—	2	2	no	—
478	#11719921	—	2	2	no	—
479	#11719921	—	2	2	no	—
480	#11719921	—	2	2	no	—
481	#11719921	—	2	2	no	—
482	#11719921	—	4	1	no	—
483	#11719921	—	4	1	no	—
484	#11719921	—	4	1	no	—
485	#11719921	—	4	1	no	—
486	#11719921	—	4	1	no	—
487	#11719921	—	4	1	no	—
488	#11719921	—	4	1	no	—
489	#11719921	—	4	1	no	—
490	#11719921	—	4	1	no	—
491	#11719921	—	4	1	no	—
492	#11719921	—	4	1	no	—
493	#11719921	—	4	1	no	—
494	#11719921	—	4	1	no	—
495	#11719921	—	4	1	no	—
496	#11719921	—	4	1	no	—
497	#11719921	—	4	1	no	—
498	#11719921	—	4	1	no	—
499	C₄⋊Dic₅₃	—	2	2	no	—
500	C₄⋊Dic₅₃	—	2	2	no	—
501	C₄⋊Dic₅₃	—	4	1	no	—
502	C₄⋊Dic₅₃	—	4	1	no	—
503	C₄⋊Dic₅₃	—	4	1	no	—
504	C₄⋊Dic₅₃	—	4	1	no	—
505	C₄⋊Dic₅₃	—	4	1	no	—
506	C₄⋊Dic₅₃	—	4	1	no	—
507	C₄⋊Dic₅₃	—	4	1	no	—
508	C₄⋊Dic₅₃	—	4	1	no	—
509	#11719919	—	2	2	no	—
510	#11719919	—	2	2	no	—
511	#11719919	—	2	2	no	—
512	#11719919	—	4	1	no	—
513	#11719919	—	4	1	no	—
514	#11719919	—	4	1	no	—
515	#11719919	—	4	1	no	—
516	#11719919	—	4	1	no	—
517	#11719919	—	4	1	no	—
518	#11719919	—	4	1	no	—
519	#11719919	—	4	1	no	—
520	#11719919	—	4	1	no	—
521	#11719919	—	4	1	no	—
522	#11719919	—	4	1	no	—
523	C₄×Dic₅₃	—	2	2	no	—
524	C₄×Dic₅₃	—	2	2	no	—
525	C₄×Dic₅₃	—	2	2	no	—
526	C₄×Dic₅₃	—	4	1	no	—
527	C₄×Dic₅₃	—	4	1	no	—
528	C₄×Dic₅₃	—	4	1	no	—
529	C₄×Dic₅₃	—	4	1	no	—
530	C₄×Dic₅₃	—	4	1	no	—
531	C₄×Dic₅₃	—	4	1	no	—
532	C₄×Dic₅₃	—	4	1	no	—
533	C₂³×C₅₃	—	2	1	no	—
534	C₂³×C₅₃	—	2	1	no	—
535	C₂³×C₅₃	—	2	1	no	—
536	C₂³×C₅₃	—	2	1	no	—
537	C₂³×C₅₃	—	2	1	no	—
538	C₂³×C₅₃	—	2	1	no	—
539	C₂³×C₅₃	—	2	1	no	—
540	C₂³×C₅₃	—	2	1	no	—
541	C₂³×C₅₃	—	2	1	no	—
542	C₂³×C₅₃	—	2	1	no	—
543	C₂³×C₅₃	—	2	1	no	—
544	C₂³×C₅₃	—	2	1	no	—
545	C₂³×C₅₃	—	2	1	no	—
546	C₂³×C₅₃	—	2	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	H(5,𝔽₂)	1	2	yes	—
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	—	4	4	no	—
569	C₂²×D₅₃	—	8	2	no	—
570	C₂²×D₅₃	—	8	2	no	—
571	C₂²×D₅₃	—	8	2	no	—
572	C₂²×D₅₃	—	8	2	no	—
573	C₂²×D₅₃	—	8	2	no	—
574	C₂²×D₅₃	—	8	2	no	—
575	C₂²×D₅₃	C₂×#41	1	2	yes	—
576	D₄×C₅₃	—	8	2	no	—
577	D₄×C₅₃	—	8	2	no	—
578	D₄×C₅₃	—	8	2	no	—
579	C₂×C₄×C₅₃	—	2	1	no	—
580	C₂×C₄×C₅₃	—	2	1	no	—
581	C₂×C₄×C₅₃	—	2	1	no	—
582	C₂×C₄×C₅₃	—	2	1	no	—
583	C₂×C₄×C₅₃	—	2	1	no	—
584	C₂×C₄×C₅₃	—	2	1	no	—
585	C₂×C₄×C₅₃	—	2	1	no	—
586	C₂×C₄×C₅₃	—	2	1	no	—
587	C₂×C₄×C₅₃	—	2	1	no	—
588	C₂×C₄×C₅₃	—	2	1	no	—
589	C₂×C₄×C₅₃	—	2	1	no	—
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	—	4	4	no	—
615	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
616	C₂²⋊D₅₃	—	4	4	no	—
617	C₂²⋊D₅₃	—	8	2	no	—
618	C₂²⋊D₅₃	—	8	2	no	—
619	C₂²⋊D₅₃	—	8	2	no	—
620	C₂×Dic₅₃	—	2	1	no	—
621	C₂×Dic₅₃	—	2	1	no	—
622	C₂×Dic₅₃	—	2	1	no	—
623	C₂×Dic₅₃	—	2	1	no	—
624	C₂×Dic₅₃	—	2	1	no	—
625	C₂×Dic₅₃	—	2	1	no	—
626	C₂×Dic₅₃	—	2	1	no	—
627	C₂×Dic₅₃	—	2	1	no	—
628	C₂×Dic₅₃	—	2	1	no	—
629	C₂×Dic₅₃	—	2	1	no	—
630	C₂×Dic₅₃	—	2	1	no	—
631	C₂×Dic₅₃	—	2	1	no	—
632	C₂×Dic₅₃	—	2	1	no	—
633	C₂×Dic₅₃	—	2	1	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	—	4	4	no	—
661	C₂×Dic₅₃	—	4	4	no	—
662	C₂×Dic₅₃	—	8	2	no	—
663	C₂×Dic₅₃	C₂×#41	1	2	yes	—
664	C₂×Dic₅₃	H(5,𝔽₂)	1	2	yes	—
665	C₄×D₅₃	—	4	4	no	—
666	C₄×D₅₃	—	8	2	no	—
667	Dic₁₀₆	—	8	2	no	—
668	Dic₁₀₆	—	8	2	no	—
669	#36784	—	53	1	no	maximal, Sylow
670	C₂²×C₅₃	—	2	2	no	—
671	C₂²×C₅₃	—	2	2	no	—
672	C₂²×C₅₃	—	2	2	no	—
673	C₂²×C₅₃	—	4	1	no	—
674	C₂²×C₅₃	—	4	1	no	—
675	C₂²×C₅₃	—	4	1	no	—
676	C₂²×C₅₃	—	4	1	no	—
677	C₂²×C₅₃	—	4	1	no	—
678	C₂²×C₅₃	—	4	1	no	—
679	C₂²×C₅₃	—	4	1	no	—
680	C₂²×C₅₃	—	4	1	no	—
681	C₂²×C₅₃	—	4	1	no	—
682	C₂²×C₅₃	—	4	1	no	—
