Subgroups — #27549346

Order 13568.

2244 conjugacy classes of subgroups.

The subgroup lattice has 1420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811286	C₂	1	1	yes	maximal, characteristic
2	#20277879	C₂	1	1	yes	maximal, characteristic, complemented
3	#20277877	C₂	1	1	yes	maximal, characteristic, complemented
4	#20277875	C₂	1	1	yes	maximal, characteristic, complemented
5	#20277803	C₂	1	1	yes	maximal, characteristic, complemented
6	#20277801	C₂	1	1	yes	maximal, characteristic, complemented
7	#20277770	C₂	1	1	yes	maximal, characteristic, complemented
8	#20277739	C₂	1	1	yes	maximal, characteristic, complemented
9	#20277737	C₂	1	1	yes	maximal, characteristic, complemented
10	#20277685	C₂	1	1	yes	maximal, characteristic
11	#20277683	C₂	1	1	yes	maximal, characteristic
12	#20277669	C₂	1	1	yes	maximal, characteristic, complemented
13	#20277661	C₂	1	1	yes	maximal, characteristic
14	#20277549	C₂	1	1	yes	maximal, characteristic, complemented
15	#20277547	C₂	1	1	yes	maximal, characteristic, complemented
16	#20277473	C₂	1	1	yes	maximal, characteristic, complemented
17	#20277469	C₂	1	1	yes	maximal, characteristic, complemented
18	#20277467	C₂	1	1	yes	maximal, characteristic, complemented
19	#20277465	C₂	1	1	yes	maximal, characteristic, complemented
20	#20277460	C₂	1	1	yes	maximal, characteristic, complemented
21	#20277458	C₂	1	1	yes	maximal, characteristic, complemented
22	#20277394	C₂	1	1	yes	maximal, characteristic, complemented
23	#20277392	C₂	1	1	yes	maximal, characteristic, complemented
24	#20277357	C₂	1	1	yes	maximal, characteristic
25	#20277356	C₂	1	1	yes	maximal, characteristic
26	#20277300	C₂	1	1	yes	maximal, characteristic, complemented
27	#20277298	C₂	1	1	yes	maximal, characteristic, complemented
28	#20277286	C₂	1	1	yes	maximal, characteristic, complemented
29	#20277188	C₂	1	1	yes	maximal, characteristic, complemented
30	#20277175	C₂	1	1	yes	maximal, characteristic
31	C₅₃×#2378	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂³×Dic₁₀₆	C₂²	1	1	yes	characteristic
33	C₂²×Q₈×D₅₃	C₂²	1	1	yes	characteristic
34	#16811286	C₄	1	16	yes	complemented
35	C₂×#13133216	C₂²	1	1	yes	characteristic
36	C₂×#13133216	C₂²	1	1	yes	characteristic
37	C₂×#13133215	C₂²	1	1	yes	characteristic
38	C₂×#13133197	C₂²	1	1	yes	characteristic
39	C₂×#13133195	C₂²	1	1	yes	characteristic
40	C₂×#13133195	C₂²	1	1	yes	characteristic
41	C₂×#13133194	C₂²	1	1	yes	characteristic
42	C₂×#13133194	C₂²	1	1	yes	characteristic
43	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
44	C₂×#13133182	C₂²	1	1	yes	characteristic
45	C₂×#13133182	C₂²	1	1	yes	characteristic
46	C₂×#13133182	C₂²	1	1	yes	characteristic
47	C₂×#13133182	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
49	C₂×#13133177	C₂²	1	1	yes	characteristic
50	C₂×#13133177	C₂²	1	1	yes	characteristic
51	C₂×#13133175	C₂²	1	1	yes	characteristic
52	C₂×#13133174	C₂²	1	1	yes	characteristic
53	C₂×#13133173	C₂²	1	1	yes	characteristic
54	C₂×#13133173	C₂²	1	1	yes	characteristic
55	#16810530	C₂²	1	1	yes	characteristic
56	#16810530	C₂²	1	1	yes	characteristic
57	#16810529	C₂²	1	1	yes	characteristic
58	#16810528	C₂²	1	1	yes	characteristic
59	#16810528	C₂²	1	1	yes	characteristic
60	#16810528	C₂²	1	1	yes	characteristic
61	#16810527	C₂²	1	1	yes	characteristic
62	#16810527	C₂²	1	1	yes	characteristic
63	#16810527	C₂²	1	1	yes	characteristic
64	#16810527	C₂²	1	1	yes	characteristic
65	#16810527	C₂²	1	1	yes	characteristic
66	#16810527	C₂²	1	1	yes	characteristic
67	#16810527	C₂²	1	1	yes	characteristic
68	#16810527	C₂²	1	1	yes	characteristic
69	#16810527	C₂²	1	1	yes	characteristic
70	#16810527	C₂²	1	1	yes	characteristic
71	#16810527	C₂²	1	1	yes	characteristic
72	#16810527	C₂²	1	1	yes	characteristic
73	#16810527	C₂²	1	1	yes	characteristic
74	#16810527	C₂²	1	1	yes	characteristic
75	#16810527	C₂²	1	1	yes	characteristic
76	#16810527	C₂²	1	1	yes	characteristic
77	#16810523	C₂²	1	1	yes	characteristic
78	#16810523	C₂²	1	1	yes	characteristic
79	#16810523	C₂²	1	1	yes	characteristic
80	#16810523	C₂²	1	1	yes	characteristic
81	#16810521	C₂²	1	1	yes	characteristic
82	#16810520	C₂²	1	1	yes	characteristic
83	#16810520	C₂²	1	1	yes	characteristic
84	#16810520	C₂²	1	1	yes	characteristic
85	#16810520	C₂²	1	1	yes	characteristic
86	#16810519	C₂²	1	1	yes	characteristic
87	#16810518	C₂²	1	1	yes	characteristic
88	#16810518	C₂²	1	1	yes	characteristic
89	#16810518	C₂²	1	1	yes	characteristic
90	#16810518	C₂²	1	1	yes	characteristic
91	#16810518	C₂²	1	1	yes	characteristic
92	#16810518	C₂²	1	1	yes	characteristic
93	#16810516	C₂²	1	1	yes	characteristic
94	#16810516	C₂²	1	1	yes	characteristic
95	#16810516	C₂²	1	1	yes	characteristic
96	#16810516	C₂²	1	1	yes	characteristic
97	#16810515	C₂²	1	1	yes	characteristic
98	#16810515	C₂²	1	1	yes	characteristic
99	#16810514	C₂²	1	1	yes	characteristic
100	#16810514	C₂²	1	1	yes	characteristic
101	#16810513	C₂²	1	1	yes	characteristic
102	#16810513	C₂²	1	1	yes	characteristic
103	#16810513	C₂²	1	1	yes	characteristic
104	#16810513	C₂²	1	1	yes	characteristic
105	#16810512	C₂²	1	1	yes	characteristic
106	#16810512	C₂²	1	1	yes	characteristic
107	#16810512	C₂²	1	1	yes	characteristic
108	#16810512	C₂²	1	1	yes	characteristic
109	#16810511	C₂²	1	1	yes	characteristic
110	#16810511	C₂²	1	1	yes	characteristic
111	#16810511	C₂²	1	1	yes	characteristic
112	#16810511	C₂²	1	1	yes	characteristic
113	#16810510	C₂²	1	1	yes	characteristic
114	#16810510	C₂²	1	1	yes	characteristic
115	#16810509	C₂²	1	1	yes	characteristic
