Subgroups — #27590906

Order 13568.

2326 conjugacy classes of subgroups.

The subgroup lattice has 1532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811253	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂²⋊Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic
3	#20283003	C₂	1	1	yes	maximal, characteristic
4	#20283001	C₂	1	1	yes	maximal, characteristic
5	#20281188	C₂	1	1	yes	maximal, characteristic, complemented
6	#20281186	C₂	1	1	yes	maximal, characteristic, complemented
7	#20281183	C₂	1	1	yes	maximal, characteristic, complemented
8	#20281181	C₂	1	1	yes	maximal, characteristic, complemented
9	#20281176	C₂	1	1	yes	maximal, characteristic, complemented
10	#20281175	C₂	1	1	yes	maximal, characteristic, complemented
11	#20281174	C₂	1	1	yes	maximal, characteristic, complemented
12	#20281032	C₂	1	1	yes	maximal, characteristic, complemented
13	#20281030	C₂	1	1	yes	maximal, characteristic, complemented
14	#20281029	C₂	1	1	yes	maximal, characteristic, complemented
15	#20281028	C₂	1	1	yes	maximal, characteristic, complemented
16	#20281028	C₂	1	1	yes	maximal, characteristic, complemented
17	#20281027	C₂	1	1	yes	maximal, characteristic, complemented
18	#20281027	C₂	1	1	yes	maximal, characteristic, complemented
19	#20281026	C₂	1	1	yes	maximal, characteristic, complemented
20	#20280533	C₂	1	1	yes	maximal, characteristic, complemented
21	#20280529	C₂	1	1	yes	maximal, characteristic, complemented
22	#20279871	C₂	1	1	yes	maximal, characteristic
23	#20279867	C₂	1	1	yes	maximal, characteristic
24	#20279003	C₂	1	1	yes	maximal, characteristic, complemented
25	#20279000	C₂	1	1	yes	maximal, characteristic, complemented
26	#20278987	C₂	1	1	yes	maximal, characteristic
27	#20278984	C₂	1	1	yes	maximal, characteristic
28	#20278358	C₂	1	1	yes	maximal, characteristic, complemented
29	#20278354	C₂	1	1	yes	maximal, characteristic, complemented
30	#20277314	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2690	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×Q₈×D₅₃	C₂²	1	1	yes	characteristic
33	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
34	#16811253	—	2	8	no	—
35	C₂×#13133217	C₂²	1	1	yes	characteristic, complemented
36	C₂×#13133217	C₂²	1	1	yes	characteristic, complemented
37	C₂×#13133216	C₂²	1	1	yes	characteristic, complemented
38	C₂×#13133216	C₂²	1	1	yes	characteristic, complemented
39	C₂×#13133216	C₂²	1	1	yes	characteristic, complemented
40	C₂×#13133216	C₂²	1	1	yes	characteristic, complemented
41	C₂×#13133216	C₂²	1	1	yes	characteristic, complemented
42	C₂×#13133215	C₂²	1	1	yes	characteristic, complemented
43	C₂×#13133208	C₂²	1	1	yes	characteristic, complemented
44	C₂×#13133207	C₂²	1	1	yes	characteristic, complemented
45	C₂×#13133207	C₂²	1	1	yes	characteristic, complemented
46	C₂×#13133197	C₂²	1	1	yes	characteristic
47	C₂×#13133197	C₂²	1	1	yes	characteristic
48	C₂×#13133197	C₂²	1	1	yes	characteristic
49	C₂×#13133197	C₂²	1	1	yes	characteristic
50	C₂×#13133196	C₂²	1	1	yes	characteristic
51	C₂×#13133196	C₂²	1	1	yes	characteristic
52	C₂×#13133195	C₂²	1	1	yes	characteristic
53	C₂×#13133195	C₂²	1	1	yes	characteristic
54	C₂×#13133195	C₂²	1	1	yes	characteristic
55	C₂×#13133195	C₂²	1	1	yes	characteristic
56	C₂×#13133195	C₂²	1	1	yes	characteristic
57	C₂×#13133194	C₂²	1	1	yes	characteristic
58	C₂×#13133194	C₂²	1	1	yes	characteristic
59	C₂×#13133194	C₂²	1	1	yes	characteristic
60	C₂×#13133193	C₂²	1	1	yes	characteristic
61	C₂²⋊Q₈×D₅₃	—	2	8	no	—
62	C₂×#13133175	C₂²	1	1	yes	characteristic
63	C₂×#13133174	C₂²	1	1	yes	characteristic
64	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
65	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
66	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
68	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
69	#16810565	C₂²	1	1	yes	characteristic, complemented
70	#16810565	C₂²	1	1	yes	characteristic, complemented
71	#16810564	C₂²	1	1	yes	characteristic, complemented
72	#16810564	C₂²	1	1	yes	characteristic, complemented
73	#16810561	C₂²	1	1	yes	characteristic, complemented
74	#16810561	C₂²	1	1	yes	characteristic, complemented
75	#16810560	C₂²	1	1	yes	characteristic
76	#16810559	C₂²	1	1	yes	characteristic
77	#16810559	C₂²	1	1	yes	characteristic
78	#16810558	C₂²	1	1	yes	characteristic
79	#16810557	C₂²	1	1	yes	characteristic, complemented
80	#16810557	C₂²	1	1	yes	characteristic, complemented
81	#16810557	C₂²	1	1	yes	characteristic, complemented
82	#16810556	C₂²	1	1	yes	characteristic, complemented
83	#16810556	C₂²	1	1	yes	characteristic, complemented
84	#16810556	C₂²	1	1	yes	characteristic, complemented
85	#16810555	C₂²	1	1	yes	characteristic, complemented
86	#16810555	C₂²	1	1	yes	characteristic, complemented
87	#16810555	C₂²	1	1	yes	characteristic, complemented
88	#16810553	C₂²	1	1	yes	characteristic, complemented
89	#16810553	C₂²	1	1	yes	characteristic, complemented
90	#16810552	C₂²	1	1	yes	characteristic
91	#16810552	C₂²	1	1	yes	characteristic
92	#16810551	C₂²	1	1	yes	characteristic
93	#16810551	C₂²	1	1	yes	characteristic
94	#16810549	C₂²	1	1	yes	characteristic
95	#16810549	C₂²	1	1	yes	characteristic
96	#16810544	C₂²	1	1	yes	characteristic, complemented
97	#16810544	C₂²	1	1	yes	characteristic, complemented
98	#16810544	C₂²	1	1	yes	characteristic, complemented
99	#16810544	C₂²	1	1	yes	characteristic, complemented
100	#16810544	C₂²	1	1	yes	characteristic, complemented
101	#16810544	C₂²	1	1	yes	characteristic, complemented
102	#16810544	C₂²	1	1	yes	characteristic, complemented
103	#16810543	C₂²	1	1	yes	characteristic, complemented
104	#16810543	C₂²	1	1	yes	characteristic, complemented
105	#16810543	C₂²	1	1	yes	characteristic, complemented
106	#16810542	C₂²	1	1	yes	characteristic, complemented