683	C₂²×C₅₃	—	4	1	no	—
684	C₂²×C₅₃	—	4	1	no	—
685	C₂²×C₅₃	—	4	1	no	—
686	C₂²×C₅₃	—	4	1	no	—
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	C₂²×#41	1	1	yes	characteristic
692	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
693	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
694	C₂²×C₅₃	#585	1	1	yes	characteristic
695	C₂²×C₅₃	#585	1	1	yes	characteristic
696	C₂²×C₅₃	#585	1	1	yes	characteristic
697	C₂²×C₅₃	#585	1	1	yes	characteristic
698	C₂×D₅₃	—	2	2	no	—
699	C₂×D₅₃	—	2	2	no	—
700	C₂×D₅₃	—	2	2	no	—
701	C₂×D₅₃	—	4	1	no	—
702	C₂×D₅₃	—	4	1	no	—
703	C₂×D₅₃	—	4	1	no	—
704	C₂×D₅₃	—	4	1	no	—
705	C₂×D₅₃	—	4	1	no	—
706	C₂×D₅₃	—	4	1	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	—	8	8	no	—
713	C₄×C₅₃	—	2	2	no	—
714	C₄×C₅₃	—	4	1	no	—
715	C₄×C₅₃	—	4	1	no	—
716	C₄×C₅₃	—	4	1	no	—
717	C₄×C₅₃	—	4	1	no	—
718	C₄×C₅₃	—	4	1	no	—
719	C₄×C₅₃	—	4	1	no	—
720	C₄×C₅₃	—	4	1	no	—
721	C₄×C₅₃	—	4	1	no	—
722	C₄×C₅₃	—	4	1	no	—
723	C₄×C₅₃	—	4	1	no	—
724	C₄×C₅₃	—	4	1	no	—
725	Dic₅₃	—	2	2	no	—
726	Dic₅₃	—	2	2	no	—
727	Dic₅₃	—	4	1	no	—
728	Dic₅₃	—	4	1	no	—
729	Dic₅₃	—	4	1	no	—
730	Dic₅₃	—	4	1	no	—
731	Dic₅₃	—	4	1	no	—
732	Dic₅₃	—	4	1	no	—
733	Dic₅₃	—	4	1	no	—
734	Dic₅₃	—	4	1	no	—
735	Dic₅₃	—	4	1	no	—
736	Dic₅₃	—	4	1	no	—
737	Dic₅₃	—	4	1	no	—
738	Dic₅₃	—	4	1	no	—
739	#2853	—	53	1	no	—
740	#2850	—	53	1	no	—
741	#2783	—	53	1	no	—
742	#2779	—	53	1	no	—
743	#2772	—	53	1	no	—
744	#2757	—	53	1	no	—
745	#2753	D₅₃	1	1	yes	characteristic, complemented
746	#2744	—	53	1	no	—
747	#2737	—	53	1	no	—
748	#2735	—	53	1	no	—
749	#2731	—	53	1	no	—
750	#2701	—	53	1	no	—
751	#2693	—	53	1	no	—
752	#2687	—	53	1	no	—
753	#2684	—	53	1	no	—
754	#2684	—	53	1	no	—
755	#2678	—	53	1	no	—
756	#2674	—	53	1	no	—
757	#2651	—	53	1	no	—
758	#2650	—	53	1	no	—
759	#2602	—	53	1	no	—
760	#2595	—	53	1	no	—
761	#2557	—	53	1	no	—
762	#2534	—	53	1	no	—
763	#2532	—	53	1	no	—
764	#2531	—	53	1	no	—
765	#2439	—	53	1	no	—
766	#2411	—	53	1	no	—
767	#2335	—	53	1	no	—
768	#2312	—	53	1	no	—
769	#2290	—	53	1	no	—
770	C₂×C₅₃	—	4	2	no	—
771	C₂×C₅₃	—	8	1	no	—
772	C₂×C₅₃	—	8	1	no	—
773	C₂×C₅₃	#3455	1	1	yes	characteristic
774	C₂×C₅₃	#3494	1	1	yes	characteristic
775	C₂×C₅₃	#3505	1	1	yes	characteristic
776	C₂×C₅₃	#3534	1	1	yes	characteristic
777	C₂×C₅₃	#3540	1	1	yes	characteristic
778	C₂×C₅₃	#3545	1	1	yes	characteristic
779	C₂×C₅₃	#3566	1	1	yes	characteristic
780	D₅₃	—	4	2	no	—
781	D₅₃	—	8	1	no	—
782	C₂×C₄⋊Q₈	—	53	1	no	—
783	C₂×#124	—	53	1	no	—
784	C₂×#124	—	53	1	no	—
785	C₂×#123	—	53	1	no	—
786	C₂×#123	—	53	1	no	—
787	C₂×#123	—	53	1	no	—
788	C₂×#123	—	53	1	no	—
789	C₂×C₂²⋊Q₈	—	53	1	no	—
790	C₂×#121	—	53	1	no	—
791	C₂×#120	—	53	1	no	—
792	C₂×#120	—	53	1	no	—
793	C₂×C₄×D₄	—	53	1	no	—
794	C₂×#117	—	53	1	no	—
795	C₂²×C₂²⋊C₄	—	53	1	no	—
796	C₂²×C₄²	—	53	1	no	—
797	#400	—	53	1	no	—
798	#400	—	53	1	no	—
799	#400	—	53	1	no	—
800	#400	—	53	1	no	—
801	#400	C₂×D₅₃	1	1	yes	characteristic, complemented
802	#399	—	53	1	no	—
803	#398	—	53	1	no	—
804	#398	—	53	1	no	—
805	#398	—	53	1	no	—
806	#398	—	53	1	no	—
807	#397	—	53	1	no	—
808	#397	—	53	1	no	—
809	#397	—	53	1	no	—
810	#397	—	53	1	no	—
811	#397	—	53	1	no	—
812	#397	—	53	1	no	—
813	#397	—	53	1	no	—
814	#397	—	53	1	no	—
815	#397	—	53	1	no	—
816	#397	—	53	1	no	—
817	#397	—	53	1	no	—
818	#397	C₂×D₅₃	1	1	yes	characteristic, complemented
819	#396	—	53	1	no	—
820	#396	—	53	1	no	—
821	#396	—	53	1	no	—
822	#396	—	53	1	no	—
823	#396	—	53	1	no	—
824	#396	—	53	1	no	—
825	#396	—	53	1	no	—
826	#396	—	53	1	no	—
827	#395	—	53	1	no	—
828	#394	—	53	1	no	—