116	#16810509	C₂²	1	1	yes	characteristic
117	#16810509	C₂²	1	1	yes	characteristic
118	#16810509	C₂²	1	1	yes	characteristic
119	#16810508	C₂²	1	1	yes	characteristic
120	#16810508	C₂²	1	1	yes	characteristic
121	#16810507	C₂²	1	1	yes	characteristic
122	#16810507	C₂²	1	1	yes	characteristic
123	#16810506	C₂²	1	1	yes	characteristic
124	#16810506	C₂²	1	1	yes	characteristic
125	#16810505	C₂²	1	1	yes	characteristic
126	#16810505	C₂²	1	1	yes	characteristic
127	#16810504	C₂²	1	1	yes	characteristic
128	#16810504	C₂²	1	1	yes	characteristic
129	#16810492	C₂²	1	1	yes	characteristic
130	#16810487	C₂²	1	1	yes	characteristic
131	#16810487	C₂²	1	1	yes	characteristic
132	#16810486	C₂²	1	1	yes	characteristic
133	#16810485	C₂²	1	1	yes	characteristic
134	#16810485	C₂²	1	1	yes	characteristic
135	#16810485	C₂²	1	1	yes	characteristic
136	#16810485	C₂²	1	1	yes	characteristic
137	#16810484	C₂²	1	1	yes	characteristic
138	#16810484	C₂²	1	1	yes	characteristic
139	#16810482	C₂²	1	1	yes	characteristic
140	#16810482	C₂²	1	1	yes	characteristic
141	#16810481	C₂²	1	1	yes	characteristic
142	#16810481	C₂²	1	1	yes	characteristic
143	#16810480	C₂²	1	1	yes	characteristic
144	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
145	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
146	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
147	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
148	C₄×#11719919	C₂²	1	1	yes	characteristic
149	C₄×#11719919	C₂²	1	1	yes	characteristic
150	C₄×#11719919	C₂²	1	1	yes	characteristic
151	C₄×#11719919	C₂²	1	1	yes	characteristic
152	C₄×#11719919	C₂²	1	1	yes	characteristic
153	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
154	#16810474	C₂²	1	1	yes	characteristic
155	#16810474	C₂²	1	1	yes	characteristic
156	#16810474	C₂²	1	1	yes	characteristic
157	#16810474	C₂²	1	1	yes	characteristic
158	#16810474	C₂²	1	1	yes	characteristic
159	#16810474	C₂²	1	1	yes	characteristic
160	#16810474	C₂²	1	1	yes	characteristic
161	#16810474	C₂²	1	1	yes	characteristic
162	#16810474	C₂²	1	1	yes	characteristic
163	#16810474	C₂²	1	1	yes	characteristic
164	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
165	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
166	C₄×#11719921	C₂²	1	1	yes	characteristic
167	C₄×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
168	#16810470	C₂²	1	1	yes	characteristic
169	#16810470	C₂²	1	1	yes	characteristic
170	#16810468	C₂²	1	1	yes	characteristic
171	#16810468	C₂²	1	1	yes	characteristic
172	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic
173	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
174	C₅₃×#391	C₂²	1	1	yes	characteristic
175	C₅₃×#391	C₂²	1	1	yes	characteristic
176	C₅₃×#389	C₂²	1	1	yes	characteristic
177	C₅₃×#389	C₂²	1	1	yes	characteristic
178	C₅₃×#388	C₂²	1	1	yes	characteristic
179	C₅₃×#388	C₂²	1	1	yes	characteristic
180	C₅₃×#388	C₂²	1	1	yes	characteristic
181	C₅₃×#388	C₂²	1	1	yes	characteristic
182	C₅₃×#387	C₂²	1	1	yes	characteristic
183	C₅₃×#387	C₂²	1	1	yes	characteristic
184	C₅₃×#387	C₂²	1	1	yes	characteristic
185	C₅₃×#387	C₂²	1	1	yes	characteristic
186	C₅₃×#381	C₂²	1	1	yes	characteristic
187	C₅₃×#380	C₂²	1	1	yes	characteristic
188	C₂²×Dic₁₀₆	—	4	2	no	—
189	C₂²×Dic₁₀₆	—	4	2	no	—
190	C₂²×Dic₁₀₆	C₂×C₄	1	8	yes	—
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	—	4	2	no	—
198	C₂×Q₈×D₅₃	—	4	2	no	—
199	C₂×Q₈×D₅₃	C₂×C₄	1	8	yes	—
200	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
201	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
202	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
203	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
204	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
205	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
206	#13133216	C₂×C₄	1	8	yes	—
207	#13133216	C₂×C₄	1	8	yes	—
208	#13133215	C₂×C₄	1	8	yes	—
209	#13133197	C₂×C₄	1	8	yes	—
210	#13133195	C₂×C₄	1	8	yes	—
211	#13133195	C₂×C₄	1	8	yes	—
212	#13133194	C₂×C₄	1	8	yes	—
213	#13133194	C₂×C₄	1	8	yes	—
214	C₄×Dic₁₀₆	—	4	2	no	—
215	#13133182	—	4	2	no	—
216	#13133182	—	4	2	no	—
217	#13133182	—	4	2	no	—
218	#13133182	C₂×C₄	1	8	yes	—
219	C₄×C₂²⋊D₅₃	C₂×C₄	1	8	yes	—
220	#13133177	C₂×C₄	1	8	yes	—
221	#13133177	C₂×C₄	1	8	yes	—
222	#13133175	—	4	2	no	—
223	#13133174	—	4	2	no	—
224	#13133173	—	4	2	no	—
225	#13133173	—	4	2	no	—
226	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
232	C₂×#11719919	C₂³	1	1	yes	characteristic
233	C₂×#11719919	C₂³	1	1	yes	characteristic
234	C₂×#11719919	C₂³	1	1	yes	characteristic
235	C₂×#11719919	C₂³	1	1	yes	characteristic
236	C₂×#11719919	C₂³	1	1	yes	characteristic
237	C₂×#11719919	C₂³	1	1	yes	characteristic
238	C₂×#11719919	C₂³	1	1	yes	characteristic
239	C₂×#11719919	C₂³	1	1	yes	characteristic
240	C₂×#11719919	C₂³	1	1	yes	characteristic
241	C₂×#11719919	C₂³	1	1	yes	characteristic
242	C₂×#11719919	C₂³	1	1	yes	characteristic
243	C₂×#11719919	C₂³	1	1	yes	characteristic
244	C₂×#11719919	C₂³	1	1	yes	characteristic
245	C₂×#11719919	C₂³	1	1	yes	characteristic
246	C₂×#11719919	C₂³	1	1	yes	characteristic
247	C₂×#11719919	C₂³	1	1	yes	characteristic
248	C₂×#11719919	C₂³	1	1	yes	characteristic
249	C₂×#11719919	C₂³	1	1	yes	characteristic
250	C₂×#11719919	C₂³	1	1	yes	characteristic
251	C₂×#11719919	C₂³	1	1	yes	characteristic
252	C₂×#11719919	C₂³	1	1	yes	characteristic
253	C₂×#11719919	C₂³	1	1	yes	characteristic
254	C₂×#11719919	C₂³	1	1	yes	characteristic
255	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