107	#16810536	C₂²	1	1	yes	characteristic
108	#16810536	C₂²	1	1	yes	characteristic
109	#16810535	C₂²	1	1	yes	characteristic
110	#16810535	C₂²	1	1	yes	characteristic
111	#16810528	C₂²	1	1	yes	characteristic, complemented
112	#16810527	C₂²	1	1	yes	characteristic, complemented
113	#16810527	C₂²	1	1	yes	characteristic, complemented
114	#16810517	C₂²	1	1	yes	characteristic
115	#16810516	C₂²	1	1	yes	characteristic
116	#16810516	C₂²	1	1	yes	characteristic
117	#16810516	C₂²	1	1	yes	characteristic
118	#16810516	C₂²	1	1	yes	characteristic
119	#16810515	C₂²	1	1	yes	characteristic
120	#16810515	C₂²	1	1	yes	characteristic
121	#16810515	C₂²	1	1	yes	characteristic
122	#16810514	C₂²	1	1	yes	characteristic
123	#16810514	C₂²	1	1	yes	characteristic
124	#16810513	C₂²	1	1	yes	characteristic
125	#16810512	C₂²	1	1	yes	characteristic
126	#16810512	C₂²	1	1	yes	characteristic
127	#16810511	C₂²	1	1	yes	characteristic
128	#16810510	C₂²	1	1	yes	characteristic, complemented
129	#16810510	C₂²	1	1	yes	characteristic, complemented
130	#16810510	C₂²	1	1	yes	characteristic, complemented
131	#16810509	C₂²	1	1	yes	characteristic, complemented
132	#16810508	C₂²	1	1	yes	characteristic, complemented
133	#16810508	C₂²	1	1	yes	characteristic, complemented
134	#16810507	C₂²	1	1	yes	characteristic, complemented
135	#16810507	C₂²	1	1	yes	characteristic, complemented
136	#16810506	C₂²	1	1	yes	characteristic, complemented
137	#16810506	C₂²	1	1	yes	characteristic, complemented
138	#16810506	C₂²	1	1	yes	characteristic, complemented
139	#16810505	C₂²	1	1	yes	characteristic, complemented
140	#16810504	C₂²	1	1	yes	characteristic, complemented
141	#16810504	C₂²	1	1	yes	characteristic, complemented
142	#16810498	C₂²	1	1	yes	characteristic
143	#16810498	C₂²	1	1	yes	characteristic
144	#16810497	C₂²	1	1	yes	characteristic
145	#16810497	C₂²	1	1	yes	characteristic
146	#16810497	C₂²	1	1	yes	characteristic
147	#16810497	C₂²	1	1	yes	characteristic
148	#16810497	C₂²	1	1	yes	characteristic
149	#16810497	C₂²	1	1	yes	characteristic
150	#16810497	C₂²	1	1	yes	characteristic
151	#16810497	C₂²	1	1	yes	characteristic
152	#16810497	C₂²	1	1	yes	characteristic
153	#16810496	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
157	#16810485	C₂²	1	1	yes	characteristic
158	#16810485	C₂²	1	1	yes	characteristic
159	#16810485	C₂²	1	1	yes	characteristic
160	#16810485	C₂²	1	1	yes	characteristic
161	#16810485	C₂²	1	1	yes	characteristic
162	#16810485	C₂²	1	1	yes	characteristic
163	#16810482	C₂²	1	1	yes	characteristic
164	#16810482	C₂²	1	1	yes	characteristic
165	#16810481	C₂²	1	1	yes	characteristic
166	#16810480	C₂²	1	1	yes	characteristic
167	#16810480	C₂²	1	1	yes	characteristic
168	#16810478	C₂²	1	1	yes	characteristic
169	#16810478	C₂²	1	1	yes	characteristic
170	#16810478	C₂²	1	1	yes	characteristic
171	#16810478	C₂²	1	1	yes	characteristic
172	C₄×#11719921	C₂²	1	1	yes	characteristic
173	#16810470	C₂²	1	1	yes	characteristic
174	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
175	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
176	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
177	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
178	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
179	C₅₃×#397	C₂²	1	1	yes	characteristic
180	C₅₃×#397	C₂²	1	1	yes	characteristic
181	C₅₃×#395	C₂²	1	1	yes	characteristic, complemented
182	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
183	C₅₃×#388	C₂²	1	1	yes	characteristic
184	C₅₃×#388	C₂²	1	1	yes	characteristic
185	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
186	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
187	C₅₃×#385	C₂²	1	1	yes	characteristic
188	C₅₃×#380	C₂²	1	1	yes	characteristic
189	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
190	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
191	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
192	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
193	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
194	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
195	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
196	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
197	C₂×Q₈×D₅₃	—	2	4	no	—
198	C₂×Q₈×D₅₃	—	4	2	no	—
199	C₂×Q₈×D₅₃	—	4	2	no	—
200	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
201	C₂²×C₄×D₅₃	—	2	4	no	—
202	C₂²×C₄×D₅₃	—	4	2	no	—
203	C₂²×C₄×D₅₃	—	4	2	no	—
204	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
205	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
206	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
207	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
208	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
209	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
210	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
211	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
212	#13133217	—	2	4	no	—
213	#13133217	—	4	2	no	—
214	#13133216	—	2	4	no	—
215	#13133216	—	2	4	no	—
216	#13133216	—	2	4	no	—
217	#13133216	—	4	2	no	—
218	#13133216	—	4	2	no	—
219	#13133215	—	4	2	no	—
220	#13133208	—	2	4	no	—
221	#13133207	—	2	4	no	—
222	#13133207	—	2	4	no	—
223	#13133197	—	2	4	no	—
224	#13133197	—	2	4	no	—
225	#13133197	—	2	4	no	—
226	#13133197	—	4	2	no	—
227	#13133196	—	2	4	no	—
228	#13133196	—	4	2	no	—
229	#13133195	—	2	4	no	—
230	#13133195	—	2	4	no	—
231	#13133195	—	2	4	no	—
232	#13133195	—	2	4	no	—
233	#13133195	—	4	2	no	—
234	#13133194	—	2	4	no	—
235	#13133194	—	2	4	no	—
236	#13133194	—	4	2	no	—
237	#13133193	—	2	4	no	—
238	#13133175	—	2	4	no	—
239	#13133174	—	2	4	no	—
240	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
241	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
242	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