829	#394	—	53	1	no	—
830	#394	—	53	1	no	—
831	#394	—	53	1	no	—
832	#394	—	53	1	no	—
833	#394	—	53	1	no	—
834	#394	—	53	1	no	—
835	#394	C₂×D₅₃	1	1	yes	characteristic
836	#394	C₂×D₅₃	1	1	yes	characteristic
837	#394	C₂×D₅₃	1	1	yes	characteristic
838	#393	—	53	1	no	—
839	#393	—	53	1	no	—
840	#393	—	53	1	no	—
841	#393	—	53	1	no	—
842	#393	—	53	1	no	—
843	#392	—	53	1	no	—
844	#392	C₂×D₅₃	1	1	yes	characteristic
845	#391	—	53	1	no	—
846	#391	—	53	1	no	—
847	#391	—	53	1	no	—
848	#390	—	53	1	no	—
849	#390	—	53	1	no	—
850	#390	—	53	1	no	—
851	#390	—	53	1	no	—
852	#390	C₂×D₅₃	1	1	yes	characteristic, complemented
853	#389	—	53	1	no	—
854	#389	—	53	1	no	—
855	#389	—	53	1	no	—
856	#389	—	53	1	no	—
857	#388	—	53	1	no	—
858	#388	—	53	1	no	—
859	#388	—	53	1	no	—
860	#388	—	53	1	no	—
861	#388	—	53	1	no	—
862	#388	—	53	1	no	—
863	#388	—	53	1	no	—
864	#388	—	53	1	no	—
865	#388	—	53	1	no	—
866	#388	—	53	1	no	—
867	#388	—	53	1	no	—
868	#388	—	53	1	no	—
869	#388	—	53	1	no	—
870	#388	—	53	1	no	—
871	#388	—	53	1	no	—
872	#388	—	53	1	no	—
873	#388	—	53	1	no	—
874	#388	—	53	1	no	—
875	#388	—	53	1	no	—
876	#388	—	53	1	no	—
877	#388	—	53	1	no	—
878	#388	—	53	1	no	—
879	#388	—	53	1	no	—
880	#388	—	53	1	no	—
881	#388	—	53	1	no	—
882	#388	—	53	1	no	—
883	#388	C₂×D₅₃	1	1	yes	characteristic
884	#388	C₂×D₅₃	1	1	yes	characteristic
885	#388	C₂×D₅₃	1	1	yes	characteristic, complemented
886	#388	C₂×D₅₃	1	1	yes	characteristic, complemented
887	#387	—	53	1	no	—
888	#387	—	53	1	no	—
889	#387	—	53	1	no	—
890	#387	—	53	1	no	—
891	#387	—	53	1	no	—
892	#387	—	53	1	no	—
893	#387	—	53	1	no	—
894	#387	—	53	1	no	—
895	#387	—	53	1	no	—
896	#387	—	53	1	no	—
897	#387	—	53	1	no	—
898	#387	—	53	1	no	—
899	#386	—	53	1	no	—
900	#386	—	53	1	no	—
901	#386	—	53	1	no	—
902	#386	—	53	1	no	—
903	#386	—	53	1	no	—
904	#386	—	53	1	no	—
905	#386	—	53	1	no	—
906	#386	—	53	1	no	—
907	#386	—	53	1	no	—
908	#386	—	53	1	no	—
909	#386	C₂×D₅₃	1	1	yes	characteristic
910	#386	C₂×D₅₃	1	1	yes	characteristic, complemented
911	#385	—	53	1	no	—
912	#385	—	53	1	no	—
913	#385	—	53	1	no	—
914	#385	—	53	1	no	—
915	#385	—	53	1	no	—
916	#385	C₂×D₅₃	1	1	yes	characteristic, complemented
917	#383	—	53	1	no	—
918	#382	—	53	1	no	—
919	#382	C₂×D₅₃	1	1	yes	characteristic, complemented
920	#381	—	53	1	no	—
921	#381	—	53	1	no	—
922	#380	—	53	1	no	—
923	#380	—	53	1	no	—
924	#380	—	53	1	no	—
925	#380	—	53	1	no	—
926	#379	—	53	1	no	—
927	#379	—	53	1	no	—
928	#379	—	53	1	no	—
929	#379	—	53	1	no	—
930	C₄×C₄⋊C₄	—	53	1	no	—
931	C₄×C₄⋊C₄	—	53	1	no	—
932	C₄×C₂²⋊C₄	—	53	1	no	—
933	C₄×C₂²⋊C₄	—	53	1	no	—
934	C₄×C₂²⋊C₄	—	53	1	no	—
935	C₄×C₂²⋊C₄	—	53	1	no	—
936	#376	—	53	1	no	—
937	C₅₃	#36784	1	1	yes	characteristic, complemented, Sylow
938	C₂⁵	—	53	1	no	—
939	C₂²×Q₈	—	53	1	no	—
940	C₂²×Q₈	—	53	1	no	—
941	C₂²×D₄	—	53	1	no	—
942	C₂²×D₄	—	53	1	no	—
943	C₂²×D₄	—	53	1	no	—
944	C₂²×D₄	—	53	1	no	—
945	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
946	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
947	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
948	C₂³×C₄	—	53	1	no	—
949	C₂³×C₄	—	53	1	no	—
950	C₂³×C₄	—	53	1	no	—
951	C₂³×C₄	—	53	1	no	—
952	C₂³×C₄	—	53	1	no	—
953	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
954	C₄⋊Q₈	—	212	2	no	—
955	#124	—	212	2	no	—
956	#124	—	212	2	no	—
957	#123	—	106	4	no	—
958	#123	—	212	2	no	—
959	#123	—	212	2	no	—
960	#123	—	212	2	no	—
961	C₂²⋊Q₈	—	212	2	no	—
962	#121	—	212	2	no	—
963	#120	—	212	2	no	—
964	#120	—	212	2	no	—
965	C₄×D₄	—	106	4	no	—
966	#117	—	212	2	no	—