258	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊Dic₅₃	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×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
272	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
273	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
274	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
275	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
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	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
287	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
288	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
289	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
290	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
291	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
292	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
293	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
294	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
295	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
296	#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	#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	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
335	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
336	C₂²⋊Q₈×C₅₃	C₂×C₄	1	8	yes	—
337	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
338	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
339	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
340	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
341	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
342	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
343	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
344	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
345	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
346	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
347	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
348	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
349	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
350	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
351	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
352	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
353	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
354	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
355	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
356	#95×C₅₃	C₂³	1	1	yes	characteristic
357	#95×C₅₃	C₂³	1	1	yes	characteristic
358	#95×C₅₃	C₂³	1	1	yes	characteristic
359	#95×C₅₃	C₂³	1	1	yes	characteristic
360	#95×C₅₃	C₂³	1	1	yes	characteristic
361	#95×C₅₃	C₂³	1	1	yes	characteristic
362	#95×C₅₃	C₂³	1	1	yes	characteristic
363	#95×C₅₃	C₂³	1	1	yes	characteristic
364	#95×C₅₃	C₂³	1	1	yes	characteristic
365	#95×C₅₃	C₂³	1	1	yes	characteristic
366	#95×C₅₃	C₂³	1	1	yes	characteristic
367	#95×C₅₃	C₂³	1	1	yes	characteristic
368	#95×C₅₃	C₂³	1	1	yes	characteristic
369	#95×C₅₃	C₂³	1	1	yes	characteristic
370	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
372	C₂×Q₈×C₅₃	—	4	1	no	—
373	C₂×Q₈×C₅₃	—	4	1	no	—
374	C₂×Q₈×C₅₃	C₂²×C₄	1	4	yes	—
375	C₂²×C₄×C₅₃	—	4	1	no	—
376	C₂²×C₄×C₅₃	—	4	1	no	—
377	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
378	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
381	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
382	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
387	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
389	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	C₂×C₂²⋊D₅₃	—	2	2	no	—
393	C₂×C₂²⋊D₅₃	—	2	2	no	—
394	C₂×C₂²⋊D₅₃	C₂²×C₄	1	4	yes	—
395	C₂²×Dic₅₃	—	2	2	no	—
396	C₂²×Dic₅₃	—	2	2	no	—
397	C₂²×Dic₅₃	—	4	1	no	—
398	C₂²×Dic₅₃	—	4	1	no	—
399	C₂²×Dic₅₃	C₂²×C₄	1	4	yes	—
400	C₂²×Dic₅₃	C₂²×C₄	1	4	yes	—
401	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
402	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
403	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
404	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
405	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
406	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
407	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
408	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
409	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
410	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
411	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
412	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
413	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
414	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
415	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
416	Q₈×D₅₃	—	4	16	no	—
417	C₂×C₄×D₅₃	—	2	2	no	—
418	C₂×C₄×D₅₃	—	2	2	no	—
419	C₂×C₄×D₅₃	—	4	1	no	—
420	C₂×C₄×D₅₃	—	4	1	no	—
421	C₂×C₄×D₅₃	—	4	1	no	—
422	C₂×C₄×D₅₃	—	4	1	no	—
423	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
424	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
425	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
426	C₂×Dic₁₀₆	—	2	2	no	—
427	C₂×Dic₁₀₆	—	2	2	no	—
428	C₂×Dic₁₀₆	—	2	2	no	—
429	C₂×Dic₁₀₆	—	2	2	no	—
430	C₂×Dic₁₀₆	—	2	2	no	—
431	C₂×Dic₁₀₆	—	2	2	no	—
432	C₂×Dic₁₀₆	—	4	16	no	—
433	C₂×Dic₁₀₆	—	4	1	no	—
434	C₂×Dic₁₀₆	—	4	1	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	C₂²×C₄	1	4	yes	—
440	C₂×Dic₁₀₆	C₂²×C₄	1	4	yes	—
441	C₂×Dic₁₀₆	C₂²×C₄	1	4	yes	—
442	C₂×Dic₁₀₆	C₂²×C₄	1	4	yes	—
443	C₂×Dic₁₀₆	C₂²×C₄	1	4	yes	—
444	C₂×Dic₁₀₆	C₂²×C₄	1	4	yes	—
445	C₄⋊C₄×C₅₃	—	4	1	no	—
446	C₄⋊C₄×C₅₃	—	4	1	no	—
447	C₄⋊C₄×C₅₃	—	4	1	no	—
448	C₄⋊C₄×C₅₃	—	4	1	no	—
