Subgroups — #28264724

Order 13568.

1818 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288514	C₂	1	2	yes	maximal, complemented
2	#20287673	C₂	1	2	yes	maximal, complemented
3	#20287669	C₂	1	2	yes	maximal, complemented
4	#20287617	C₂	1	2	yes	maximal, complemented
5	#20287609	C₂	1	2	yes	maximal, complemented
6	#20287583	C₂	1	1	yes	maximal, characteristic, complemented
7	#20287582	C₂	1	1	yes	maximal, characteristic, complemented
8	#20287582	C₂	1	1	yes	maximal, characteristic, complemented
9	#20287579	C₂	1	1	yes	maximal, characteristic, complemented
10	#20287579	C₂	1	1	yes	maximal, characteristic, complemented
11	D₈×Dic₁₀₆	C₂	1	1	yes	maximal, characteristic, complemented
12	#20287567	C₂	1	1	yes	maximal, characteristic, complemented
13	#20285252	C₂	1	1	yes	maximal, characteristic, complemented
14	#20285248	C₂	1	1	yes	maximal, characteristic, complemented
15	#20285228	C₂	1	1	yes	maximal, characteristic, complemented
16	#20284545	C₂	1	2	yes	maximal, complemented
17	#20284541	C₂	1	2	yes	maximal, complemented
18	#20284510	C₂	1	2	yes	maximal, complemented
19	#20283644	C₂	1	1	yes	maximal, characteristic, complemented
20	#20283562	C₂	1	1	yes	maximal, characteristic
21	#20283562	C₂	1	1	yes	maximal, characteristic
22	C₄×D₈×D₅₃	C₂	1	1	yes	maximal, characteristic
23	C₅₃×#3380	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×D₈×D₅₃	C₂²	1	1	yes	characteristic
25	#16811333	C₂²	1	2	yes	complemented
26	#16811332	C₂²	1	2	yes	complemented
27	#16811332	C₂²	1	2	yes	complemented
28	#16811329	C₂²	1	2	yes	complemented
29	#16811329	C₂²	1	2	yes	complemented
30	#16811328	—	2	2	no	—
31	#16811327	—	2	2	no	—
32	#16811327	—	2	2	no	—
33	D₄×Dic₁₀₆	C₂²	1	2	yes	complemented
34	#16811288	C₂²	1	2	yes	complemented
35	#16811286	—	2	2	no	—
36	#16811253	C₂²	1	2	yes	—
37	#16811250	C₂²	1	2	yes	—
38	#16811248	—	2	2	no	—
39	#16811248	—	2	2	no	—
40	#16811179	C₂²	1	2	yes	—
41	#16811177	C₂²	1	1	yes	characteristic
42	C₂×#13133195	—	2	2	no	—
43	C₂²⋊Q₈×D₅₃	—	2	2	no	—
44	#16811095	C₂²	1	2	yes	—
45	#16811095	C₂²	1	2	yes	—
46	C₄×D₄×D₅₃	C₂²	1	2	yes	—
47	#16811033	C₂²	1	2	yes	complemented
48	#16811031	C₂²	1	2	yes	complemented
49	#16811030	C₂²	1	2	yes	complemented
50	#16811029	C₂²	1	2	yes	complemented
51	#16811028	C₂²	1	1	yes	characteristic, complemented
52	#16811027	C₂²	1	1	yes	characteristic, complemented
53	#16811027	C₂²	1	1	yes	characteristic, complemented
54	#16811027	C₂²	1	1	yes	characteristic, complemented
55	#16811027	C₂²	1	1	yes	characteristic, complemented
56	#16811025	C₂²	1	1	yes	characteristic, complemented
57	#16811025	C₂²	1	1	yes	characteristic, complemented
58	#16811024	C₂²	1	1	yes	characteristic, complemented
59	#16811024	C₂²	1	1	yes	characteristic, complemented
60	#16811022	C₂²	1	2	yes	complemented
61	#16811020	C₂²	1	2	yes	complemented
62	#16810925	C₂²	1	2	yes	complemented
63	#16810925	C₂²	1	2	yes	complemented
64	#16810924	C₂²	1	2	yes	complemented
65	#16810924	C₂²	1	2	yes	complemented
66	#16810923	C₂²	1	2	yes	complemented
67	#16810923	C₂²	1	2	yes	complemented
68	#16810922	C₂²	1	2	yes	complemented
69	#16810922	C₂²	1	2	yes	complemented
70	#16810920	C₂²	1	2	yes	complemented
71	#16810920	C₂²	1	2	yes	complemented