967	C₂×C₄⋊C₄	—	53	1	no	—
968	C₂×C₄⋊C₄	—	53	1	no	—
969	C₂×C₄⋊C₄	—	53	1	no	—
970	C₂×C₄⋊C₄	—	53	1	no	—
971	C₂×C₄⋊C₄	—	53	1	no	—
972	C₂×C₄⋊C₄	—	53	1	no	—
973	C₂×C₄⋊C₄	—	53	1	no	—
974	C₂×C₄⋊C₄	—	53	1	no	—
975	C₂×C₄⋊C₄	—	53	1	no	—
976	C₂×C₄⋊C₄	—	53	1	no	—
977	C₂×C₄⋊C₄	—	53	1	no	—
978	C₂×C₄⋊C₄	—	53	1	no	—
979	C₂×C₄⋊C₄	—	53	1	no	—
980	C₂×C₄⋊C₄	—	53	1	no	—
981	C₂×C₄⋊C₄	—	53	1	no	—
982	C₂×C₄⋊C₄	—	53	1	no	—
983	C₂×C₄⋊C₄	—	53	1	no	—
984	C₂×C₄⋊C₄	—	53	1	no	—
985	C₂×C₄⋊C₄	—	53	1	no	—
986	C₂×C₄⋊C₄	—	53	1	no	—
987	C₂×C₄⋊C₄	—	53	1	no	—
988	C₂×C₄⋊C₄	—	53	1	no	—
989	C₂×C₄⋊C₄	—	53	1	no	—
990	C₂×C₄⋊C₄	—	53	1	no	—
991	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
992	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
993	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
994	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
995	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
996	C₂×C₂²⋊C₄	—	53	1	no	—
997	C₂×C₂²⋊C₄	—	53	1	no	—
998	C₂×C₂²⋊C₄	—	53	1	no	—
999	C₂×C₂²⋊C₄	—	53	1	no	—
1000	C₂×C₂²⋊C₄	—	53	1	no	—
1001	C₂×C₂²⋊C₄	—	53	1	no	—
1002	C₂×C₂²⋊C₄	—	53	1	no	—
1003	C₂×C₂²⋊C₄	—	53	1	no	—
1004	C₂×C₂²⋊C₄	—	53	1	no	—
1005	C₂×C₂²⋊C₄	—	53	1	no	—
1006	C₂×C₂²⋊C₄	—	53	1	no	—
1007	C₂×C₂²⋊C₄	—	53	1	no	—
1008	C₂×C₂²⋊C₄	—	53	1	no	—
1009	C₂×C₂²⋊C₄	—	53	1	no	—
1010	C₂×C₂²⋊C₄	—	53	1	no	—
1011	C₂×C₂²⋊C₄	—	53	1	no	—
1012	C₂×C₂²⋊C₄	—	53	1	no	—
1013	C₂×C₂²⋊C₄	—	53	1	no	—
1014	C₂×C₂²⋊C₄	—	53	1	no	—
1015	C₂×C₂²⋊C₄	—	53	1	no	—
1016	C₂×C₂²⋊C₄	—	53	1	no	—
1017	C₂×C₂²⋊C₄	—	53	1	no	—
1018	C₂×C₂²⋊C₄	—	53	1	no	—
1019	C₂×C₂²⋊C₄	—	53	1	no	—
1020	C₂×C₂²⋊C₄	—	53	1	no	—
1021	C₂×C₂²⋊C₄	—	53	1	no	—
1022	C₂×C₂²⋊C₄	—	53	1	no	—
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	—	106	4	no	—
1035	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1036	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1037	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1038	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1039	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1040	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1041	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1042	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1043	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1044	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1045	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1046	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1047	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1048	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1049	C₂×C₄²	—	53	1	no	—
1050	C₂×C₄²	—	53	1	no	—
1051	C₂×C₄²	—	53	1	no	—
1052	C₂×C₄²	—	53	1	no	—
1053	C₂×C₄²	—	53	1	no	—
1054	C₂×C₄²	—	53	1	no	—
1055	C₂×C₄²	—	53	1	no	—
1056	C₂×C₄²	—	53	1	no	—
1057	C₂×C₄²	—	53	1	no	—
1058	C₂×C₄²	—	53	1	no	—
1059	C₂×C₄²	—	212	2	no	—
1060	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1061	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1062	#95	—	53	1	no	—
1063	#95	—	53	1	no	—
1064	#95	—	53	1	no	—
1065	#95	—	53	1	no	—
1066	#95	—	53	1	no	—
1067	#95	—	53	1	no	—
1068	#95	—	53	1	no	—
1069	#95	—	53	1	no	—
1070	#95	—	53	1	no	—
1071	#95	—	53	1	no	—
1072	#95	—	53	1	no	—
1073	#95	—	53	1	no	—
1074	#95	—	53	1	no	—
1075	#95	—	53	1	no	—
1076	#95	—	53	1	no	—
1077	#95	—	53	1	no	—
1078	#95	—	53	1	no	—
1079	#95	—	53	1	no	—
1080	#95	—	53	1	no	—
1081	#95	—	53	1	no	—
1082	#95	—	53	1	no	—
1083	#95	—	53	1	no	—
1084	#95	—	53	1	no	—
1085	#95	—	53	1	no	—
1086	#95	—	53	1	no	—
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	C₂²×D₅₃	1	1	yes	characteristic