449	C₄⋊C₄×C₅₃	—	4	1	no	—
450	C₄⋊C₄×C₅₃	—	4	1	no	—
451	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
452	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
453	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
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	C₂²×C₄	1	4	yes	—
459	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
460	C₄²×C₅₃	—	4	1	no	—
461	C₄²×C₅₃	—	4	1	no	—
462	C₄²×C₅₃	—	4	1	no	—
463	C₄²×C₅₃	—	4	1	no	—
464	C₂²⋊Dic₅₃	—	2	2	no	—
465	C₂²⋊Dic₅₃	—	4	1	no	—
466	C₂²⋊Dic₅₃	—	4	1	no	—
467	C₂²⋊Dic₅₃	—	4	1	no	—
468	C₂²⋊Dic₅₃	C₂²×C₄	1	4	yes	—
469	#11719921	—	2	2	no	—
470	#11719921	—	4	1	no	—
471	#11719921	—	4	1	no	—
472	#11719921	—	4	1	no	—
473	#11719921	—	4	1	no	—
474	#11719921	—	4	1	no	—
475	#11719921	—	4	1	no	—
476	#11719921	—	4	1	no	—
477	#11719921	C₂²×C₄	1	4	yes	—
478	#11719921	C₂²×C₄	1	4	yes	—
479	#11719921	C₂²×C₄	1	4	yes	—
480	C₄⋊Dic₅₃	—	2	2	no	—
481	C₄⋊Dic₅₃	—	4	1	no	—
482	C₄⋊Dic₅₃	—	4	1	no	—
483	C₄⋊Dic₅₃	—	4	1	no	—
484	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
485	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
486	#11719919	—	2	2	no	—
487	#11719919	—	2	2	no	—
488	#11719919	—	2	2	no	—
489	#11719919	—	2	2	no	—
490	#11719919	—	2	2	no	—
491	#11719919	—	2	2	no	—
492	#11719919	—	2	2	no	—
493	#11719919	—	2	2	no	—
494	#11719919	—	2	2	no	—
495	#11719919	—	4	1	no	—
496	#11719919	—	4	1	no	—
497	#11719919	—	4	1	no	—
498	#11719919	—	4	1	no	—
499	#11719919	—	4	1	no	—
500	#11719919	—	4	1	no	—
501	#11719919	—	4	1	no	—
502	#11719919	C₂²×C₄	1	4	yes	—
503	#11719919	C₂²×C₄	1	4	yes	—
504	#11719919	C₂²×C₄	1	4	yes	—
505	#11719919	C₂²×C₄	1	4	yes	—
506	#11719919	C₂²×C₄	1	4	yes	—
507	#11719919	C₂²×C₄	1	4	yes	—
508	#11719919	C₂²×C₄	1	4	yes	—
509	C₄×Dic₅₃	—	2	2	no	—
510	C₄×Dic₅₃	—	2	2	no	—
511	C₄×Dic₅₃	—	2	2	no	—
512	C₄×Dic₅₃	—	2	2	no	—
513	C₄×Dic₅₃	—	2	2	no	—
514	C₄×Dic₅₃	—	2	2	no	—
515	C₄×Dic₅₃	—	2	2	no	—
516	C₄×Dic₅₃	—	2	2	no	—
517	C₄×Dic₅₃	—	2	2	no	—
518	C₄×Dic₅₃	—	4	1	no	—
519	C₄×Dic₅₃	—	4	1	no	—
520	C₄×Dic₅₃	—	4	1	no	—
521	C₄×Dic₅₃	—	4	1	no	—
522	C₄×Dic₅₃	—	4	1	no	—
523	C₄×Dic₅₃	—	4	1	no	—
524	C₄×Dic₅₃	—	4	1	no	—
525	C₄×Dic₅₃	—	4	1	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	C₂²×C₄	1	4	yes	—
532	C₄×Dic₅₃	C₂²×C₄	1	4	yes	—
533	C₄×Dic₅₃	C₂²×C₄	1	4	yes	—
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	C₂³×C₄	1	2	yes	—
541	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
542	C₂²×D₅₃	—	2	1	no	—
543	C₂²×D₅₃	—	2	1	no	—
544	C₂²×D₅₃	—	2	1	no	—
545	C₂²×D₅₃	—	2	1	no	—
546	C₂²×D₅₃	—	2	1	no	—
547	C₂²×D₅₃	—	2	1	no	—
548	C₂²×D₅₃	C₂³×C₄	1	2	yes	—
549	Q₈×C₅₃	—	4	4	no	—
550	C₂×C₄×C₅₃	—	2	1	no	—
551	C₂×C₄×C₅₃	—	2	1	no	—
552	C₂×C₄×C₅₃	—	2	1	no	—
553	C₂×C₄×C₅₃	—	2	1	no	—
554	C₂×C₄×C₅₃	—	2	1	no	—
555	C₂×C₄×C₅₃	—	2	1	no	—
556	C₂×C₄×C₅₃	—	2	1	no	—
557	C₂×C₄×C₅₃	—	2	1	no	—
558	C₂×C₄×C₅₃	—	2	1	no	—
559	C₂×C₄×C₅₃	—	2	1	no	—
560	C₂×C₄×C₅₃	—	2	1	no	—
561	C₂×C₄×C₅₃	—	2	1	no	—
562	C₂×C₄×C₅₃	—	2	1	no	—
563	C₂×C₄×C₅₃	—	2	1	no	—
564	C₂×C₄×C₅₃	—	2	1	no	—
565	C₂×C₄×C₅₃	—	2	1	no	—
566	C₂×C₄×C₅₃	—	2	1	no	—
567	C₂×C₄×C₅₃	—	2	1	no	—
568	C₂×C₄×C₅₃	—	2	1	no	—
569	C₂×C₄×C₅₃	—	2	1	no	—
570	C₂×C₄×C₅₃	—	2	1	no	—
571	C₂×C₄×C₅₃	—	2	1	no	—
572	C₂×C₄×C₅₃	—	2	1	no	—
573	C₂×C₄×C₅₃	—	2	1	no	—
574	C₂×C₄×C₅₃	—	2	1	no	—
575	C₂×C₄×C₅₃	—	2	1	no	—
576	C₂×C₄×C₅₃	—	2	1	no	—
577	C₂×C₄×C₅₃	—	2	1	no	—
578	C₂×C₄×C₅₃	—	2	1	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	—	4	4	no	—
587	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
588	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
589	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
590	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
591	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
592	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
593	C₂²⋊D₅₃	—	2	8	no	—
594	C₂×Dic₅₃	—	2	1	no	—
595	C₂×Dic₅₃	—	2	1	no	—
596	C₂×Dic₅₃	—	2	1	no	—
597	C₂×Dic₅₃	—	2	1	no	—
598	C₂×Dic₅₃	—	2	1	no	—
599	C₂×Dic₅₃	—	2	1	no	—
600	C₂×Dic₅₃	—	2	1	no	—
601	C₂×Dic₅₃	—	2	1	no	—
602	C₂×Dic₅₃	—	2	1	no	—
603	C₂×Dic₅₃	—	2	1	no	—
604	C₂×Dic₅₃	—	2	1	no	—
605	C₂×Dic₅₃	—	2	1	no	—
606	C₂×Dic₅₃	—	2	8	no	—
607	C₂×Dic₅₃	—	2	1	no	—
608	C₂×Dic₅₃	—	2	1	no	—
609	C₂×Dic₅₃	—	2	1	no	—
610	C₂×Dic₅₃	—	2	1	no	—
611	C₂×Dic₅₃	—	2	1	no	—
612	C₂×Dic₅₃	—	2	1	no	—
613	C₂×Dic₅₃	—	2	1	no	—
614	C₂×Dic₅₃	—	2	1	no	—
615	C₂×Dic₅₃	—	2	1	no	—
616	C₂×Dic₅₃	—	2	1	no	—
617	C₂×Dic₅₃	—	2	1	no	—
618	C₂×Dic₅₃	—	2	1	no	—
619	C₂×Dic₅₃	—	2	1	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	—	4	4	no	—
629	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
630	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
631	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
632	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
633	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
634	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
635	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
636	C₂×Dic₅₃	H(5,𝔽₂)	1	2	yes	—
637	C₂×Dic₅₃	H(5,𝔽₂)	1	2	yes	—
638	C₂×Dic₅₃	2₋¹⁺⁴	1	2	yes	—
639	C₂×Dic₅₃	2₋¹⁺⁴	1	2	yes	—
640	C₂×Dic₅₃	2₋¹⁺⁴	1	2	yes	—
641	C₄×D₅₃	—	2	8	no	—
642	C₄×D₅₃	—	4	4	no	—
643	C₄×D₅₃	—	4	4	no	—
644	Dic₁₀₆	—	2	8	no	—
645	Dic₁₀₆	—	2	8	no	—
646	Dic₁₀₆	—	2	8	no	—
647	Dic₁₀₆	—	4	4	no	—
648	Dic₁₀₆	—	4	4	no	—
649	Dic₁₀₆	—	4	4	no	—
650	#34487	—	53	1	no	maximal, Sylow
651	C₂²×C₅₃	—	2	2	no	—
652	C₂²×C₅₃	—	2	2	no	—
653	C₂²×C₅₃	—	2	2	no	—
654	C₂²×C₅₃	—	4	1	no	—
655	C₂²×C₅₃	—	4	1	no	—
656	C₂²×C₅₃	—	4	1	no	—
657	C₂²×C₅₃	—	4	1	no	—
658	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
659	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