255	C₂×#11719919	C₂³	1	1	yes	characteristic
256	C₂×#11719919	C₂³	1	1	yes	characteristic
257	C₂×#11719919	C₂³	1	1	yes	characteristic
258	C₂×#11719919	C₂³	1	1	yes	characteristic
259	C₂×#11719919	C₂³	1	1	yes	characteristic
260	C₂×#11719919	C₂³	1	1	yes	characteristic
261	C₂×#11719919	C₂³	1	1	yes	characteristic
262	C₂×#11719919	C₂³	1	1	yes	characteristic
263	C₂×#11719919	C₂³	1	1	yes	characteristic
264	C₂×#11719919	C₂³	1	1	yes	characteristic
265	C₂×#11719919	C₂³	1	1	yes	characteristic
266	C₂×#11719919	C₂³	1	1	yes	characteristic
267	C₂×#11719919	C₂³	1	1	yes	characteristic
268	C₂×#11719919	C₂³	1	1	yes	characteristic
269	C₂×#11719919	C₂³	1	1	yes	characteristic
270	C₂×#11719919	C₂³	1	1	yes	characteristic
271	C₂×#11719919	C₂³	1	1	yes	characteristic
272	C₂×#11719919	C₂³	1	1	yes	characteristic
273	C₂×#11719919	C₂³	1	1	yes	characteristic
274	C₂×#11719919	C₂³	1	1	yes	characteristic
275	C₂×#11719919	C₂³	1	1	yes	characteristic
276	C₂×#11719919	C₂³	1	1	yes	characteristic
277	C₄⋊C₄×D₅₃	—	2	4	no	—
278	C₄⋊C₄×D₅₃	—	2	4	no	—
279	C₄⋊C₄×D₅₃	D₄	1	8	yes	—
280	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
281	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
286	C₂×#11719921	C₂³	1	1	yes	characteristic
287	C₂×#11719921	C₂³	1	1	yes	characteristic
288	C₂×#11719921	C₂³	1	1	yes	characteristic
289	C₂×#11719921	C₂³	1	1	yes	characteristic
290	C₂×#11719921	C₂³	1	1	yes	characteristic
291	C₂×#11719921	C₂³	1	1	yes	characteristic
292	C₂×#11719921	C₂³	1	1	yes	characteristic
293	C₂×#11719921	C₂³	1	1	yes	characteristic
294	C₂×#11719921	C₂³	1	1	yes	characteristic
295	C₂×#11719921	C₂³	1	1	yes	characteristic
296	C₂×#11719921	C₂³	1	1	yes	characteristic
297	C₂×#11719921	C₂³	1	1	yes	characteristic
298	C₂×#11719921	C₂³	1	1	yes	characteristic
299	C₂×#11719921	C₂³	1	1	yes	characteristic
300	C₂×#11719921	C₂³	1	1	yes	characteristic
301	C₂×#11719921	C₂³	1	1	yes	characteristic
302	C₂×#11719921	C₂³	1	1	yes	characteristic
303	C₂×#11719921	C₂³	1	1	yes	characteristic
304	C₂×#11719921	C₂³	1	1	yes	characteristic
305	C₂×#11719921	C₂³	1	1	yes	characteristic
306	C₂²⋊C₄×D₅₃	—	2	4	no	—
307	C₂²⋊C₄×D₅₃	—	2	4	no	—
308	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
309	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
310	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
311	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
312	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
313	C₂×C₄×Dic₅₃	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	#13133124	C₂³	1	1	yes	characteristic
329	#13133124	C₂³	1	1	yes	characteristic
330	#13133124	C₂³	1	1	yes	characteristic
331	#13133124	C₂³	1	1	yes	characteristic
332	#13133124	C₂³	1	1	yes	characteristic
333	#13133124	C₂³	1	1	yes	characteristic
334	#13133124	C₂³	1	1	yes	characteristic
335	#13133124	C₂³	1	1	yes	characteristic
336	#13133124	C₂³	1	1	yes	characteristic
337	#13133124	C₂³	1	1	yes	characteristic
338	#13133124	C₂³	1	1	yes	characteristic
339	#13133124	C₂³	1	1	yes	characteristic
340	#13133124	C₂³	1	1	yes	characteristic
341	#13133124	C₂³	1	1	yes	characteristic
342	#13133124	C₂³	1	1	yes	characteristic
343	#13133124	C₂³	1	1	yes	characteristic
344	#13133124	C₂³	1	1	yes	characteristic
345	#13133124	C₂³	1	1	yes	characteristic
346	#13133124	C₂³	1	1	yes	characteristic
347	#13133124	C₂³	1	1	yes	characteristic
348	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
349	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
350	#125×C₅₃	—	2	4	no	—
351	C₂²⋊Q₈×C₅₃	—	2	4	no	—
352	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
353	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
354	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
355	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
356	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
357	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
358	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
359	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
360	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
361	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
362	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
363	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
364	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
365	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
366	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
367	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
368	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
369	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
370	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
371	#95×C₅₃	C₂³	1	1	yes	characteristic
372	#95×C₅₃	C₂³	1	1	yes	characteristic
373	#95×C₅₃	C₂³	1	1	yes	characteristic
374	#95×C₅₃	C₂³	1	1	yes	characteristic
375	#95×C₅₃	C₂³	1	1	yes	characteristic
376	#95×C₅₃	C₂³	1	1	yes	characteristic
377	#95×C₅₃	C₂³	1	1	yes	characteristic
378	#95×C₅₃	C₂³	1	1	yes	characteristic
379	#95×C₅₃	C₂³	1	1	yes	characteristic
380	#95×C₅₃	C₂³	1	1	yes	characteristic
381	#95×C₅₃	C₂³	1	1	yes	characteristic
382	#95×C₅₃	C₂³	1	1	yes	characteristic
383	#95×C₅₃	C₂³	1	1	yes	characteristic
384	#95×C₅₃	C₂³	1	1	yes	characteristic
385	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂³×D₅₃	—	2	2	no	—
387	C₂³×D₅₃	—	2	2	no	—
388	C₂³×D₅₃	—	2	2	no	—
389	C₂³×D₅₃	—	2	2	no	—
390	C₂³×D₅₃	—	2	2	no	—
391	C₂³×D₅₃	—	4	1	no	—
392	C₂³×D₅₃	—	4	1	no	—
393	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
394	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
395	C₂×Q₈×C₅₃	—	2	2	no	—
396	C₂×Q₈×C₅₃	—	2	2	no	—
397	C₂×Q₈×C₅₃	—	4	1	no	—
398	C₂²×C₄×C₅₃	—	2	2	no	—
399	C₂²×C₄×C₅₃	—	2	2	no	—
400	C₂²×C₄×C₅₃	—	4	1	no	—
401	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