1099	#95	C₂²×D₅₃	1	1	yes	characteristic
1100	#95	C₂²×D₅₃	1	1	yes	characteristic
1101	#95	C₂²×D₅₃	1	1	yes	characteristic
1102	#95	C₂²×D₅₃	1	1	yes	characteristic
1103	#95	C₂²×D₅₃	1	1	yes	characteristic
1104	#95	C₂²×D₅₃	1	1	yes	characteristic
1105	#95	C₂²×D₅₃	1	1	yes	characteristic
1106	#95	C₂²×D₅₃	1	1	yes	characteristic
1107	#95	C₂²×D₅₃	1	1	yes	characteristic
1108	C₂⁴	—	53	1	no	—
1109	C₂⁴	—	53	1	no	—
1110	C₂⁴	—	106	2	no	—
1111	C₂⁴	—	212	1	no	—
1112	C₂⁴	—	212	1	no	—
1113	C₂⁴	—	212	1	no	—
1114	C₂⁴	—	212	1	no	—
1115	C₂⁴	—	212	1	no	—
1116	C₂⁴	—	212	1	no	—
1117	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1118	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1119	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1120	C₂×Q₈	—	106	2	no	—
1121	C₂×Q₈	—	212	1	no	—
1122	C₂×Q₈	—	212	1	no	—
1123	C₂×Q₈	—	212	1	no	—
1124	C₂×Q₈	—	212	1	no	—
1125	C₂×Q₈	—	212	1	no	—
1126	C₂×D₄	—	2	2	no	—
1127	C₂×D₄	—	2	2	no	—
1128	C₂×D₄	—	4	1	no	—
1129	C₂×D₄	—	4	1	no	—
1130	C₂×D₄	—	4	1	no	—
1131	C₂×D₄	—	4	1	no	—
1132	C₂×D₄	—	4	1	no	—
1133	C₂×D₄	—	4	1	no	—
1134	C₂×D₄	—	4	1	no	—
1135	C₂×D₄	—	106	2	no	—
1136	C₂×D₄	—	106	2	no	—
1137	C₂×D₄	—	106	2	no	—
1138	C₂×D₄	—	106	2	no	—
1139	C₂×D₄	—	106	2	no	—
1140	C₂×D₄	—	212	1	no	—
1141	C₂×D₄	—	212	1	no	—
1142	C₂×D₄	—	212	1	no	—
1143	C₂×D₄	—	212	1	no	—
1144	C₂×D₄	—	212	1	no	—
1145	C₂×D₄	—	212	1	no	—
1146	C₂×D₄	—	212	1	no	—
1147	C₂²×C₄	—	4	1	no	—
1148	C₂²×C₄	—	4	1	no	—
1149	C₂²×C₄	—	4	1	no	—
1150	C₂²×C₄	—	53	1	no	—
1151	C₂²×C₄	—	53	1	no	—
1152	C₂²×C₄	—	53	4	no	—
1153	C₂²×C₄	—	53	1	no	—
1154	C₂²×C₄	—	53	1	no	—
1155	C₂²×C₄	—	53	1	no	—
1156	C₂²×C₄	—	53	1	no	—
1157	C₂²×C₄	—	53	1	no	—
1158	C₂²×C₄	—	53	1	no	—
1159	C₂²×C₄	—	53	1	no	—
1160	C₂²×C₄	—	53	1	no	—
1161	C₂²×C₄	—	53	1	no	—
1162	C₂²×C₄	—	53	1	no	—
1163	C₂²×C₄	—	53	1	no	—
1164	C₂²×C₄	—	53	1	no	—
1165	C₂²×C₄	—	106	2	no	—
1166	C₂²×C₄	—	106	2	no	—
1167	C₂²×C₄	—	106	2	no	—
1168	C₂²×C₄	—	106	2	no	—
1169	C₂²×C₄	—	212	1	no	—
1170	C₂²×C₄	—	212	1	no	—
1171	C₂²×C₄	—	212	1	no	—
1172	C₂²×C₄	—	212	1	no	—
1173	C₂²×C₄	—	212	1	no	—
1174	C₂²×C₄	—	212	1	no	—
1175	C₂²×C₄	—	212	1	no	—
1176	C₂²×C₄	—	212	1	no	—
1177	C₂²×C₄	—	212	1	no	—
1178	C₂²×C₄	—	212	1	no	—
1179	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1180	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1181	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1182	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1183	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1184	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1185	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1186	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1187	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1188	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1189	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1190	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1191	C₄⋊C₄	—	4	1	no	—
1192	C₄⋊C₄	—	4	1	no	—
1193	C₄⋊C₄	—	4	1	no	—
1194	C₄⋊C₄	—	4	1	no	—
1195	C₄⋊C₄	—	4	1	no	—
1196	C₄⋊C₄	—	106	2	no	—
1197	C₄⋊C₄	—	106	2	no	—
1198	C₄⋊C₄	—	106	2	no	—
1199	C₄⋊C₄	—	106	2	no	—
1200	C₄⋊C₄	—	106	2	no	—
1201	C₄⋊C₄	—	212	1	no	—
1202	C₄⋊C₄	—	212	1	no	—
1203	C₄⋊C₄	—	212	1	no	—
1204	C₄⋊C₄	—	212	1	no	—
1205	C₄⋊C₄	—	212	1	no	—
1206	C₄⋊C₄	—	212	1	no	—
1207	C₄⋊C₄	—	212	1	no	—
1208	C₄⋊C₄	—	212	1	no	—
1209	C₄⋊C₄	—	212	1	no	—
1210	C₄⋊C₄	—	212	1	no	—
1211	C₄⋊C₄	—	212	1	no	—
1212	C₄⋊C₄	—	212	1	no	—
1213	C₄⋊C₄	—	212	1	no	—
1214	C₄⋊C₄	—	212	1	no	—
1215	C₄⋊C₄	—	212	1	no	—
1216	C₄⋊C₄	—	212	1	no	—