660	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
661	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
662	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
663	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
664	C₂²×C₅₃	#585	1	1	yes	characteristic
665	C₂×D₅₃	—	2	2	no	—
666	C₂×D₅₃	—	2	2	no	—
667	C₂×D₅₃	—	2	2	no	—
668	C₂×D₅₃	—	4	1	no	—
669	C₂×D₅₃	—	4	1	no	—
670	C₂×D₅₃	—	4	1	no	—
671	C₂×D₅₃	—	4	1	no	—
672	C₄×C₅₃	—	2	2	no	—
673	C₄×C₅₃	—	2	2	no	—
674	C₄×C₅₃	—	2	2	no	—
675	C₄×C₅₃	—	2	2	no	—
676	C₄×C₅₃	—	2	2	no	—
677	C₄×C₅₃	—	2	2	no	—
678	C₄×C₅₃	—	4	1	no	—
679	C₄×C₅₃	—	4	1	no	—
680	C₄×C₅₃	—	4	1	no	—
681	C₄×C₅₃	—	4	1	no	—
682	C₄×C₅₃	—	4	1	no	—
683	C₄×C₅₃	—	4	1	no	—
684	C₄×C₅₃	—	4	1	no	—
685	C₄×C₅₃	—	4	1	no	—
686	Dic₅₃	—	2	2	no	—
687	Dic₅₃	—	2	2	no	—
688	Dic₅₃	—	2	2	no	—
689	Dic₅₃	—	2	2	no	—
690	Dic₅₃	—	2	2	no	—
691	Dic₅₃	—	2	2	no	—
692	Dic₅₃	—	4	1	no	—
693	Dic₅₃	—	4	1	no	—
694	Dic₅₃	—	4	1	no	—
695	Dic₅₃	—	4	1	no	—
696	Dic₅₃	—	4	1	no	—
697	Dic₅₃	—	4	1	no	—
698	Dic₅₃	—	4	1	no	—
699	Dic₅₃	#518	1	4	yes	—
700	Dic₅₃	#519	1	4	yes	—
701	C₂×D₄×Q₈	—	53	1	no	—
702	#2378	—	53	1	no	—
703	#2378	—	53	1	no	—
704	#2378	—	53	1	no	—
705	#2378	D₅₃	1	1	yes	characteristic, complemented
706	#2369	—	53	1	no	—
707	#2369	—	53	1	no	—
708	#2365	—	53	1	no	—
709	#2362	—	53	1	no	—
710	#2362	—	53	1	no	—
711	#2357	—	53	1	no	—
712	#2357	—	53	1	no	—
713	#2355	—	53	1	no	—
714	#2354	—	53	1	no	—
715	Q₈×C₂²⋊C₄	—	53	1	no	—
716	Q₈×C₂²⋊C₄	—	53	1	no	—
717	#2332	—	53	1	no	—
718	#2332	—	53	1	no	—
719	#2332	—	53	1	no	—
720	#2332	—	53	1	no	—
721	#2331	—	53	1	no	—
722	#2331	—	53	1	no	—
723	#2323	—	53	1	no	—
724	#2323	—	53	1	no	—
725	#2319	—	53	1	no	—
726	#2319	—	53	1	no	—
727	#2310	—	53	1	no	—
728	#2310	—	53	1	no	—
729	C₄×C₄⋊Q₈	—	53	1	no	—
730	#2295	—	53	1	no	—
731	#2293	—	53	1	no	—
732	C₂×C₅₃	—	4	2	no	—
733	C₂×C₅₃	C₂×#518	1	1	yes	characteristic
734	C₂×C₅₃	C₂×#519	1	1	yes	characteristic
735	C₂×C₅₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
736	C₂×C₅₃	#3547	1	1	yes	characteristic
737	C₂×C₅₃	#3550	1	1	yes	characteristic
738	C₂×C₅₃	#3552	1	1	yes	characteristic
739	C₂×C₅₃	#3554	1	1	yes	characteristic
740	D₅₃	—	4	2	no	—
741	C₂³×Q₈	—	53	1	no	—
742	C₂³×Q₈	—	53	1	no	—
743	D₄×Q₈	—	53	16	no	—
744	C₂×C₄⋊Q₈	—	53	1	no	—
745	C₂×C₄⋊Q₈	—	53	1	no	—
746	C₂×C₄⋊Q₈	—	53	1	no	—
747	C₂×C₂²⋊Q₈	—	53	1	no	—
748	C₂×C₂²⋊Q₈	—	53	1	no	—
749	C₂×C₂²⋊Q₈	—	53	1	no	—
750	C₂×C₂²⋊Q₈	—	53	1	no	—
751	C₂×C₂²⋊Q₈	—	53	1	no	—
752	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
753	C₂×C₄×Q₈	—	53	1	no	—
754	C₂×C₄×Q₈	—	53	1	no	—
755	C₂×C₄×Q₈	—	53	1	no	—
756	C₂×C₄×Q₈	—	53	1	no	—
757	C₂×C₄×Q₈	—	53	1	no	—
758	C₂×C₄×D₄	—	53	1	no	—
759	C₂×C₄×D₄	—	53	1	no	—
760	C₂×C₄×D₄	—	53	1	no	—
761	C₂×#117	—	53	1	no	—
762	C₂×#117	—	53	1	no	—
763	C₂×#117	—	53	1	no	—
764	C₂×#117	—	53	1	no	—
765	#391	—	53	1	no	—
766	#391	—	53	1	no	—
767	#391	—	53	1	no	—
768	#391	—	53	1	no	—
769	#391	—	53	1	no	—
770	#391	—	53	1	no	—
771	#391	—	53	1	no	—
772	#391	—	53	1	no	—
773	#391	—	53	1	no	—
774	#391	—	53	1	no	—
775	#391	—	53	1	no	—
776	#391	—	53	1	no	—
777	#391	—	53	1	no	—
778	#391	—	53	1	no	—
779	#391	—	53	1	no	—
780	#391	—	53	1	no	—
781	#391	—	53	1	no	—
782	#391	—	53	1	no	—
783	#391	—	53	1	no	—
784	#391	—	53	1	no	—
785	#391	—	53	1	no	—
786	#391	—	53	1	no	—
787	#391	C₂×D₅₃	1	1	yes	characteristic
788	#391	C₂×D₅₃	1	1	yes	characteristic
789	#390	—	53	1	no	—
790	#390	—	53	1	no	—
791	#390	—	53	1	no	—
792	#390	—	53	1	no	—
793	#389	—	53	1	no	—
794	#389	—	53	1	no	—
795	#389	—	53	1	no	—
796	#389	—	53	1	no	—
797	#389	—	53	1	no	—
798	#389	—	53	1	no	—
799	#389	—	53	1	no	—
800	#389	—	53	1	no	—
801	#389	—	53	1	no	—
802	#389	—	53	1	no	—
803	#389	—	53	1	no	—
804	#389	—	53	1	no	—
805	#389	C₂×D₅₃	1	1	yes	characteristic
806	#389	C₂×D₅₃	1	1	yes	characteristic
807	#388	—	53	1	no	—
808	#388	—	53	1	no	—
809	#388	—	53	1	no	—
810	#388	—	53	1	no	—
811	#388	—	53	1	no	—
812	#388	—	53	1	no	—
813	#388	—	53	1	no	—
814	#388	—	53	1	no	—
815	#388	—	53	1	no	—
816	#388	—	53	1	no	—
817	#388	—	53	1	no	—
818	#388	—	53	1	no	—
819	#388	—	53	1	no	—
820	#388	—	53	1	no	—
821	#388	—	53	1	no	—
822	#388	—	53	1	no	—
823	#388	—	53	1	no	—
824	#388	—	53	1	no	—
825	#388	—	53	1	no	—
826	#388	—	53	1	no	—
827	#388	C₂×D₅₃	1	1	yes	characteristic
828	#388	C₂×D₅₃	1	1	yes	characteristic
829	#388	C₂×D₅₃	1	1	yes	characteristic
830	#388	C₂×D₅₃	1	1	yes	characteristic
831	#387	—	53	1	no	—
832	#387	—	53	1	no	—
833	#387	—	53	1	no	—
834	#387	—	53	1	no	—
835	#387	—	53	1	no	—
836	#387	—	53	1	no	—
837	#387	—	53	1	no	—
838	#387	—	53	1	no	—
839	#387	—	53	1	no	—
840	#387	—	53	1	no	—
841	#387	—	53	1	no	—
842	#387	—	53	1	no	—
843	#387	—	53	1	no	—
844	#387	—	53	1	no	—
845	#387	—	53	1	no	—
846	#387	—	53	1	no	—
847	#387	C₂×D₅₃	1	1	yes	characteristic
848	#387	C₂×D₅₃	1	1	yes	characteristic
849	#387	C₂×D₅₃	1	1	yes	characteristic
850	#387	C₂×D₅₃	1	1	yes	characteristic
851	#384	—	53	1	no	—
852	#382	—	53	1	no	—
853	#382	—	53	1	no	—
854	#381	—	53	1	no	—
855	#381	—	53	1	no	—
856	#381	—	53	1	no	—
857	#381	—	53	1	no	—
858	#381	—	53	1	no	—
859	#381	—	53	1	no	—
860	#381	—	53	1	no	—
861	#381	C₂×D₅₃	1	1	yes	characteristic
862	#380	—	53	1	no	—
863	#380	—	53	1	no	—
864	#380	—	53	1	no	—
865	#380	—	53	1	no	—
866	#380	—	53	1	no	—
867	#380	C₂×D₅₃	1	1	yes	characteristic
868	C₄×C₄⋊C₄	—	53	1	no	—
869	C₄×C₄⋊C₄	—	53	1	no	—
870	C₄×C₄⋊C₄	—	53	1	no	—
871	C₄×C₄⋊C₄	—	53	1	no	—
872	C₄×C₄⋊C₄	—	53	1	no	—
873	C₄×C₄⋊C₄	—	53	1	no	—
874	C₄×C₄⋊C₄	—	53	1	no	—
875	C₄×C₄⋊C₄	—	53	1	no	—
876	C₄×C₄⋊C₄	—	53	1	no	—