410	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
411	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
412	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
413	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
414	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
415	C₂²×Dic₅₃	—	2	2	no	—
416	C₂²×Dic₅₃	—	2	2	no	—
417	C₂²×Dic₅₃	—	4	1	no	—
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	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
429	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
430	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
431	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
432	Q₈×D₅₃	—	4	16	no	—
433	C₂×C₄×D₅₃	—	2	2	no	—
434	C₂×C₄×D₅₃	—	2	2	no	—
435	C₂×C₄×D₅₃	—	2	2	no	—
436	C₂×C₄×D₅₃	—	2	2	no	—
437	C₂×C₄×D₅₃	—	2	2	no	—
438	C₂×C₄×D₅₃	—	2	2	no	—
439	C₂×C₄×D₅₃	—	2	2	no	—
440	C₂×C₄×D₅₃	—	2	2	no	—
441	C₂×C₄×D₅₃	—	2	2	no	—
442	C₂×C₄×D₅₃	—	2	2	no	—
443	C₂×C₄×D₅₃	—	2	2	no	—
444	C₂×C₄×D₅₃	—	2	2	no	—
445	C₂×C₄×D₅₃	—	2	2	no	—
446	C₂×C₄×D₅₃	—	4	16	no	—
447	C₂×C₄×D₅₃	—	4	1	no	—
448	C₂×C₄×D₅₃	—	4	1	no	—
449	C₂×C₄×D₅₃	—	4	1	no	—
450	C₂×C₄×D₅₃	—	4	1	no	—
451	C₂×C₄×D₅₃	—	4	1	no	—
452	C₂×C₄×D₅₃	—	4	1	no	—
453	C₂×C₄×D₅₃	—	4	1	no	—
454	C₂×C₄×D₅₃	—	4	1	no	—
455	C₂×C₄×D₅₃	C₂×D₄	1	4	yes	—
456	C₂×C₄×D₅₃	C₂×D₄	1	4	yes	—
457	C₂×C₄×D₅₃	C₂×D₄	1	4	yes	—
458	C₂×Dic₁₀₆	—	2	2	no	—
459	C₂×Dic₁₀₆	—	2	2	no	—
460	C₂×Dic₁₀₆	—	2	2	no	—
461	C₂×Dic₁₀₆	—	2	2	no	—
462	C₂×Dic₁₀₆	—	2	2	no	—
463	C₂×Dic₁₀₆	—	2	2	no	—
464	C₂×Dic₁₀₆	—	2	2	no	—
465	C₂×Dic₁₀₆	—	2	2	no	—
466	C₂×Dic₁₀₆	—	2	2	no	—
467	C₂×Dic₁₀₆	—	2	2	no	—
468	C₂×Dic₁₀₆	—	4	1	no	—
469	C₂×Dic₁₀₆	—	4	1	no	—
470	C₂×Dic₁₀₆	—	4	1	no	—
471	C₂×Dic₁₀₆	—	4	1	no	—
472	C₂×Dic₁₀₆	—	4	1	no	—
473	C₂×Dic₁₀₆	—	4	1	no	—
474	C₂×Dic₁₀₆	—	4	1	no	—
475	C₂×Dic₁₀₆	—	4	1	no	—
476	C₂×Dic₁₀₆	—	4	1	no	—
477	C₂×Dic₁₀₆	—	4	1	no	—
478	C₂×Dic₁₀₆	—	4	1	no	—
479	C₄⋊C₄×C₅₃	—	2	2	no	—
480	C₄⋊C₄×C₅₃	—	2	2	no	—
481	C₄⋊C₄×C₅₃	—	2	2	no	—
482	C₄⋊C₄×C₅₃	—	2	2	no	—
483	C₄⋊C₄×C₅₃	—	2	2	no	—
484	C₄⋊C₄×C₅₃	—	2	2	no	—
485	C₄⋊C₄×C₅₃	—	2	2	no	—
486	C₄⋊C₄×C₅₃	—	2	2	no	—
487	C₄⋊C₄×C₅₃	—	4	1	no	—
488	C₄⋊C₄×C₅₃	—	4	1	no	—
489	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
490	C₂²⋊C₄×C₅₃	—	2	2	no	—
491	C₂²⋊C₄×C₅₃	—	2	2	no	—
492	C₂²⋊C₄×C₅₃	—	2	2	no	—
493	C₂²⋊C₄×C₅₃	—	2	2	no	—
494	C₂²⋊C₄×C₅₃	—	2	2	no	—
495	C₂²⋊C₄×C₅₃	—	4	1	no	—
496	C₄²×C₅₃	—	2	2	no	—
497	C₄²×C₅₃	—	4	1	no	—
498	C₂²⋊Dic₅₃	—	2	2	no	—
499	C₂²⋊Dic₅₃	—	2	2	no	—
500	C₂²⋊Dic₅₃	—	2	2	no	—
501	C₂²⋊Dic₅₃	—	4	1	no	—
502	C₂²⋊Dic₅₃	—	4	1	no	—
503	C₂²⋊Dic₅₃	—	4	1	no	—
504	#11719921	—	2	2	no	—
505	#11719921	—	2	2	no	—
506	#11719921	—	2	2	no	—
507	#11719921	—	2	2	no	—
508	#11719921	—	2	2	no	—
509	#11719921	—	2	2	no	—
510	#11719921	—	2	2	no	—
511	#11719921	—	2	2	no	—
512	#11719921	—	2	2	no	—
513	#11719921	—	2	2	no	—
514	#11719921	—	2	2	no	—
515	#11719921	—	2	2	no	—
516	#11719921	—	2	2	no	—
517	#11719921	—	2	2	no	—
518	#11719921	—	2	2	no	—
519	#11719921	—	2	2	no	—
520	#11719921	—	4	1	no	—
521	#11719921	—	4	1	no	—
522	#11719921	—	4	1	no	—
523	#11719921	—	4	1	no	—
524	C₄⋊Dic₅₃	—	2	2	no	—
525	C₄⋊Dic₅₃	—	2	2	no	—
526	C₄⋊Dic₅₃	—	2	2	no	—
527	C₄⋊Dic₅₃	—	2	2	no	—
528	C₄⋊Dic₅₃	—	2	2	no	—
529	C₄⋊Dic₅₃	—	2	2	no	—
530	C₄⋊Dic₅₃	—	2	2	no	—
531	C₄⋊Dic₅₃	—	2	2	no	—
532	C₄⋊Dic₅₃	—	2	2	no	—
533	C₄⋊Dic₅₃	—	2	2	no	—
534	C₄⋊Dic₅₃	—	4	1	no	—
535	C₄⋊Dic₅₃	—	4	1	no	—
536	C₄⋊Dic₅₃	—	4	1	no	—
537	C₄⋊Dic₅₃	—	4	1	no	—
538	C₄⋊Dic₅₃	C₂×D₄	1	4	yes	—
539	#11719919	—	2	2	no	—
540	#11719919	—	2	2	no	—
541	#11719919	—	2	2	no	—
542	#11719919	—	2	2	no	—
543	#11719919	—	2	2	no	—
544	#11719919	—	2	2	no	—
545	#11719919	—	2	2	no	—
546	#11719919	—	2	2	no	—
547	#11719919	—	2	2	no	—
548	#11719919	—	2	2	no	—
549	#11719919	—	2	2	no	—
550	#11719919	—	2	2	no	—
551	#11719919	—	2	2	no	—
552	#11719919	—	2	2	no	—
553	#11719919	—	4	1	no	—
554	#11719919	—	4	1	no	—
555	#11719919	—	4	1	no	—
556	#11719919	—	4	1	no	—
557	#11719919	—	4	1	no	—
558	#11719919	—	4	1	no	—
559	#11719919	C₂×D₄	1	4	yes	—
560	#11719919	C₂×D₄	1	4	yes	—
561	C₄×Dic₅₃	—	2	2	no	—
562	C₄×Dic₅₃	—	2	2	no	—
563	C₄×Dic₅₃	—	2	2	no	—
564	C₄×Dic₅₃	—	4	1	no	—
565	C₄×Dic₅₃	—	4	1	no	—
566	C₄×Dic₅₃	—	4	1	no	—
567	C₂³×C₅₃	—	2	1	no	—
568	C₂³×C₅₃	—	2	1	no	—
569	C₂³×C₅₃	—	2	1	no	—
570	C₂³×C₅₃	—	2	1	no	—
571	C₂³×C₅₃	—	2	1	no	—
572	C₂³×C₅₃	—	2	1	no	—
573	C₂³×C₅₃	2₋¹⁺⁴	1	2	yes	—
574	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
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	8	no	—
580	C₂²×D₅₃	—	2	1	no	—
581	C₂²×D₅₃	—	2	1	no	—
582	C₂²×D₅₃	—	2	1	no	—
583	C₂²×D₅₃	—	2	1	no	—
584	C₂²×D₅₃	—	2	1	no	—
585	C₂²×D₅₃	—	2	1	no	—
586	C₂²×D₅₃	—	4	4	no	—
587	C₂²×D₅₃	—	4	4	no	—
588	C₂²×D₅₃	—	4	4	no	—
589	C₂²×D₅₃	—	4	4	no	—
590	C₂²×D₅₃	—	4	4	no	—
591	C₂²×D₅₃	—	4	4	no	—
592	C₂²×D₅₃	C₂²×D₄	1	2	yes	—
593	C₂²×D₅₃	2₋¹⁺⁴	1	2	yes	—
594	C₂²×D₅₃	2₋¹⁺⁴	1	2	yes	—
595	C₂²×D₅₃	2₋¹⁺⁴	1	2	yes	—
596	Q₈×C₅₃	—	4	4	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	—	2	1	no	—
631	C₂×C₄×C₅₃	—	2	1	no	—
632	C₂×C₄×C₅₃	—	2	1	no	—
633	C₂×C₄×C₅₃	—	2	1	no	—
634	C₂×C₄×C₅₃	—	2	1	no	—
635	C₂×C₄×C₅₃	—	4	4	no	—
636	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
637	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
638	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
639	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
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	—	2	1	no	—
669	C₂×Dic₅₃	—	2	1	no	—
670	C₂×Dic₅₃	—	2	1	no	—
671	C₂×Dic₅₃	—	2	1	no	—
672	C₂×Dic₅₃	—	2	1	no	—
673	C₂×Dic₅₃	—	2	1	no	—
674	C₂×Dic₅₃	—	2	1	no	—
675	C₂×Dic₅₃	—	2	1	no	—
676	C₂×Dic₅₃	—	2	1	no	—
677	C₂×Dic₅₃	—	2	1	no	—
678	C₂×Dic₅₃	—	4	4	no	—
679	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
680	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