72	#16810914	C₂²	1	2	yes	complemented
73	#16810912	C₂²	1	2	yes	complemented
74	#16810912	C₂²	1	2	yes	complemented
75	#16810911	C₂²	1	2	yes	complemented
76	#16810911	C₂²	1	2	yes	complemented
77	#16810903	C₂²	1	2	yes	complemented
78	#16810902	C₂²	1	2	yes	complemented
79	#16810902	C₂²	1	2	yes	complemented
80	#16810901	C₂²	1	2	yes	complemented
81	#16810901	C₂²	1	2	yes	complemented
82	#16810900	C₂²	1	2	yes	complemented
83	#16810754	C₂²	1	1	yes	characteristic, complemented
84	#16810752	C₂²	1	1	yes	characteristic, complemented
85	#16810752	C₂²	1	1	yes	characteristic, complemented
86	#16810750	C₂²	1	1	yes	characteristic, complemented
87	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
88	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
89	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
90	#16810733	C₂²	1	2	yes	—
91	#16810733	C₂²	1	2	yes	—
92	#16810732	C₂²	1	2	yes	—
93	#16810732	C₂²	1	2	yes	—
94	C₄×D₄₂₄	C₂²	1	1	yes	characteristic
95	C₄×D₄₂₄	C₂²	1	1	yes	characteristic
96	C₄×D₄₂₄	C₂²	1	1	yes	characteristic
97	D₈×Dic₅₃	C₂²	1	1	yes	characteristic
98	D₈×Dic₅₃	C₂²	1	1	yes	characteristic
99	D₈×Dic₅₃	C₂²	1	1	yes	characteristic
100	#16810705	C₂²	1	1	yes	characteristic
101	#16810705	C₂²	1	1	yes	characteristic
102	#16810705	C₂²	1	1	yes	characteristic
103	C₄×#11719922	C₂²	1	2	yes	—
104	#16810703	C₂²	1	2	yes	—
105	#16810664	C₂²	1	2	yes	—
106	#16810662	C₂²	1	2	yes	—
107	#16810660	C₂²	1	1	yes	characteristic
108	#16810660	C₂²	1	1	yes	characteristic
109	#16810658	C₂²	1	2	yes	—
110	#107×D₅₃	C₂²	1	1	yes	characteristic
111	#16810648	C₂²	1	1	yes	characteristic
112	#16810648	C₂²	1	1	yes	characteristic
113	#16810645	C₂²	1	1	yes	characteristic
114	#16810626	C₂²	1	2	yes	—
115	#16810626	C₂²	1	2	yes	—
116	#102×D₅₃	C₂²	1	2	yes	—
117	#16810577	C₂²	1	1	yes	characteristic
118	#16810577	C₂²	1	1	yes	characteristic
119	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
120	C₅₃×#554	C₂²	1	2	yes	complemented
121	C₅₃×#500	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#499	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#499	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#478	C₂²	1	2	yes	complemented
125	C₅₃×#478	C₂²	1	2	yes	complemented
126	C₅₃×#476	C₂²	1	2	yes	complemented
127	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
128	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
129	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
130	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
131	C₂²×Dic₁₀₆	—	2	2	no	—
132	C₂×Q₈×D₅₃	—	2	2	no	—
133	C₂×D₄×D₅₃	C₂³	1	2	yes	—
134	C₂²×C₄×D₅₃	—	2	2	no	—
135	C₂×D₄₂₄	C₂³	1	1	yes	characteristic
136	C₂×#11719922	C₂³	1	2	yes	—
137	D₈×D₅₃	Q₈	1	8	yes	complemented
138	C₂×#11719912	C₂³	1	1	yes	characteristic
139	C₂×#11719912	C₂³	1	1	yes	characteristic
140	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
141	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
142	#13133217	C₂³	1	2	yes	—
143	#13133216	—	2	2	no	—
144	#13133216	D₄	1	1	yes	characteristic
145	#13133216	C₂³	1	2	yes	—
146	#13133216	C₂³	1	2	yes	—
147	#13133216	C₂³	1	2	yes	—
148	#13133216	C₂³	1	2	yes	—
149	#13133215	—	2	2	no	—
150	#13133215	D₄	1	1	yes	characteristic
151	#13133209	C₂³	1	2	yes	—