877	C₄×C₄⋊C₄	—	53	1	no	—
878	C₄×C₄⋊C₄	—	53	1	no	—
879	C₄×C₄⋊C₄	—	53	1	no	—
880	C₄×C₄⋊C₄	—	53	1	no	—
881	C₄×C₄⋊C₄	—	53	1	no	—
882	C₄×C₄⋊C₄	—	53	1	no	—
883	C₄×C₄⋊C₄	—	53	1	no	—
884	C₄×C₄⋊C₄	—	53	1	no	—
885	C₄×C₄⋊C₄	—	53	1	no	—
886	C₄×C₄⋊C₄	—	53	1	no	—
887	C₄×C₄⋊C₄	—	53	1	no	—
888	C₄×C₂²⋊C₄	—	53	1	no	—
889	C₄×C₂²⋊C₄	—	53	1	no	—
890	C₄×C₂²⋊C₄	—	53	1	no	—
891	C₄×C₂²⋊C₄	—	53	1	no	—
892	C₄×C₂²⋊C₄	—	53	1	no	—
893	C₄×C₂²⋊C₄	—	53	1	no	—
894	#376	—	53	1	no	—
895	#376	—	53	1	no	—
896	C₄³	—	53	1	no	—
897	C₅₃	#34487	1	1	yes	characteristic, complemented, Sylow
898	C₂²×Q₈	—	53	8	no	—
899	C₂²×Q₈	—	53	8	no	—
900	C₂²×Q₈	—	53	1	no	—
901	C₂²×Q₈	—	53	1	no	—
902	C₂²×Q₈	—	53	1	no	—
903	C₂²×Q₈	—	53	1	no	—
904	C₂²×Q₈	—	53	1	no	—
905	C₂²×Q₈	—	53	1	no	—
906	C₂²×Q₈	—	212	2	no	—
907	C₂²×Q₈	—	212	2	no	—
908	C₂²×Q₈	—	212	2	no	—
909	C₂²×Q₈	—	212	2	no	—
910	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
911	C₂²×D₄	—	53	1	no	—
912	C₂³×C₄	—	53	1	no	—
913	C₂³×C₄	—	53	1	no	—
914	C₂³×C₄	—	53	1	no	—
915	C₂³×C₄	—	53	1	no	—
916	C₂³×C₄	—	53	1	no	—
917	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
918	C₄⋊Q₈	—	53	8	no	—
919	C₄⋊Q₈	—	53	8	no	—
920	C₄⋊Q₈	—	53	8	no	—
921	C₂²⋊Q₈	—	53	8	no	—
922	C₂²⋊Q₈	—	53	8	no	—
923	C₂²⋊Q₈	—	53	8	no	—
924	C₂²⋊Q₈	—	53	8	no	—
925	C₂²⋊Q₈	—	53	8	no	—
926	C₂²⋊Q₈	C₄×D₅₃	1	8	yes	—
927	C₄×Q₈	—	53	8	no	—
928	C₄×Q₈	—	212	2	no	—
929	C₄×Q₈	—	212	2	no	—
930	C₄×Q₈	—	212	2	no	—
931	C₄×Q₈	—	212	2	no	—
932	C₄×D₄	—	53	8	no	—
933	C₄×D₄	—	53	8	no	—
934	C₄×D₄	—	53	8	no	—
935	#117	—	212	2	no	—
936	#117	—	212	2	no	—
937	#117	—	212	2	no	—
938	#117	—	212	2	no	—
939	C₂×C₄⋊C₄	—	53	1	no	—
940	C₂×C₄⋊C₄	—	53	1	no	—
941	C₂×C₄⋊C₄	—	53	1	no	—
942	C₂×C₄⋊C₄	—	53	1	no	—
943	C₂×C₄⋊C₄	—	53	1	no	—
944	C₂×C₄⋊C₄	—	53	1	no	—
945	C₂×C₄⋊C₄	—	53	1	no	—
946	C₂×C₄⋊C₄	—	53	1	no	—
947	C₂×C₄⋊C₄	—	53	1	no	—
948	C₂×C₄⋊C₄	—	53	1	no	—
949	C₂×C₄⋊C₄	—	53	1	no	—
950	C₂×C₄⋊C₄	—	53	1	no	—
951	C₂×C₄⋊C₄	—	53	1	no	—
952	C₂×C₄⋊C₄	—	53	1	no	—
953	C₂×C₄⋊C₄	—	53	1	no	—
954	C₂×C₄⋊C₄	—	53	1	no	—
955	C₂×C₄⋊C₄	—	53	1	no	—
956	C₂×C₄⋊C₄	—	53	1	no	—
957	C₂×C₄⋊C₄	—	53	1	no	—
958	C₂×C₄⋊C₄	—	53	1	no	—
959	C₂×C₄⋊C₄	—	53	1	no	—
960	C₂×C₄⋊C₄	—	53	1	no	—
961	C₂×C₄⋊C₄	—	53	1	no	—
962	C₂×C₄⋊C₄	—	53	1	no	—
963	C₂×C₄⋊C₄	—	53	1	no	—
964	C₂×C₄⋊C₄	—	53	1	no	—
965	C₂×C₄⋊C₄	—	53	1	no	—
966	C₂×C₄⋊C₄	—	53	1	no	—
967	C₂×C₄⋊C₄	—	53	1	no	—
968	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
969	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
970	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
971	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
972	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
973	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
974	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
975	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
976	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
977	C₂×C₂²⋊C₄	—	53	1	no	—
978	C₂×C₂²⋊C₄	—	53	1	no	—
979	C₂×C₂²⋊C₄	—	53	1	no	—
980	C₂×C₂²⋊C₄	—	53	1	no	—
981	C₂×C₂²⋊C₄	—	53	1	no	—
982	C₂×C₂²⋊C₄	—	53	1	no	—
983	C₂×C₂²⋊C₄	—	53	1	no	—
984	C₂×C₂²⋊C₄	—	53	1	no	—
985	C₂×C₂²⋊C₄	—	53	1	no	—
986	C₂×C₂²⋊C₄	—	53	1	no	—
987	C₂×C₂²⋊C₄	—	53	1	no	—
988	C₂×C₂²⋊C₄	—	53	1	no	—
989	C₂×C₂²⋊C₄	—	53	1	no	—
990	C₂×C₂²⋊C₄	—	53	1	no	—
991	C₂×C₂²⋊C₄	—	53	1	no	—
992	C₂×C₂²⋊C₄	—	53	1	no	—
993	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
994	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
995	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
996	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
997	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
998	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
999	C₂×C₄²	—	53	1	no	—
1000	C₂×C₄²	—	53	1	no	—
1001	C₂×C₄²	—	53	1	no	—
1002	C₂×C₄²	—	53	1	no	—
1003	C₂×C₄²	—	53	1	no	—
1004	C₂×C₄²	—	53	1	no	—
1005	C₂×C₄²	—	53	1	no	—
1006	C₂×C₄²	—	53	1	no	—
1007	C₂×C₄²	—	53	1	no	—
1008	C₂×C₄²	—	53	1	no	—
1009	C₂×C₄²	—	53	1	no	—
1010	C₂×C₄²	—	53	1	no	—
1011	C₂×C₄²	—	53	1	no	—
1012	C₂×C₄²	—	53	1	no	—
1013	C₂×C₄²	—	53	1	no	—
1014	C₂×C₄²	—	53	1	no	—
1015	C₂×C₄²	—	53	1	no	—
1016	C₂×C₄²	—	53	1	no	—
1017	C₂×C₄²	—	53	1	no	—
1018	C₂×C₄²	—	53	1	no	—
1019	C₂×C₄²	—	53	1	no	—
1020	C₂×C₄²	—	53	1	no	—
1021	C₂×C₄²	—	53	1	no	—
1022	C₂×C₄²	—	53	1	no	—
1023	C₂×C₄²	—	53	1	no	—
1024	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1025	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1026	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1027	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1028	#95	—	53	1	no	—
1029	#95	—	53	1	no	—
1030	#95	—	53	1	no	—
1031	#95	—	53	1	no	—
1032	#95	—	53	1	no	—
1033	#95	—	53	1	no	—
1034	#95	—	53	1	no	—
1035	#95	—	53	1	no	—
1036	#95	—	53	1	no	—
1037	#95	—	53	1	no	—
1038	#95	—	53	1	no	—
1039	#95	—	53	1	no	—
1040	#95	—	53	1	no	—
1041	#95	—	53	1	no	—
1042	#95	—	53	1	no	—
1043	#95	—	53	1	no	—
1044	#95	—	53	1	no	—
1045	#95	—	53	1	no	—
1046	#95	—	53	1	no	—
1047	#95	—	53	1	no	—
1048	#95	—	53	1	no	—
1049	#95	—	53	1	no	—
1050	#95	—	53	1	no	—
1051	#95	—	53	1	no	—
1052	#95	—	53	1	no	—
1053	#95	—	53	1	no	—
1054	#95	—	53	1	no	—
1055	#95	—	53	1	no	—
1056	#95	—	53	1	no	—
1057	#95	—	53	1	no	—
1058	#95	—	53	1	no	—
1059	#95	—	53	1	no	—
1060	#95	—	53	1	no	—
1061	#95	—	53	1	no	—
1062	#95	—	53	1	no	—
1063	#95	—	53	1	no	—
1064	#95	—	53	1	no	—
1065	#95	—	53	1	no	—
1066	#95	C₂²×D₅₃	1	1	yes	characteristic
1067	#95	C₂²×D₅₃	1	1	yes	characteristic
1068	#95	C₂²×D₅₃	1	1	yes	characteristic
1069	#95	C₂²×D₅₃	1	1	yes	characteristic
1070	#95	C₂²×D₅₃	1	1	yes	characteristic