1217	C₄⋊C₄	—	212	1	no	—
1218	C₄⋊C₄	—	212	1	no	—
1219	C₄⋊C₄	—	212	1	no	—
1220	C₂²⋊C₄	—	2	2	no	—
1221	C₂²⋊C₄	—	2	2	no	—
1222	C₂²⋊C₄	—	2	2	no	—
1223	C₂²⋊C₄	—	2	2	no	—
1224	C₂²⋊C₄	—	4	1	no	—
1225	C₂²⋊C₄	—	4	1	no	—
1226	C₂²⋊C₄	—	4	1	no	—
1227	C₂²⋊C₄	—	4	1	no	—
1228	C₂²⋊C₄	—	4	1	no	—
1229	C₂²⋊C₄	—	4	1	no	—
1230	C₂²⋊C₄	—	4	1	no	—
1231	C₂²⋊C₄	—	4	1	no	—
1232	C₂²⋊C₄	—	4	1	no	—
1233	C₂²⋊C₄	—	4	1	no	—
1234	C₂²⋊C₄	—	106	2	no	—
1235	C₂²⋊C₄	—	106	2	no	—
1236	C₂²⋊C₄	—	106	2	no	—
1237	C₂²⋊C₄	—	106	2	no	—
1238	C₂²⋊C₄	—	106	2	no	—
1239	C₂²⋊C₄	—	106	2	no	—
1240	C₂²⋊C₄	—	106	2	no	—
1241	C₂²⋊C₄	—	106	2	no	—
1242	C₂²⋊C₄	—	106	2	no	—
1243	C₂²⋊C₄	—	106	2	no	—
1244	C₂²⋊C₄	—	106	2	no	—
1245	C₂²⋊C₄	—	212	1	no	—
1246	C₂²⋊C₄	—	212	1	no	—
1247	C₂²⋊C₄	—	212	1	no	—
1248	C₂²⋊C₄	—	212	1	no	—
1249	C₂²⋊C₄	—	212	1	no	—
1250	C₂²⋊C₄	—	212	1	no	—
1251	C₂²⋊C₄	—	212	1	no	—
1252	C₂²⋊C₄	—	212	1	no	—
1253	C₂²⋊C₄	—	212	1	no	—
1254	C₂²⋊C₄	—	212	1	no	—
1255	C₂²⋊C₄	—	212	1	no	—
1256	C₂²⋊C₄	—	212	1	no	—
1257	C₂²⋊C₄	—	212	1	no	—
1258	C₂²⋊C₄	—	212	1	no	—
1259	C₂²⋊C₄	—	212	1	no	—
1260	C₂²⋊C₄	—	212	1	no	—
1261	C₂²⋊C₄	—	212	1	no	—
1262	C₂²⋊C₄	—	212	1	no	—
1263	C₂²⋊C₄	—	212	1	no	—
1264	C₂²⋊C₄	—	212	1	no	—
1265	C₂²⋊C₄	—	212	1	no	—
1266	C₂²⋊C₄	—	212	1	no	—
1267	C₂²⋊C₄	—	212	1	no	—
1268	C₂²⋊C₄	—	212	1	no	—
1269	C₂²⋊C₄	—	212	1	no	—
1270	C₂²⋊C₄	—	212	1	no	—
1271	C₂²⋊C₄	—	212	1	no	—
1272	C₄²	—	4	1	no	—
1273	C₄²	—	4	1	no	—
1274	C₄²	—	106	2	no	—
1275	C₄²	—	106	2	no	—
1276	C₄²	—	106	2	no	—
1277	C₄²	—	212	1	no	—
1278	C₄²	—	212	1	no	—
1279	C₄²	—	212	1	no	—
1280	C₄²	—	212	1	no	—
1281	C₄²	—	212	1	no	—
1282	C₄²	—	212	1	no	—
1283	C₄²	—	212	1	no	—
1284	C₂³	—	2	1	no	—
1285	C₂³	—	2	1	no	—
1286	C₂³	—	2	1	no	—
1287	C₂³	—	2	1	no	—
1288	C₂³	—	2	1	no	—
1289	C₂³	—	2	1	no	—
1290	C₂³	—	2	1	no	—
1291	C₂³	—	2	1	no	—
1292	C₂³	—	2	1	no	—
1293	C₂³	—	2	1	no	—
1294	C₂³	—	2	1	no	—
1295	C₂³	—	2	1	no	—
1296	C₂³	—	2	1	no	—
1297	C₂³	—	2	1	no	—
1298	C₂³	—	2	1	no	—
1299	C₂³	—	2	1	no	—
1300	C₂³	—	2	1	no	—
1301	C₂³	—	2	1	no	—
1302	C₂³	—	2	1	no	—
1303	C₂³	—	2	1	no	—
1304	C₂³	—	53	2	no	—
1305	C₂³	—	106	1	no	—
1306	C₂³	—	106	1	no	—
1307	C₂³	—	106	1	no	—
1308	C₂³	—	106	1	no	—
1309	C₂³	—	106	1	no	—
1310	C₂³	—	106	1	no	—
1311	C₂³	—	106	1	no	—
1312	C₂³	—	106	1	no	—
1313	C₂³	—	106	1	no	—
1314	C₂³	—	106	1	no	—
1315	C₂³	—	106	1	no	—
1316	C₂³	—	106	1	no	—
1317	C₂³	—	106	1	no	—
1318	C₂³	—	424	2	no	—
1319	C₂³	—	424	2	no	—
1320	C₂³	—	424	2	no	—
1321	C₂³	—	424	2	no	—
1322	C₂³	—	424	2	no	—
1323	C₂³	—	424	2	no	—
1324	C₂³	—	212	4	no	—
1325	C₂³	#13133263	1	2	yes	—
1326	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1327	Q₈	—	424	2	no	—
1328	Q₈	—	424	2	no	—
1329	D₄	—	8	2	no	—
1330	D₄	—	8	2	no	—
1331	D₄	—	8	2	no	—
1332	D₄	—	424	2	no	—
1333	D₄	—	424	2	no	—
1334	D₄	—	424	2	no	—
1335	D₄	—	212	4	no	—
1336	C₂×C₄	—	2	1	no	—
1337	C₂×C₄	—	2	1	no	—
1338	C₂×C₄	—	2	1	no	—
1339	C₂×C₄	—	2	1	no	—
1340	C₂×C₄	—	2	1	no	—
1341	C₂×C₄	—	2	1	no	—
1342	C₂×C₄	—	2	1	no	—
1343	C₂×C₄	—	2	1	no	—
1344	C₂×C₄	—	2	1	no	—
1345	C₂×C₄	—	2	1	no	—
1346	C₂×C₄	—	2	1	no	—
1347	C₂×C₄	—	2	1	no	—
1348	C₂×C₄	—	2	1	no	—
1349	C₂×C₄	—	2	1	no	—
1350	C₂×C₄	—	2	1	no	—
1351	C₂×C₄	—	2	1	no	—
1352	C₂×C₄	—	2	1	no	—
1353	C₂×C₄	—	2	1	no	—
1354	C₂×C₄	—	2	1	no	—
1355	C₂×C₄	—	2	1	no	—
1356	C₂×C₄	—	2	1	no	—
1357	C₂×C₄	—	2	1	no	—
1358	C₂×C₄	—	2	1	no	—
1359	C₂×C₄	—	2	1	no	—
1360	C₂×C₄	—	2	1	no	—
1361	C₂×C₄	—	2	1	no	—
1362	C₂×C₄	—	2	1	no	—
1363	C₂×C₄	—	2	1	no	—
1364	C₂×C₄	—	2	1	no	—
1365	C₂×C₄	—	2	1	no	—
1366	C₂×C₄	—	2	1	no	—
1367	C₂×C₄	—	2	1	no	—
1368	C₂×C₄	—	2	1	no	—