681	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
682	C₂×Dic₅₃	H(5,𝔽₂)	1	2	yes	—
683	C₄×D₅₃	—	2	8	no	—
684	C₄×D₅₃	—	2	8	no	—
685	C₄×D₅₃	—	4	4	no	—
686	C₄×D₅₃	—	4	4	no	—
687	C₄×D₅₃	—	4	4	no	—
688	C₄×D₅₃	—	4	4	no	—
689	C₄×D₅₃	—	4	4	no	—
690	C₄×D₅₃	—	4	4	no	—
691	Dic₁₀₆	—	4	4	no	—
692	Dic₁₀₆	—	4	4	no	—
693	Dic₁₀₆	—	4	4	no	—
694	Dic₁₀₆	—	8	2	no	—
695	Dic₁₀₆	—	8	2	no	—
696	Dic₁₀₆	—	8	2	no	—
697	Dic₁₀₆	—	8	2	no	—
698	#36708	—	53	1	no	maximal, Sylow
699	C₂²×C₅₃	—	2	2	no	—
700	C₂²×C₅₃	—	2	2	no	—
701	C₂²×C₅₃	—	2	2	no	—
702	C₂²×C₅₃	—	4	1	no	—
703	C₂²×C₅₃	—	4	1	no	—
704	C₂²×C₅₃	—	4	1	no	—
705	C₂²×C₅₃	—	4	1	no	—
706	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
707	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
708	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
709	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
710	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
711	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
712	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
713	C₂×D₅₃	—	2	2	no	—
714	C₂×D₅₃	—	2	2	no	—
715	C₂×D₅₃	—	2	2	no	—
716	C₂×D₅₃	—	2	2	no	—
717	C₂×D₅₃	—	2	2	no	—
718	C₂×D₅₃	—	2	2	no	—
719	C₂×D₅₃	—	2	2	no	—
720	C₂×D₅₃	—	2	2	no	—
721	C₂×D₅₃	—	2	2	no	—
722	C₂×D₅₃	—	4	16	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	#536	1	4	yes	—
728	C₄×C₅₃	—	2	2	no	—
729	C₄×C₅₃	—	2	2	no	—
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	Dic₅₃	—	2	2	no	—
743	Dic₅₃	—	2	2	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	C₂×#544	—	53	1	no	—
757	C₂²×C₂²⋊Q₈	—	53	1	no	—
758	#2848	—	53	1	no	—
759	#2848	—	53	1	no	—
760	#2690	—	53	1	no	—
761	#2690	—	53	1	no	—
762	#2690	—	53	1	no	—
763	#2690	—	53	1	no	—
764	#2690	—	53	1	no	—
765	#2690	—	53	1	no	—
766	#2690	—	53	1	no	—
767	#2690	D₅₃	1	1	yes	characteristic, complemented
768	#2677	—	53	1	no	—
769	#2677	—	53	1	no	—
770	#2677	—	53	1	no	—
771	#2677	—	53	1	no	—
772	#2677	—	53	1	no	—
773	#2677	—	53	1	no	—
774	#2677	—	53	1	no	—
775	#2677	—	53	1	no	—
776	#2627	—	53	1	no	—
777	#2627	—	53	1	no	—
778	#2561	—	53	1	no	—
779	#2561	—	53	1	no	—
780	#2484	—	53	1	no	—
781	#2484	—	53	1	no	—
782	#2482	—	53	1	no	—
783	#2482	—	53	1	no	—
784	#2434	—	53	1	no	—
785	#2434	—	53	1	no	—
786	#2313	—	53	1	no	—
787	C₂×C₅₃	—	4	2	no	—
788	C₂×C₅₃	C₂×#536	1	1	yes	characteristic
789	C₂×C₅₃	#3484	1	1	yes	characteristic
790	C₂×C₅₃	#3486	1	1	yes	characteristic
791	C₂×C₅₃	#3538	1	1	yes	characteristic
792	C₂×C₅₃	#3538	1	1	yes	characteristic
793	C₂×C₅₃	#3538	1	1	yes	characteristic
794	C₂×C₅₃	#3538	1	1	yes	characteristic
795	D₅₃	—	2	4	no	—
796	D₅₃	—	4	2	no	—
797	C₂³×Q₈	—	53	1	no	—
798	C₂⁴×C₄	—	53	1	no	—
799	#544	—	106	8	no	—
800	C₂×C₄⋊Q₈	—	53	1	no	—
801	C₂×C₄⋊Q₈	—	53	1	no	—
802	C₂×C₄⋊Q₈	—	53	1	no	—
803	C₂×C₄⋊Q₈	—	53	1	no	—
804	C₂×C₄⋊Q₈	—	53	1	no	—
805	C₂×C₄⋊Q₈	—	53	1	no	—
806	C₂×C₄⋊Q₈	—	53	1	no	—
807	C₂×C₄⋊Q₈	—	53	1	no	—
808	C₂×#125	—	53	1	no	—
809	C₂×#125	—	53	1	no	—
810	C₂×#125	—	53	1	no	—
811	C₂×#125	C₂×D₅₃	1	1	yes	characteristic, complemented
812	C₂×C₂²⋊Q₈	—	53	1	no	—
813	C₂×C₂²⋊Q₈	—	53	1	no	—
814	C₂×C₂²⋊Q₈	—	53	1	no	—
815	C₂×C₂²⋊Q₈	—	53	1	no	—
816	C₂×C₂²⋊Q₈	—	53	1	no	—
817	C₂×C₂²⋊Q₈	—	53	1	no	—
818	C₂×C₂²⋊Q₈	—	53	1	no	—
819	C₂×C₂²⋊Q₈	—	53	1	no	—
820	C₂×C₂²⋊Q₈	—	53	1	no	—
821	C₂×C₂²⋊Q₈	—	53	1	no	—
822	C₂×C₂²⋊Q₈	—	53	1	no	—
823	C₂×C₂²⋊Q₈	—	53	1	no	—
824	C₂×C₂²⋊Q₈	—	53	1	no	—
825	C₂×C₂²⋊Q₈	—	53	1	no	—
826	C₂×C₂²⋊Q₈	—	53	1	no	—
827	C₂×C₂²⋊Q₈	—	106	8	no	—
828	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
829	C₂×#117	—	53	1	no	—
830	C₂×#117	—	53	1	no	—
831	C₂²×C₄⋊C₄	—	53	1	no	—
832	C₂²×C₄⋊C₄	—	53	1	no	—
833	C₂²×C₄⋊C₄	—	53	1	no	—
834	C₂²×C₂²⋊C₄	—	53	1	no	—
835	C₂²×C₂²⋊C₄	—	53	1	no	—
836	#400	—	53	1	no	—
837	#400	—	53	1	no	—
838	#400	—	53	1	no	—
839	#400	—	53	1	no	—
840	#400	—	53	1	no	—
841	#400	—	53	1	no	—
842	#400	C₂×D₅₃	1	1	yes	characteristic, complemented
843	#400	C₂×D₅₃	1	1	yes	characteristic, complemented
844	#399	—	53	1	no	—
845	#399	—	53	1	no	—
846	#399	—	53	1	no	—
847	#399	—	53	1	no	—
848	#398	—	53	1	no	—
849	#398	—	53	1	no	—
850	#398	—	53	1	no	—
851	#398	—	53	1	no	—
852	#398	—	53	1	no	—
853	#398	—	53	1	no	—
854	#398	—	53	1	no	—
855	#398	—	53	1	no	—
856	#398	—	53	1	no	—
857	#398	—	53	1	no	—
858	#398	—	53	1	no	—
859	#398	C₂×D₅₃	1	1	yes	characteristic, complemented
860	#397	—	53	1	no	—
861	#397	—	53	1	no	—
862	#397	—	53	1	no	—
863	#397	—	53	1	no	—
864	#397	—	53	1	no	—
865	#397	—	53	1	no	—
866	#397	C₂×D₅₃	1	1	yes	characteristic
867	#397	C₂×D₅₃	1	1	yes	characteristic
868	#395	—	53	1	no	—
869	#395	—	53	1	no	—
870	#395	—	53	1	no	—
871	#395	—	53	1	no	—
872	#395	—	53	1	no	—
873	#395	—	53	1	no	—
874	#395	—	53	1	no	—
875	#395	—	53	1	no	—
876	#395	—	53	1	no	—
877	#395	—	53	1	no	—
878	#395	—	53	1	no	—
879	#395	C₂×D₅₃	1	1	yes	characteristic, complemented
880	#393	—	53	1	no	—
881	#393	—	53	1	no	—
882	#393	—	53	1	no	—
883	#393	—	53	1	no	—
884	#391	—	53	1	no	—
885	#391	—	53	1	no	—
886	#391	—	53	1	no	—
887	#391	C₂×D₅₃	1	1	yes	characteristic, complemented
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	C₂×D₅₃	1	1	yes	characteristic
903	#388	C₂×D₅₃	1	1	yes	characteristic
904	#387	—	53	1	no	—
905	#387	—	53	1	no	—
906	#387	—	53	1	no	—
907	#387	—	53	1	no	—
908	#387	—	53	1	no	—
909	#387	—	53	1	no	—
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	—	53	1	no	—
918	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
919	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
920	#385	—	53	1	no	—
921	#385	—	53	1	no	—
922	#385	—	53	1	no	—
923	#385	—	53	1	no	—
924	#385	—	53	1	no	—
925	#385	—	53	1	no	—
926	#385	—	53	1	no	—
927	#385	—	53	1	no	—
928	#385	—	53	1	no	—
929	#385	—	53	1	no	—
930	#385	—	53	1	no	—
931	#385	—	53	1	no	—
932	#385	—	53	1	no	—
933	#385	—	53	1	no	—
934	#385	—	53	1	no	—
935	#385	C₂×D₅₃	1	1	yes	characteristic