1071	#95	C₂²×D₅₃	1	1	yes	characteristic
1072	#95	C₂²×D₅₃	1	1	yes	characteristic
1073	#95	C₂²×D₅₃	1	1	yes	characteristic
1074	#95	C₂²×D₅₃	1	1	yes	characteristic
1075	#95	C₂²×D₅₃	1	1	yes	characteristic
1076	#95	C₂²×D₅₃	1	1	yes	characteristic
1077	#95	C₂²×D₅₃	1	1	yes	characteristic
1078	#95	C₂²×D₅₃	1	1	yes	characteristic
1079	#95	C₂²×D₅₃	1	1	yes	characteristic
1080	C₂⁴	—	53	1	no	—
1081	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1082	C₂×Q₈	—	4	1	no	—
1083	C₂×Q₈	—	4	1	no	—
1084	C₂×Q₈	—	53	4	no	—
1085	C₂×Q₈	—	53	4	no	—
1086	C₂×Q₈	—	53	4	no	—
1087	C₂×Q₈	—	53	4	no	—
1088	C₂×Q₈	—	53	4	no	—
1089	C₂×Q₈	—	53	4	no	—
1090	C₂×Q₈	—	106	2	no	—
1091	C₂×Q₈	—	106	2	no	—
1092	C₂×Q₈	—	106	2	no	—
1093	C₂×Q₈	—	106	2	no	—
1094	C₂×Q₈	—	106	2	no	—
1095	C₂×Q₈	—	106	2	no	—
1096	C₂×Q₈	—	212	1	no	—
1097	C₂×Q₈	—	212	1	no	—
1098	C₂×Q₈	—	212	1	no	—
1099	C₂×Q₈	—	212	1	no	—
1100	C₂×Q₈	—	212	1	no	—
1101	C₂×Q₈	—	212	1	no	—
1102	C₂×Q₈	—	212	16	no	—
1103	C₂×Q₈	—	212	16	no	—
1104	C₂×Q₈	C₂×C₄×D₅₃	1	4	yes	—
1105	C₂×D₄	—	53	4	no	—
1106	C₂×D₄	—	106	2	no	—
1107	C₂×D₄	—	106	2	no	—
1108	C₂²×C₄	—	4	1	no	—
1109	C₂²×C₄	—	4	1	no	—
1110	C₂²×C₄	—	53	1	no	—
1111	C₂²×C₄	—	53	1	no	—
1112	C₂²×C₄	—	53	4	no	—
1113	C₂²×C₄	—	53	1	no	—
1114	C₂²×C₄	—	53	1	no	—
1115	C₂²×C₄	—	53	1	no	—
1116	C₂²×C₄	—	53	1	no	—
1117	C₂²×C₄	—	53	1	no	—
1118	C₂²×C₄	—	53	1	no	—
1119	C₂²×C₄	—	53	4	no	—
1120	C₂²×C₄	—	53	4	no	—
1121	C₂²×C₄	—	53	4	no	—
1122	C₂²×C₄	—	53	4	no	—
1123	C₂²×C₄	—	53	1	no	—
1124	C₂²×C₄	—	53	1	no	—
1125	C₂²×C₄	—	53	1	no	—
1126	C₂²×C₄	—	53	1	no	—
1127	C₂²×C₄	—	53	1	no	—
1128	C₂²×C₄	—	53	1	no	—
1129	C₂²×C₄	—	53	1	no	—
1130	C₂²×C₄	—	106	2	no	—
1131	C₂²×C₄	—	106	2	no	—
1132	C₂²×C₄	—	106	2	no	—
1133	C₂²×C₄	—	106	2	no	—
1134	C₂²×C₄	—	212	1	no	—
1135	C₂²×C₄	—	212	1	no	—
1136	C₂²×C₄	—	212	1	no	—
1137	C₂²×C₄	—	212	1	no	—
1138	C₂²×C₄	—	212	1	no	—
1139	C₂²×C₄	—	212	1	no	—
1140	C₂²×C₄	C₂×C₄×D₅₃	1	4	yes	—
1141	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1142	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1143	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1144	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1145	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1146	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1147	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1148	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1149	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1150	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1151	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1152	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1153	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1154	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1155	C₄⋊C₄	—	4	1	no	—
1156	C₄⋊C₄	—	4	1	no	—
1157	C₄⋊C₄	—	4	1	no	—
1158	C₄⋊C₄	—	4	1	no	—
1159	C₄⋊C₄	—	4	1	no	—
1160	C₄⋊C₄	—	4	1	no	—
1161	C₄⋊C₄	—	53	4	no	—
1162	C₄⋊C₄	—	53	4	no	—
1163	C₄⋊C₄	—	53	4	no	—
1164	C₄⋊C₄	—	53	4	no	—
1165	C₄⋊C₄	—	53	4	no	—
1166	C₄⋊C₄	—	53	4	no	—
1167	C₄⋊C₄	—	53	4	no	—
1168	C₄⋊C₄	—	53	4	no	—
1169	C₄⋊C₄	—	53	4	no	—
1170	C₄⋊C₄	—	106	2	no	—
1171	C₄⋊C₄	—	106	2	no	—
1172	C₄⋊C₄	—	106	2	no	—
1173	C₄⋊C₄	—	106	2	no	—
1174	C₄⋊C₄	—	106	2	no	—
1175	C₄⋊C₄	—	106	2	no	—
1176	C₄⋊C₄	—	106	2	no	—
1177	C₄⋊C₄	—	106	2	no	—
1178	C₄⋊C₄	—	106	2	no	—
1179	C₄⋊C₄	—	106	2	no	—
1180	C₄⋊C₄	—	212	1	no	—
1181	C₄⋊C₄	—	212	1	no	—
1182	C₄⋊C₄	—	212	1	no	—
1183	C₄⋊C₄	—	212	1	no	—
1184	C₄⋊C₄	—	212	1	no	—
1185	C₄⋊C₄	—	212	1	no	—
1186	C₄⋊C₄	—	212	1	no	—
1187	C₄⋊C₄	—	212	1	no	—
1188	C₄⋊C₄	—	212	1	no	—
1189	C₄⋊C₄	—	212	1	no	—
1190	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1191	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1192	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1193	C₂²⋊C₄	—	4	1	no	—
1194	C₂²⋊C₄	—	4	1	no	—
1195	C₂²⋊C₄	—	4	1	no	—
1196	C₂²⋊C₄	—	4	1	no	—
1197	C₂²⋊C₄	—	53	4	no	—
1198	C₂²⋊C₄	—	53	4	no	—
1199	C₂²⋊C₄	—	53	4	no	—
1200	C₂²⋊C₄	—	53	4	no	—
1201	C₂²⋊C₄	—	106	2	no	—
1202	C₂²⋊C₄	—	106	2	no	—
1203	C₂²⋊C₄	—	212	1	no	—
1204	C₂²⋊C₄	—	212	1	no	—
1205	C₂²⋊C₄	—	212	1	no	—
1206	C₂²⋊C₄	—	212	1	no	—
1207	C₂²⋊C₄	—	212	1	no	—
1208	C₂²⋊C₄	—	212	1	no	—
1209	C₂²⋊C₄	—	212	1	no	—
1210	C₂²⋊C₄	—	212	1	no	—
1211	C₂²⋊C₄	—	212	1	no	—
1212	C₂²⋊C₄	—	212	1	no	—
1213	C₂²⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1214	C₂²⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1215	C₄²	—	4	1	no	—
1216	C₄²	—	4	1	no	—
1217	C₄²	—	4	1	no	—
1218	C₄²	—	4	1	no	—
1219	C₄²	—	53	4	no	—
1220	C₄²	—	53	4	no	—
1221	C₄²	—	53	4	no	—
1222	C₄²	—	106	2	no	—
1223	C₄²	—	106	2	no	—
1224	C₄²	—	106	2	no	—
1225	C₄²	—	106	2	no	—
1226	C₄²	—	106	2	no	—
1227	C₄²	—	106	2	no	—
1228	C₄²	—	106	2	no	—
1229	C₄²	—	106	2	no	—
1230	C₄²	—	106	2	no	—
1231	C₄²	—	212	1	no	—
1232	C₄²	—	212	1	no	—
1233	C₄²	—	212	1	no	—
1234	C₄²	—	212	1	no	—
1235	C₄²	—	212	1	no	—
1236	C₄²	—	212	1	no	—
1237	C₄²	—	212	1	no	—
1238	C₄²	—	212	1	no	—
1239	C₄²	—	212	1	no	—
1240	C₄²	—	212	1	no	—
1241	C₄²	—	212	1	no	—
1242	C₄²	—	212	1	no	—
1243	C₄²	—	212	1	no	—
1244	C₂³	—	2	1	no	—
1245	C₂³	—	2	1	no	—
1246	C₂³	—	2	1	no	—
1247	C₂³	—	2	1	no	—
1248	C₂³	—	2	1	no	—
1249	C₂³	—	2	1	no	—
1250	C₂³	—	53	2	no	—
1251	C₂³	—	106	1	no	—
1252	C₂³	—	106	1	no	—
1253	C₂³	—	106	1	no	—
1254	C₂³	—	106	1	no	—
1255	C₂³	—	106	1	no	—
1256	C₂³	—	106	1	no	—
1257	C₂³	C₂²×C₄×D₅₃	1	2	yes	—
1258	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1259	Q₈	—	4	4	no	—
1260	Q₈	—	106	8	no	—
1261	Q₈	—	106	8	no	—
1262	Q₈	—	106	8	no	—
1263	Q₈	—	212	4	no	—
1264	Q₈	—	212	4	no	—
1265	Q₈	—	212	4	no	—
1266	D₄	—	106	8	no	—