1369	C₂×C₄	—	2	1	no	—
1370	C₂×C₄	—	2	1	no	—
1371	C₂×C₄	—	4	4	no	—
1372	C₂×C₄	—	53	2	no	—
1373	C₂×C₄	—	53	2	no	—
1374	C₂×C₄	—	106	1	no	—
1375	C₂×C₄	—	106	1	no	—
1376	C₂×C₄	—	106	1	no	—
1377	C₂×C₄	—	106	1	no	—
1378	C₂×C₄	—	106	1	no	—
1379	C₂×C₄	—	106	1	no	—
1380	C₂×C₄	—	106	1	no	—
1381	C₂×C₄	—	106	1	no	—
1382	C₂×C₄	—	106	1	no	—
1383	C₂×C₄	—	106	1	no	—
1384	C₂×C₄	—	106	1	no	—
1385	C₂×C₄	—	106	1	no	—
1386	C₂×C₄	—	106	1	no	—
1387	C₂×C₄	—	106	1	no	—
1388	C₂×C₄	—	106	1	no	—
1389	C₂×C₄	—	106	1	no	—
1390	C₂×C₄	—	106	1	no	—
1391	C₂×C₄	—	106	1	no	—
1392	C₂×C₄	—	106	1	no	—
1393	C₂×C₄	—	106	1	no	—
1394	C₂×C₄	—	106	1	no	—
1395	C₂×C₄	—	106	1	no	—
1396	C₂×C₄	—	106	1	no	—
1397	C₂×C₄	—	106	1	no	—
1398	C₂×C₄	—	106	1	no	—
1399	C₂×C₄	—	106	1	no	—
1400	C₂×C₄	—	106	1	no	—
1401	C₂×C₄	—	106	1	no	—
1402	C₂×C₄	—	106	1	no	—
1403	C₂×C₄	—	106	1	no	—
1404	C₂×C₄	—	106	1	no	—
1405	C₂×C₄	—	106	1	no	—
1406	C₂×C₄	—	106	1	no	—
1407	C₂×C₄	—	106	1	no	—
1408	C₂×C₄	—	106	1	no	—
1409	C₂×C₄	—	106	1	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	—	424	2	no	—
1415	C₂×C₄	—	424	2	no	—
1416	C₂×C₄	—	212	4	no	—
1417	C₂×C₄	—	212	4	no	—
1418	C₂×C₄	—	212	4	no	—
1419	C₂×C₄	#41×D₅₃	1	2	yes	—
1420	C₂²	—	2	2	no	—
1421	C₂²	—	2	2	no	—
1422	C₂²	—	2	2	no	—
1423	C₂²	—	4	1	no	—
1424	C₂²	—	4	1	no	—
1425	C₂²	—	4	1	no	—
1426	C₂²	—	4	1	no	—
1427	C₂²	—	4	1	no	—
1428	C₂²	—	4	1	no	—
1429	C₂²	—	4	1	no	—
1430	C₂²	—	4	1	no	—
1431	C₂²	—	4	1	no	—
1432	C₂²	—	4	1	no	—
1433	C₂²	—	4	1	no	—
1434	C₂²	—	4	1	no	—
1435	C₂²	—	4	1	no	—
1436	C₂²	—	4	1	no	—
1437	C₂²	—	4	1	no	—
1438	C₂²	—	4	1	no	—
1439	C₂²	—	4	1	no	—
1440	C₂²	—	4	1	no	—
1441	C₂²	—	106	2	no	—
1442	C₂²	—	106	2	no	—
1443	C₂²	—	106	2	no	—
1444	C₂²	—	424	8	no	—
1445	C₂²	—	212	1	no	—
1446	C₂²	—	212	1	no	—
1447	C₂²	—	212	1	no	—
1448	C₂²	—	212	1	no	—
1449	C₂²	—	212	1	no	—
1450	C₂²	—	212	1	no	—
1451	C₂²	—	212	1	no	—
1452	C₂²	—	212	1	no	—
1453	C₂²	—	212	1	no	—
1454	C₂²	—	212	1	no	—
1455	C₂²	—	212	1	no	—
1456	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1457	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1458	C₂²	C₂×#13133263	1	1	yes	characteristic
1459	C₂²	#16811458	1	1	yes	characteristic
1460	C₂²	#16811458	1	1	yes	characteristic
1461	C₂²	#16811458	1	1	yes	characteristic
1462	C₂²	#16811459	1	1	yes	characteristic
1463	C₄	—	2	2	no	—
1464	C₄	—	4	1	no	—
1465	C₄	—	4	1	no	—
1466	C₄	—	4	1	no	—
1467	C₄	—	4	1	no	—
1468	C₄	—	4	1	no	—
1469	C₄	—	4	1	no	—
1470	C₄	—	4	1	no	—
1471	C₄	—	4	1	no	—
1472	C₄	—	4	1	no	—
1473	C₄	—	4	1	no	—
1474	C₄	—	4	1	no	—
1475	C₄	—	106	2	no	—
1476	C₄	—	106	2	no	—
1477	C₄	—	212	1	no	—
1478	C₄	—	212	1	no	—
1479	C₄	—	212	1	no	—
1480	C₄	—	212	1	no	—
1481	C₄	—	212	1	no	—
1482	C₄	—	212	1	no	—
1483	C₄	—	212	1	no	—
1484	C₄	—	212	1	no	—
1485	C₄	—	212	1	no	—
1486	C₄	—	212	1	no	—
1487	C₄	—	212	1	no	—
1488	C₄	—	212	1	no	—
1489	C₂	—	4	2	no	—
1490	C₂	—	8	1	no	—
1491	C₂	—	8	1	no	—
1492	C₂	—	424	1	no	—
1493	C₂	—	212	2	no	—
1494	C₂	#20288099	1	1	yes	characteristic
1495	C₂	#20288446	1	1	yes	characteristic
1496	C₂	#20288548	1	1	yes	characteristic
1497	C₂	#20288906	1	1	yes	characteristic
1498	C₂	#20288988	1	1	yes	characteristic
1499	C₂	#20289071	1	1	yes	characteristic
1500	C₂	#20289387	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator, socle, cosocle	C₂³×C₅₃	C₂⁵
Fitting	C₅₃×#2753	C₂
prime radical	#20281042	C₂
hypercenter	#2753	D₅₃
hypocenter	C₅₃	#36784
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #2753

Complements

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

N	H ≅ G/N	type
1. #20283036	C₂	semidirect