936	#381	—	53	1	no	—
937	#381	—	53	1	no	—
938	#381	—	53	1	no	—
939	#381	—	53	1	no	—
940	#381	—	53	1	no	—
941	#381	—	53	1	no	—
942	#380	—	53	1	no	—
943	#380	—	53	1	no	—
944	#380	—	53	1	no	—
945	#380	—	53	1	no	—
946	#380	—	53	1	no	—
947	#380	C₂×D₅₃	1	1	yes	characteristic
948	#379	—	53	1	no	—
949	#379	—	53	1	no	—
950	#379	—	53	1	no	—
951	#379	—	53	1	no	—
952	C₄×C₂²⋊C₄	—	53	1	no	—
953	C₄×C₂²⋊C₄	—	53	1	no	—
954	C₅₃	#36708	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×Q₈	—	53	1	no	—
960	C₂²×Q₈	—	53	1	no	—
961	C₂²×Q₈	—	53	1	no	—
962	C₂²×Q₈	—	53	1	no	—
963	C₂²×Q₈	—	106	4	no	—
964	C₂²×Q₈	—	212	2	no	—
965	C₂²×Q₈	—	212	2	no	—
966	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
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	C₂³×C₄	—	53	1	no	—
975	C₂³×C₄	—	53	1	no	—
976	C₂³×C₄	—	106	4	no	—
977	C₂³×C₄	—	212	2	no	—
978	C₂³×C₄	—	212	2	no	—
979	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
980	C₄⋊Q₈	—	106	4	no	—
981	C₄⋊Q₈	—	106	4	no	—
982	C₄⋊Q₈	—	106	4	no	—
983	C₄⋊Q₈	—	106	4	no	—
984	C₄⋊Q₈	—	212	2	no	—
985	C₄⋊Q₈	—	212	2	no	—
986	C₄⋊Q₈	—	212	2	no	—
987	C₄⋊Q₈	—	212	2	no	—
988	#125	—	2	4	no	—
989	#125	—	106	4	no	—
990	#125	—	106	4	no	—
991	#125	—	106	4	no	—
992	C₂²⋊Q₈	—	2	4	no	—
993	C₂²⋊Q₈	—	106	4	no	—
994	C₂²⋊Q₈	—	106	4	no	—
995	C₂²⋊Q₈	—	106	4	no	—
996	C₂²⋊Q₈	—	106	4	no	—
997	C₂²⋊Q₈	—	106	4	no	—
998	C₂²⋊Q₈	—	106	4	no	—
999	C₂²⋊Q₈	—	106	4	no	—
1000	C₂²⋊Q₈	—	106	4	no	—
1001	C₂²⋊Q₈	—	106	4	no	—
1002	C₂²⋊Q₈	—	106	4	no	—
1003	C₂²⋊Q₈	—	106	4	no	—
1004	C₂²⋊Q₈	—	212	2	no	—
1005	C₂²⋊Q₈	—	212	2	no	—
1006	C₂²⋊Q₈	—	212	2	no	—
1007	C₂²⋊Q₈	—	212	2	no	—
1008	#117	—	106	4	no	—
1009	#117	—	106	4	no	—
1010	C₂×C₄⋊C₄	—	53	1	no	—
1011	C₂×C₄⋊C₄	—	53	1	no	—
1012	C₂×C₄⋊C₄	—	53	1	no	—
1013	C₂×C₄⋊C₄	—	53	8	no	—
1014	C₂×C₄⋊C₄	—	53	1	no	—
1015	C₂×C₄⋊C₄	—	53	1	no	—
1016	C₂×C₄⋊C₄	—	53	1	no	—
1017	C₂×C₄⋊C₄	—	53	1	no	—
1018	C₂×C₄⋊C₄	—	53	1	no	—
1019	C₂×C₄⋊C₄	—	53	1	no	—
1020	C₂×C₄⋊C₄	—	53	1	no	—
1021	C₂×C₄⋊C₄	—	53	1	no	—
1022	C₂×C₄⋊C₄	—	53	1	no	—
1023	C₂×C₄⋊C₄	—	53	1	no	—
1024	C₂×C₄⋊C₄	—	53	1	no	—
1025	C₂×C₄⋊C₄	—	53	1	no	—
1026	C₂×C₄⋊C₄	—	53	1	no	—
1027	C₂×C₄⋊C₄	—	53	1	no	—
1028	C₂×C₄⋊C₄	—	53	1	no	—
1029	C₂×C₄⋊C₄	—	53	1	no	—
1030	C₂×C₄⋊C₄	—	53	1	no	—
1031	C₂×C₄⋊C₄	—	53	1	no	—
1032	C₂×C₄⋊C₄	—	53	1	no	—
1033	C₂×C₄⋊C₄	—	53	1	no	—
1034	C₂×C₄⋊C₄	—	53	1	no	—
1035	C₂×C₄⋊C₄	—	53	1	no	—
1036	C₂×C₄⋊C₄	—	53	1	no	—
1037	C₂×C₄⋊C₄	—	53	1	no	—
1038	C₂×C₄⋊C₄	—	53	1	no	—
1039	C₂×C₄⋊C₄	—	53	1	no	—
1040	C₂×C₄⋊C₄	—	53	1	no	—
1041	C₂×C₄⋊C₄	—	53	1	no	—
1042	C₂×C₄⋊C₄	—	53	1	no	—
1043	C₂×C₄⋊C₄	—	53	1	no	—
1044	C₂×C₄⋊C₄	—	53	1	no	—
1045	C₂×C₄⋊C₄	—	53	1	no	—
1046	C₂×C₄⋊C₄	—	53	1	no	—
1047	C₂×C₄⋊C₄	—	53	1	no	—
1048	C₂×C₄⋊C₄	—	106	4	no	—
1049	C₂×C₄⋊C₄	—	106	4	no	—
1050	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1051	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1052	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1053	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1054	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1055	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1056	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1057	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1058	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1059	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1060	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
1067	C₂×C₂²⋊C₄	—	53	1	no	—
1068	C₂×C₂²⋊C₄	—	53	1	no	—
1069	C₂×C₂²⋊C₄	—	53	1	no	—
1070	C₂×C₂²⋊C₄	—	53	1	no	—
1071	C₂×C₂²⋊C₄	—	53	1	no	—
1072	C₂×C₂²⋊C₄	—	53	1	no	—
1073	C₂×C₂²⋊C₄	—	53	1	no	—
1074	C₂×C₂²⋊C₄	—	53	1	no	—
1075	C₂×C₂²⋊C₄	—	53	1	no	—
1076	C₂×C₂²⋊C₄	—	53	1	no	—
1077	C₂×C₂²⋊C₄	—	53	1	no	—
1078	C₂×C₂²⋊C₄	—	53	1	no	—
1079	C₂×C₂²⋊C₄	—	53	1	no	—
1080	C₂×C₂²⋊C₄	—	53	1	no	—
1081	C₂×C₂²⋊C₄	—	53	1	no	—
1082	C₂×C₂²⋊C₄	—	53	1	no	—
1083	C₂×C₂²⋊C₄	—	53	1	no	—
1084	C₂×C₂²⋊C₄	—	53	1	no	—
1085	C₂×C₂²⋊C₄	—	53	1	no	—
1086	C₂×C₂²⋊C₄	—	53	1	no	—
1087	C₂×C₂²⋊C₄	—	106	4	no	—
1088	C₂×C₂²⋊C₄	—	106	4	no	—
1089	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1090	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1091	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1092	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1093	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1094	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1095	C₂×C₄²	—	53	1	no	—
1096	C₂×C₄²	—	53	1	no	—
1097	C₂×C₄²	—	53	1	no	—
1098	C₂×C₄²	—	53	1	no	—
1099	C₂×C₄²	—	53	1	no	—
1100	C₂×C₄²	—	53	1	no	—
1101	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1102	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
1118	#95	—	53	1	no	—
1119	#95	—	53	1	no	—
1120	#95	—	53	1	no	—
1121	#95	—	53	1	no	—
1122	#95	—	53	1	no	—
1123	#95	—	53	1	no	—
1124	#95	—	53	1	no	—
1125	#95	—	53	1	no	—
1126	#95	—	53	1	no	—
1127	#95	—	53	1	no	—
1128	#95	—	53	1	no	—
1129	#95	—	53	1	no	—
1130	#95	—	53	1	no	—
1131	#95	—	53	1	no	—
1132	#95	—	53	1	no	—
1133	#95	—	53	1	no	—
1134	#95	—	53	1	no	—
1135	#95	—	53	1	no	—
1136	#95	—	53	1	no	—
1137	#95	C₂²×D₅₃	1	1	yes	characteristic
1138	#95	C₂²×D₅₃	1	1	yes	characteristic
1139	#95	C₂²×D₅₃	1	1	yes	characteristic
1140	#95	C₂²×D₅₃	1	1	yes	characteristic
1141	#95	C₂²×D₅₃	1	1	yes	characteristic
1142	#95	C₂²×D₅₃	1	1	yes	characteristic
1143	#95	C₂²×D₅₃	1	1	yes	characteristic
1144	#95	C₂²×D₅₃	1	1	yes	characteristic
1145	#95	C₂²×D₅₃	1	1	yes	characteristic
1146	#95	C₂²×D₅₃	1	1	yes	characteristic
1147	#95	C₂²×D₅₃	1	1	yes	characteristic
1148	#95	C₂²×D₅₃	1	1	yes	characteristic
1149	#95	C₂²×D₅₃	1	1	yes	characteristic
1150	#95	C₂²×D₅₃	1	1	yes	characteristic
1151	C₂⁴	—	53	1	no	—
1152	C₂⁴	—	53	1	no	—
1153	C₂⁴	—	106	2	no	—
1154	C₂⁴	—	106	2	no	—
1155	C₂⁴	—	106	2	no	—
1156	C₂⁴	—	106	2	no	—
1157	C₂⁴	—	106	2	no	—