1267	C₂×C₄	—	2	1	no	—
1268	C₂×C₄	—	2	1	no	—
1269	C₂×C₄	—	2	1	no	—
1270	C₂×C₄	—	2	1	no	—
1271	C₂×C₄	—	2	1	no	—
1272	C₂×C₄	—	2	1	no	—
1273	C₂×C₄	—	2	1	no	—
1274	C₂×C₄	—	2	1	no	—
1275	C₂×C₄	—	2	1	no	—
1276	C₂×C₄	—	2	1	no	—
1277	C₂×C₄	—	2	1	no	—
1278	C₂×C₄	—	2	1	no	—
1279	C₂×C₄	—	2	1	no	—
1280	C₂×C₄	—	2	1	no	—
1281	C₂×C₄	—	2	1	no	—
1282	C₂×C₄	—	2	1	no	—
1283	C₂×C₄	—	2	1	no	—
1284	C₂×C₄	—	2	1	no	—
1285	C₂×C₄	—	2	1	no	—
1286	C₂×C₄	—	2	1	no	—
1287	C₂×C₄	—	2	1	no	—
1288	C₂×C₄	—	2	1	no	—
1289	C₂×C₄	—	2	1	no	—
1290	C₂×C₄	—	2	1	no	—
1291	C₂×C₄	—	2	1	no	—
1292	C₂×C₄	—	2	1	no	—
1293	C₂×C₄	—	2	1	no	—
1294	C₂×C₄	—	2	1	no	—
1295	C₂×C₄	—	2	1	no	—
1296	C₂×C₄	—	2	1	no	—
1297	C₂×C₄	—	2	1	no	—
1298	C₂×C₄	—	2	1	no	—
1299	C₂×C₄	—	2	1	no	—
1300	C₂×C₄	—	2	1	no	—
1301	C₂×C₄	—	2	1	no	—
1302	C₂×C₄	—	2	1	no	—
1303	C₂×C₄	—	4	4	no	—
1304	C₂×C₄	—	53	2	no	—
1305	C₂×C₄	—	53	2	no	—
1306	C₂×C₄	—	53	2	no	—
1307	C₂×C₄	—	53	2	no	—
1308	C₂×C₄	—	53	2	no	—
1309	C₂×C₄	—	53	2	no	—
1310	C₂×C₄	—	53	2	no	—
1311	C₂×C₄	—	53	2	no	—
1312	C₂×C₄	—	53	2	no	—
1313	C₂×C₄	—	53	2	no	—
1314	C₂×C₄	—	53	2	no	—
1315	C₂×C₄	—	53	2	no	—
1316	C₂×C₄	—	106	8	no	—
1317	C₂×C₄	—	106	8	no	—
1318	C₂×C₄	—	106	1	no	—
1319	C₂×C₄	—	106	1	no	—
1320	C₂×C₄	—	106	1	no	—
1321	C₂×C₄	—	106	1	no	—
1322	C₂×C₄	—	106	1	no	—
1323	C₂×C₄	—	106	1	no	—
1324	C₂×C₄	—	106	1	no	—
1325	C₂×C₄	—	106	1	no	—
1326	C₂×C₄	—	106	1	no	—
1327	C₂×C₄	—	106	1	no	—
1328	C₂×C₄	—	106	1	no	—
1329	C₂×C₄	—	106	1	no	—
1330	C₂×C₄	—	106	1	no	—
1331	C₂×C₄	—	106	1	no	—
1332	C₂×C₄	—	106	1	no	—
1333	C₂×C₄	—	106	1	no	—
1334	C₂×C₄	—	106	1	no	—
1335	C₂×C₄	—	106	1	no	—
1336	C₂×C₄	—	106	1	no	—
1337	C₂×C₄	—	106	1	no	—
1338	C₂×C₄	—	106	1	no	—
1339	C₂×C₄	—	106	1	no	—
1340	C₂×C₄	—	106	1	no	—
1341	C₂×C₄	—	106	1	no	—
1342	C₂×C₄	—	106	1	no	—
1343	C₂×C₄	—	106	1	no	—
1344	C₂×C₄	—	106	1	no	—
1345	C₂×C₄	—	106	1	no	—
1346	C₂×C₄	—	106	1	no	—
1347	C₂×C₄	—	106	1	no	—
1348	C₂×C₄	—	106	1	no	—
1349	C₂×C₄	—	106	1	no	—
1350	C₂×C₄	—	106	1	no	—
1351	C₂×C₄	—	212	4	no	—
1352	C₂×C₄	—	212	4	no	—
1353	C₂×C₄	—	212	4	no	—
1354	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1355	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1356	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1357	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1358	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1359	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1360	C₂²	—	2	2	no	—
1361	C₂²	—	2	2	no	—
1362	C₂²	—	2	2	no	—
1363	C₂²	—	4	1	no	—
1364	C₂²	—	4	1	no	—
1365	C₂²	—	4	1	no	—
1366	C₂²	—	4	1	no	—
1367	C₂²	—	106	2	no	—
1368	C₂²	—	106	2	no	—
1369	C₂²	—	106	2	no	—
1370	C₂²	—	212	1	no	—
1371	C₂²	—	212	1	no	—
1372	C₂²	—	212	1	no	—
1373	C₂²	—	212	1	no	—
1374	C₂²	C₂³×C₄×D₅₃	1	1	yes	characteristic
1375	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1376	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1377	C₂²	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1378	C₂²	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1379	C₂²	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1380	C₂²	#16811458	1	1	yes	characteristic
1381	C₄	—	2	2	no	—
1382	C₄	—	2	2	no	—
1383	C₄	—	2	2	no	—
1384	C₄	—	2	2	no	—
1385	C₄	—	2	2	no	—
1386	C₄	—	2	2	no	—
1387	C₄	—	4	1	no	—
1388	C₄	—	4	1	no	—
1389	C₄	—	4	1	no	—
1390	C₄	—	4	1	no	—
1391	C₄	—	4	1	no	—
1392	C₄	—	4	1	no	—
1393	C₄	—	4	1	no	—
1394	C₄	—	4	1	no	—
1395	C₄	—	53	4	no	—
1396	C₄	—	53	4	no	—
1397	C₄	—	106	2	no	—
1398	C₄	—	106	2	no	—
1399	C₄	—	106	2	no	—
1400	C₄	—	106	2	no	—
1401	C₄	—	106	2	no	—
1402	C₄	—	106	2	no	—
1403	C₄	—	212	1	no	—
1404	C₄	—	212	1	no	—
1405	C₄	—	212	1	no	—
1406	C₄	—	212	1	no	—
1407	C₄	—	212	1	no	—
1408	C₄	—	212	1	no	—
1409	C₄	—	212	1	no	—
1410	C₂	—	4	2	no	—
1411	C₂	—	212	2	no	—
1412	C₂	#518×D₅₃	1	1	yes	characteristic
1413	C₂	#519×D₅₃	1	1	yes	characteristic
1414	C₂	#20287926	1	1	yes	characteristic
1415	C₂	#20289095	1	1	yes	characteristic
1416	C₂	#20289125	1	1	yes	characteristic
1417	C₂	#20289149	1	1	yes	characteristic
1418	C₂	#20289177	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator	C₂²×C₅₃	C₂⁴×C₄
Fitting	C₅₃×#2378	C₂
socle, cosocle	C₂³×C₅₃	C₂⁵
prime radical	C₂²×C₂²⋊D₅₃	C₂³
hypercenter	#2378	D₅₃
hypocenter	C₅₃	#34487
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #2378

Complements

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

N	H ≅ G/N	type
2. #20277879	C₂	semidirect
3. #20277877	C₂	semidirect
4. #20277875	C₂	semidirect
5. #20277803	C₂	semidirect
6. #20277801	C₂	semidirect
7. #20277770	C₂	semidirect
8. #20277739	C₂	semidirect
9. #20277737	C₂	semidirect
12. #20277669	C₂	semidirect
14. #20277549	C₂	semidirect
15. #20277547	C₂	semidirect
16. #20277473	C₂	semidirect
17. #20277469	C₂	semidirect
18. #20277467	C₂	semidirect
19. #20277465	C₂	semidirect
20. #20277460	C₂	semidirect
21. #20277458	C₂	semidirect
22. #20277394	C₂	semidirect
23. #20277392	C₂	semidirect
26. #20277300	C₂	semidirect
27. #20277298	C₂	semidirect
28. #20277286	C₂	semidirect
29. #20277188	C₂	semidirect
31. C₅₃×#2378	C₂	semidirect
34. #16811286	C₄	semidirect
705. #2378	D₅₃	semidirect
897. C₅₃	#34487	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16811286	2
#20277879	2
#20277877	2
#20277875	2
#20277803	2
#20277801	2
#20277770	2
#20277739	2
#20277737	2
#20277685	2
#20277683	2
#20277669	2
#20277661	2
#20277549	2
#20277547	2
#20277473	2
#20277469	2
#20277467	2
#20277465	2
#20277460	2
#20277458	2
#20277394	2
#20277392	2
#20277357	2
#20277356	2
#20277300	2
#20277298	2
#20277286	2
#20277188	2
#20277175	2
C₅₃×#2378	2
#34487	53