2. #20283012	C₂	semidirect
3. #20282405	C₂	semidirect
4. #20282341	C₂	semidirect
5. #20282239	C₂	semidirect
6. #20282053	C₂	semidirect
7. #20281874	C₂	semidirect
8. #20281769	C₂	semidirect
9. #20281753	C₂	semidirect
10. #20281722	C₂	semidirect
11. #20281326	C₂	semidirect
12. #20281221	C₂	semidirect
13. #20281134	C₂	semidirect
14. #20281094	C₂	semidirect
15. #20281090	C₂	semidirect
17. #20280998	C₂	semidirect
18. #20280749	C₂	semidirect
19. #20280728	C₂	semidirect
20. #20280324	C₂	semidirect
21. #20280240	C₂	semidirect
22. #20279807	C₂	semidirect
23. #20279600	C₂	semidirect
24. #20279575	C₂	semidirect
25. #20279563	C₂	semidirect
26. #20278409	C₂	semidirect
27. #20278093	C₂	semidirect
28. #20277512	C₂	semidirect
29. #20277309	C₂	semidirect
30. #20277151	C₂	semidirect
31. C₅₃×#2753	C₂	semidirect
32. C₂×#13133216	C₂²	semidirect
38. C₂×#13133198	C₂²	semidirect
39. C₂×#13133194	C₂²	semidirect
46. C₂²×C₄×Dic₅₃	C₂²	semidirect
47. #16810565	C₂²	semidirect
48. #16810565	C₂²	semidirect
49. #16810564	C₂²	semidirect
50. #16810563	C₂²	semidirect
52. #16810556	C₂²	semidirect
53. #16810555	C₂²	semidirect
54. #16810553	C₂²	semidirect
55. #16810553	C₂²	semidirect
59. #16810551	C₂²	semidirect
65. #16810548	C₂²	semidirect
66. #16810548	C₂²	semidirect
71. #16810546	C₂²	semidirect
75. #16810544	C₂²	semidirect
87. #16810535	C₂²	semidirect
89. #16810529	C₂²	semidirect
90. #16810527	C₂²	semidirect
91. #16810527	C₂²	semidirect
96. #16810521	C₂²	semidirect
97. #16810521	C₂²	semidirect
98. #16810519	C₂²	semidirect
99. #16810518	C₂²	semidirect
102. #16810517	C₂²	semidirect
103. #16810517	C₂²	semidirect
108. #16810516	C₂²	semidirect
109. #16810516	C₂²	semidirect
125. #16810511	C₂²	semidirect
126. #16810510	C₂²	semidirect
127. #16810510	C₂²	semidirect
128. #16810509	C₂²	semidirect
129. #16810509	C₂²	semidirect
130. #16810506	C₂²	semidirect
131. #16810506	C₂²	semidirect
132. #16810506	C₂²	semidirect
133. #16810505	C₂²	semidirect
134. #16810505	C₂²	semidirect
135. #16810505	C₂²	semidirect
136. #16810505	C₂²	semidirect
137. #16810504	C₂²	semidirect
140. #16810503	C₂²	semidirect
148. #16810498	C₂²	semidirect
149. #16810498	C₂²	semidirect
150. #16810498	C₂²	semidirect
152. #16810496	C₂²	semidirect
153. #16810490	C₂²	semidirect
154. #16810487	C₂²	semidirect
156. #16810484	C₂²	semidirect
158. #16810481	C₂²	semidirect
165. C₄⋊C₄×Dic₅₃	C₂²	semidirect
166. C₄×C₄⋊Dic₅₃	C₂²	semidirect
167. C₂²⋊C₄×Dic₅₃	C₂²	semidirect
168. C₂²⋊C₄×Dic₅₃	C₂²	semidirect
171. #16810468	C₂²	semidirect
172. C₅₃×#400	C₂²	semidirect
173. C₅₃×#397	C₂²	semidirect
178. C₅₃×#390	C₂²	semidirect
181. C₅₃×#388	C₂²	semidirect
182. C₅₃×#388	C₂²	semidirect
184. C₅₃×#386	C₂²	semidirect
185. C₅₃×#385	C₂²	semidirect
186. C₅₃×#382	C₂²	semidirect
745. #2753	D₅₃	semidirect
801. #400	C₂×D₅₃	semidirect
818. #397	C₂×D₅₃	semidirect
852. #390	C₂×D₅₃	semidirect
885. #388	C₂×D₅₃	semidirect
886. #388	C₂×D₅₃	semidirect
910. #386	C₂×D₅₃	semidirect
916. #385	C₂×D₅₃	semidirect
919. #382	C₂×D₅₃	semidirect
937. C₅₃	#36784	semidirect

Maximal subgroups

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

subgroup	index
#20283036	2
#20283012	2
#20282405	2
#20282341	2
#20282239	2
#20282053	2
#20281874	2
#20281769	2
#20281753	2
#20281722	2
#20281326	2
#20281221	2
#20281134	2
#20281094	2
#20281090	2
#20281042	2
#20280998	2
#20280749	2
#20280728	2
#20280324	2
#20280240	2
#20279807	2
#20279600	2
#20279575	2
#20279563	2
#20278409	2
#20278093	2
#20277512	2
#20277309	2
#20277151	2
C₅₃×#2753	2
#36784	53