1158	C₂⁴	—	212	1	no	—
1159	C₂⁴	—	212	1	no	—
1160	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1161	C₂×Q₈	—	2	2	no	—
1162	C₂×Q₈	—	2	2	no	—
1163	C₂×Q₈	—	4	1	no	—
1164	C₂×Q₈	—	106	2	no	—
1165	C₂×Q₈	—	106	2	no	—
1166	C₂×Q₈	—	106	2	no	—
1167	C₂×Q₈	—	106	2	no	—
1168	C₂×Q₈	—	106	2	no	—
1169	C₂×Q₈	—	106	2	no	—
1170	C₂×Q₈	—	106	2	no	—
1171	C₂×Q₈	—	106	2	no	—
1172	C₂×Q₈	—	106	2	no	—
1173	C₂×Q₈	—	106	2	no	—
1174	C₂×Q₈	—	212	1	no	—
1175	C₂×Q₈	—	212	1	no	—
1176	C₂×Q₈	—	212	1	no	—
1177	C₂×Q₈	—	212	1	no	—
1178	C₂×Q₈	—	212	1	no	—
1179	C₂×Q₈	—	212	1	no	—
1180	C₂×Q₈	—	212	1	no	—
1181	C₂×Q₈	—	212	1	no	—
1182	C₂×Q₈	—	212	1	no	—
1183	C₂×Q₈	—	212	1	no	—
1184	C₂×Q₈	—	212	1	no	—
1185	C₂×Q₈	—	212	16	no	—
1186	C₂²×C₄	—	2	2	no	—
1187	C₂²×C₄	—	2	2	no	—
1188	C₂²×C₄	—	4	1	no	—
1189	C₂²×C₄	—	53	1	no	—
1190	C₂²×C₄	—	53	1	no	—
1191	C₂²×C₄	—	53	1	no	—
1192	C₂²×C₄	—	53	1	no	—
1193	C₂²×C₄	—	53	4	no	—
1194	C₂²×C₄	—	53	4	no	—
1195	C₂²×C₄	—	53	4	no	—
1196	C₂²×C₄	—	53	1	no	—
1197	C₂²×C₄	—	53	1	no	—
1198	C₂²×C₄	—	53	1	no	—
1199	C₂²×C₄	—	53	1	no	—
1200	C₂²×C₄	—	53	1	no	—
1201	C₂²×C₄	—	53	1	no	—
1202	C₂²×C₄	—	53	1	no	—
1203	C₂²×C₄	—	53	1	no	—
1204	C₂²×C₄	—	53	1	no	—
1205	C₂²×C₄	—	53	1	no	—
1206	C₂²×C₄	—	106	2	no	—
1207	C₂²×C₄	—	106	2	no	—
1208	C₂²×C₄	—	106	2	no	—
1209	C₂²×C₄	—	106	2	no	—
1210	C₂²×C₄	—	106	2	no	—
1211	C₂²×C₄	—	106	2	no	—
1212	C₂²×C₄	—	106	2	no	—
1213	C₂²×C₄	—	106	2	no	—
1214	C₂²×C₄	—	106	2	no	—
1215	C₂²×C₄	—	106	2	no	—
1216	C₂²×C₄	—	106	2	no	—
1217	C₂²×C₄	—	106	2	no	—
1218	C₂²×C₄	—	106	2	no	—
1219	C₂²×C₄	—	106	2	no	—
1220	C₂²×C₄	—	106	2	no	—
1221	C₂²×C₄	—	212	1	no	—
1222	C₂²×C₄	—	212	1	no	—
1223	C₂²×C₄	—	212	1	no	—
1224	C₂²×C₄	—	212	1	no	—
1225	C₂²×C₄	—	212	1	no	—
1226	C₂²×C₄	—	212	1	no	—
1227	C₂²×C₄	—	212	1	no	—
1228	C₂²×C₄	—	212	1	no	—
1229	C₂²×C₄	—	212	16	no	—
1230	C₂²×C₄	—	212	1	no	—
1231	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1232	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1233	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1234	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1235	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1236	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1237	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1238	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1239	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1240	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1241	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1242	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1243	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1244	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1245	C₄⋊C₄	—	2	2	no	—
1246	C₄⋊C₄	—	2	2	no	—
1247	C₄⋊C₄	—	2	2	no	—
1248	C₄⋊C₄	—	2	2	no	—
1249	C₄⋊C₄	—	2	2	no	—
1250	C₄⋊C₄	—	2	2	no	—
1251	C₄⋊C₄	—	2	2	no	—
1252	C₄⋊C₄	—	2	2	no	—
1253	C₄⋊C₄	—	4	1	no	—
1254	C₄⋊C₄	—	4	1	no	—
1255	C₄⋊C₄	—	53	4	no	—
1256	C₄⋊C₄	—	53	4	no	—
1257	C₄⋊C₄	—	53	4	no	—
1258	C₄⋊C₄	—	106	2	no	—
1259	C₄⋊C₄	—	106	2	no	—
1260	C₄⋊C₄	—	106	2	no	—
1261	C₄⋊C₄	—	106	2	no	—
1262	C₄⋊C₄	—	106	2	no	—
1263	C₄⋊C₄	—	106	2	no	—
1264	C₄⋊C₄	—	106	2	no	—
1265	C₄⋊C₄	—	106	2	no	—
1266	C₄⋊C₄	—	106	2	no	—
1267	C₄⋊C₄	—	106	2	no	—
1268	C₄⋊C₄	—	106	2	no	—
1269	C₄⋊C₄	—	106	2	no	—
1270	C₄⋊C₄	—	106	2	no	—
1271	C₄⋊C₄	—	106	2	no	—
1272	C₄⋊C₄	—	106	2	no	—
1273	C₄⋊C₄	—	106	2	no	—
1274	C₄⋊C₄	—	106	2	no	—
1275	C₄⋊C₄	—	106	2	no	—
1276	C₄⋊C₄	—	106	2	no	—
1277	C₄⋊C₄	—	106	2	no	—
1278	C₄⋊C₄	—	106	2	no	—
1279	C₄⋊C₄	—	106	2	no	—
1280	C₄⋊C₄	—	106	2	no	—
1281	C₄⋊C₄	—	106	2	no	—
1282	C₄⋊C₄	—	212	1	no	—
1283	C₄⋊C₄	—	212	1	no	—
1284	C₄⋊C₄	—	212	1	no	—
1285	C₄⋊C₄	—	212	1	no	—
1286	C₄⋊C₄	—	212	1	no	—
1287	C₄⋊C₄	—	212	1	no	—
1288	C₄⋊C₄	—	212	1	no	—
1289	C₄⋊C₄	—	212	1	no	—
1290	C₄⋊C₄	—	212	1	no	—
1291	C₄⋊C₄	—	212	1	no	—
1292	C₄⋊C₄	D₄×D₅₃	1	4	yes	—
1293	C₂²⋊C₄	—	2	2	no	—
1294	C₂²⋊C₄	—	2	2	no	—
1295	C₂²⋊C₄	—	2	2	no	—
1296	C₂²⋊C₄	—	2	2	no	—
1297	C₂²⋊C₄	—	2	2	no	—
1298	C₂²⋊C₄	—	4	1	no	—
1299	C₂²⋊C₄	—	106	2	no	—
1300	C₂²⋊C₄	—	106	2	no	—
1301	C₂²⋊C₄	—	106	2	no	—
1302	C₂²⋊C₄	—	106	2	no	—
1303	C₂²⋊C₄	—	106	2	no	—
1304	C₂²⋊C₄	—	106	2	no	—
1305	C₂²⋊C₄	—	106	2	no	—
1306	C₂²⋊C₄	—	106	2	no	—
1307	C₂²⋊C₄	—	106	2	no	—
1308	C₂²⋊C₄	—	106	2	no	—
1309	C₂²⋊C₄	—	106	2	no	—
1310	C₂²⋊C₄	—	106	2	no	—
1311	C₂²⋊C₄	—	106	2	no	—
1312	C₂²⋊C₄	—	106	2	no	—
1313	C₂²⋊C₄	—	106	2	no	—
1314	C₂²⋊C₄	—	106	2	no	—
1315	C₂²⋊C₄	—	106	2	no	—
1316	C₂²⋊C₄	—	106	2	no	—
1317	C₂²⋊C₄	—	106	2	no	—
1318	C₂²⋊C₄	—	212	1	no	—
1319	C₂²⋊C₄	—	212	1	no	—
1320	C₂²⋊C₄	—	212	1	no	—
1321	C₂²⋊C₄	—	212	1	no	—
1322	C₂²⋊C₄	—	212	1	no	—
1323	C₂²⋊C₄	—	212	1	no	—
1324	C₂²⋊C₄	—	212	1	no	—
1325	C₄²	—	2	2	no	—
1326	C₄²	—	4	1	no	—
1327	C₄²	—	106	2	no	—
1328	C₄²	—	106	2	no	—
1329	C₄²	—	106	2	no	—
1330	C₄²	—	212	1	no	—
1331	C₄²	—	212	1	no	—
1332	C₄²	—	212	1	no	—
1333	C₂³	—	2	1	no	—
1334	C₂³	—	2	1	no	—
1335	C₂³	—	2	1	no	—
1336	C₂³	—	2	1	no	—
1337	C₂³	—	2	1	no	—
1338	C₂³	—	2	1	no	—
1339	C₂³	—	53	2	no	—
1340	C₂³	—	53	2	no	—
1341	C₂³	—	53	2	no	—
1342	C₂³	—	53	2	no	—
1343	C₂³	—	106	8	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	—	106	1	no	—
1351	C₂³	—	106	1	no	—
1352	C₂³	—	106	1	no	—
1353	C₂³	—	106	1	no	—
1354	C₂³	—	212	4	no	—
1355	C₂³	—	212	4	no	—
1356	C₂³	—	212	4	no	—
1357	C₂³	—	212	4	no	—
1358	C₂³	—	212	4	no	—
1359	C₂³	—	212	4	no	—
1360	C₂³	#13133264	1	2	yes	—
1361	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1362	Q₈	—	4	4	no	—
1363	Q₈	—	424	2	no	—
1364	Q₈	—	424	2	no	—
1365	Q₈	—	424	2	no	—
1366	Q₈	—	424	2	no	—
1367	Q₈	—	212	4	no	—
1368	Q₈	—	212	4	no	—
1369	Q₈	—	212	4	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	—	4	4	no	—
1409	C₂×C₄	—	53	2	no	—
1410	C₂×C₄	—	53	2	no	—
1411	C₂×C₄	—	53	2	no	—
1412	C₂×C₄	—	53	2	no	—
1413	C₂×C₄	—	106	8	no	—
1414	C₂×C₄	—	106	8	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	—	106	1	no	—
1445	C₂×C₄	—	106	1	no	—
1446	C₂×C₄	—	106	1	no	—
1447	C₂×C₄	—	106	1	no	—
1448	C₂×C₄	—	106	1	no	—
1449	C₂×C₄	—	106	1	no	—
1450	C₂×C₄	—	106	1	no	—
1451	C₂×C₄	—	106	1	no	—
1452	C₂×C₄	—	106	1	no	—
1453	C₂×C₄	—	212	4	no	—
1454	C₂×C₄	—	212	4	no	—
1455	C₂×C₄	—	212	4	no	—
1456	C₂×C₄	—	212	4	no	—
1457	C₂×C₄	—	212	4	no	—
1458	C₂×C₄	—	212	4	no	—
1459	C₂×C₄	—	212	4	no	—
1460	C₂×C₄	C₂×D₄×D₅₃	1	2	yes	—
1461	C₂×C₄	C₂×D₄×D₅₃	1	2	yes	—
1462	C₂×C₄	C₂×D₄×D₅₃	1	2	yes	—
1463	C₂×C₄	#13133263	1	2	yes	—
1464	C₂²	—	2	2	no	—
1465	C₂²	—	2	2	no	—
1466	C₂²	—	2	2	no	—
1467	C₂²	—	4	1	no	—
1468	C₂²	—	4	1	no	—
1469	C₂²	—	4	1	no	—
1470	C₂²	—	4	1	no	—
1471	C₂²	—	53	4	no	—
1472	C₂²	—	106	2	no	—
1473	C₂²	—	106	2	no	—
1474	C₂²	—	106	2	no	—
1475	C₂²	—	106	2	no	—
1476	C₂²	—	106	2	no	—
1477	C₂²	—	106	2	no	—
1478	C₂²	—	106	2	no	—
1479	C₂²	—	106	2	no	—
1480	C₂²	—	106	2	no	—
1481	C₂²	—	212	16	no	—
1482	C₂²	—	212	1	no	—
1483	C₂²	—	212	1	no	—
1484	C₂²	—	212	1	no	—
1485	C₂²	—	212	1	no	—
1486	C₂²	C₂²×D₄×D₅₃	1	1	yes	characteristic
1487	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1488	C₂²	C₂×#13133263	1	1	yes	characteristic
1489	C₂²	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1490	C₂²	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1491	C₂²	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1492	C₂²	C₂×#13133264	1	1	yes	characteristic
1493	C₄	—	2	2	no	—
1494	C₄	—	2	2	no	—
1495	C₄	—	2	2	no	—
1496	C₄	—	2	2	no	—
1497	C₄	—	4	1	no	—
1498	C₄	—	4	1	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	—	106	2	no	—
1508	C₄	—	106	2	no	—
1509	C₄	—	106	2	no	—
1510	C₄	—	106	2	no	—
1511	C₄	—	212	1	no	—
1512	C₄	—	212	1	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	C₂	—	4	2	no	—
1522	C₂	—	106	4	no	—
1523	C₂	—	212	2	no	—
1524	C₂	#536×D₅₃	1	1	yes	characteristic
1525	C₂	#20288345	1	1	yes	characteristic
1526	C₂	#20288361	1	1	yes	characteristic
1527	C₂	#20288959	1	1	yes	characteristic
1528	C₂	#20288961	1	1	yes	characteristic
1529	C₂	#20288962	1	1	yes	characteristic
1530	C₂	#20288963	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator, socle, cosocle	C₂³×C₅₃	C₂⁵
Fitting	C₅₃×#2690	C₂
prime radical	C₂⁴×D₅₃	C₂³
hypercenter	#2690	D₅₃
hypocenter	C₅₃	#36708
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #2690

Complements

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

N	H ≅ G/N	type
1. C₂×#16811253	C₂	semidirect
5. #20281188	C₂	semidirect
6. #20281186	C₂	semidirect
7. #20281183	C₂	semidirect
8. #20281181	C₂	semidirect
9. #20281176	C₂	semidirect
10. #20281175	C₂	semidirect
11. #20281174	C₂	semidirect
12. #20281032	C₂	semidirect
13. #20281030	C₂	semidirect
14. #20281029	C₂	semidirect
15. #20281028	C₂	semidirect
16. #20281028	C₂	semidirect
17. #20281027	C₂	semidirect
18. #20281027	C₂	semidirect
19. #20281026	C₂	semidirect
20. #20280533	C₂	semidirect
21. #20280529	C₂	semidirect
24. #20279003	C₂	semidirect
25. #20279000	C₂	semidirect
28. #20278358	C₂	semidirect
29. #20278354	C₂	semidirect
30. #20277314	C₂	semidirect
31. C₅₃×#2690	C₂	semidirect
35. C₂×#13133217	C₂²	semidirect
36. C₂×#13133217	C₂²	semidirect
37. C₂×#13133216	C₂²	semidirect
38. C₂×#13133216	C₂²	semidirect
39. C₂×#13133216	C₂²	semidirect
40. C₂×#13133216	C₂²	semidirect
41. C₂×#13133216	C₂²	semidirect
42. C₂×#13133215	C₂²	semidirect
43. C₂×#13133208	C₂²	semidirect
44. C₂×#13133207	C₂²	semidirect
45. C₂×#13133207	C₂²	semidirect
69. #16810565	C₂²	semidirect
70. #16810565	C₂²	semidirect
71. #16810564	C₂²	semidirect
72. #16810564	C₂²	semidirect
73. #16810561	C₂²	semidirect
74. #16810561	C₂²	semidirect
79. #16810557	C₂²	semidirect
80. #16810557	C₂²	semidirect
81. #16810557	C₂²	semidirect
82. #16810556	C₂²	semidirect
83. #16810556	C₂²	semidirect
84. #16810556	C₂²	semidirect
85. #16810555	C₂²	semidirect
86. #16810555	C₂²	semidirect
87. #16810555	C₂²	semidirect
88. #16810553	C₂²	semidirect
89. #16810553	C₂²	semidirect
96. #16810544	C₂²	semidirect
97. #16810544	C₂²	semidirect
98. #16810544	C₂²	semidirect
99. #16810544	C₂²	semidirect
100. #16810544	C₂²	semidirect
101. #16810544	C₂²	semidirect
102. #16810544	C₂²	semidirect
103. #16810543	C₂²	semidirect
104. #16810543	C₂²	semidirect
105. #16810543	C₂²	semidirect
106. #16810542	C₂²	semidirect
111. #16810528	C₂²	semidirect
112. #16810527	C₂²	semidirect
113. #16810527	C₂²	semidirect
128. #16810510	C₂²	semidirect
129. #16810510	C₂²	semidirect
130. #16810510	C₂²	semidirect
131. #16810509	C₂²	semidirect
132. #16810508	C₂²	semidirect
133. #16810508	C₂²	semidirect
134. #16810507	C₂²	semidirect
135. #16810507	C₂²	semidirect
136. #16810506	C₂²	semidirect
137. #16810506	C₂²	semidirect
138. #16810506	C₂²	semidirect
139. #16810505	C₂²	semidirect
140. #16810504	C₂²	semidirect
141. #16810504	C₂²	semidirect
174. C₂×#125×C₅₃	C₂²	semidirect
176. C₅₃×#400	C₂²	semidirect
177. C₅₃×#400	C₂²	semidirect
178. C₅₃×#398	C₂²	semidirect
181. C₅₃×#395	C₂²	semidirect
182. C₅₃×#391	C₂²	semidirect
185. C₅₃×#387	C₂²	semidirect
186. C₅₃×#387	C₂²	semidirect
767. #2690	D₅₃	semidirect
811. C₂×#125	C₂×D₅₃	semidirect
842. #400	C₂×D₅₃	semidirect
843. #400	C₂×D₅₃	semidirect
859. #398	C₂×D₅₃	semidirect
879. #395	C₂×D₅₃	semidirect
887. #391	C₂×D₅₃	semidirect
918. #387	C₂×D₅₃	semidirect
919. #387	C₂×D₅₃	semidirect
954. C₅₃	#36708	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16811253	2
C₂×C₂²⋊Q₈×D₅₃	2
#20283003	2
#20283001	2
#20281188	2
#20281186	2
#20281183	2
#20281181	2
#20281176	2
#20281175	2
#20281174	2
#20281032	2
#20281030	2
#20281029	2
#20281028	2
#20281027	2
#20281026	2
#20280533	2
#20280529	2
#20279871	2
#20279867	2
#20279003	2
#20279000	2
#20278987	2
#20278984	2
#20278358	2
#20278354	2
#20277314	2
C₅₃×#2690	2
#36708	53