152	#13133209	C₂³	1	2	yes	—
153	#13133208	C₂³	1	2	yes	—
154	#13133208	C₂³	1	2	yes	—
155	#13133207	—	2	2	no	—
156	#13133207	—	2	2	no	—
157	#13133207	D₄	1	1	yes	characteristic
158	#13133207	D₄	1	1	yes	characteristic
159	#13133197	—	2	2	no	—
160	#13133197	—	2	2	no	—
161	#13133197	—	2	2	no	—
162	#13133197	D₄	1	1	yes	characteristic
163	#13133196	—	2	2	no	—
164	#13133196	—	2	2	no	—
165	#13133196	—	2	2	no	—
166	#13133195	—	2	2	no	—
167	#13133195	—	2	2	no	—
168	#13133195	—	2	2	no	—
169	#13133195	—	2	2	no	—
170	#13133195	—	2	2	no	—
171	#13133195	—	2	2	no	—
172	#13133195	—	2	2	no	—
173	#13133195	—	2	2	no	—
174	#13133195	—	2	2	no	—
175	#13133195	—	2	2	no	—
176	#13133195	—	2	2	no	—
177	#13133195	—	2	2	no	—
178	#13133195	D₄	1	1	yes	characteristic
179	#13133195	D₄	1	1	yes	characteristic
180	#13133194	—	2	2	no	—
181	#13133194	—	2	2	no	—
182	#13133194	—	2	2	no	—
183	#13133194	—	2	2	no	—
184	#13133194	—	2	2	no	—
185	#13133194	—	2	2	no	—
186	#13133193	—	2	2	no	—
187	#13133193	—	2	2	no	—
188	#13133193	—	2	2	no	—
189	#13133193	D₄	1	1	yes	characteristic
190	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
191	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
192	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
193	#13133182	—	2	2	no	—
194	#13133182	—	2	2	no	—
195	C₄×D₂₁₂	C₂³	1	2	yes	—
196	C₄×D₂₁₂	C₂³	1	2	yes	—
197	C₄×D₂₁₂	C₂³	1	2	yes	—
198	D₄×Dic₅₃	C₂³	1	2	yes	—
199	D₄×Dic₅₃	C₂³	1	2	yes	—
200	D₄×Dic₅₃	C₂³	1	2	yes	—
201	#13133179	C₂³	1	2	yes	—
202	#13133179	C₂³	1	2	yes	—
203	#13133179	C₂³	1	2	yes	—
204	C₄×C₂²⋊D₅₃	—	2	2	no	—
205	C₄×C₂²⋊D₅₃	—	2	2	no	—
206	C₄×C₂²⋊D₅₃	—	2	2	no	—
207	#13133177	—	2	2	no	—
208	#13133177	—	2	2	no	—
209	#13133177	—	2	2	no	—
210	#13133175	C₂³	1	2	yes	—
211	#13133175	C₂³	1	2	yes	—
212	#13133174	C₂³	1	1	yes	characteristic
213	#13133174	C₂³	1	1	yes	characteristic
214	C₂×#11719919	—	2	2	no	—
215	C₂×#11719919	—	2	2	no	—
216	C₄⋊C₄×D₅₃	—	2	2	no	—
217	C₄⋊C₄×D₅₃	—	2	2	no	—
218	C₄⋊C₄×D₅₃	—	2	2	no	—
219	C₄⋊C₄×D₅₃	C₂³	1	2	yes	—
220	C₂×#11719921	—	2	2	no	—
221	C₂×#11719921	—	2	2	no	—
222	C₂²⋊C₄×D₅₃	—	2	2	no	—
223	C₂²⋊C₄×D₅₃	—	2	2	no	—
224	C₂²⋊C₄×D₅₃	—	2	2	no	—
225	C₄²×D₅₃	C₂³	1	1	yes	characteristic
226	#13133151	C₂³	1	1	yes	characteristic
227	#13133151	C₂³	1	1	yes	characteristic
228	#13133151	C₂³	1	1	yes	characteristic
229	#13133151	C₂³	1	2	yes	—
230	#13133150	C₂³	1	2	yes	—
231	#13133150	C₂³	1	2	yes	—
232	#13133150	C₂³	1	2	yes	—
233	#13133150	C₂³	1	2	yes	—
234	#13133150	C₂³	1	2	yes	—
235	#13133149	C₂³	1	2	yes	—
236	#13133149	C₂³	1	2	yes	—
237	#13133148	C₂³	1	2	yes	—
238	#13133148	C₂³	1	2	yes	—
239	#13133148	C₂³	1	2	yes	—
240	#13133148	C₂³	1	2	yes	—
241	C₄⋊#88322	C₂³	1	1	yes	characteristic
242	C₄⋊#88322	C₂³	1	1	yes	characteristic
243	C₄⋊#88322	C₂³	1	1	yes	characteristic
244	#13133146	C₂³	1	1	yes	characteristic
245	#13133146	C₂³	1	1	yes	characteristic
246	#13133146	C₂³	1	1	yes	characteristic
247	#13133146	C₂³	1	1	yes	characteristic
248	#13133146	C₂³	1	1	yes	characteristic
249	#13133146	C₂³	1	1	yes	characteristic
250	#13133139	C₂³	1	2	yes	—
251	#13133139	C₂³	1	2	yes	—
252	#13133139	C₂³	1	2	yes	—
253	#13133138	C₂³	1	2	yes	—
254	#13133138	C₂³	1	2	yes	—
255	#13133138	C₂³	1	2	yes	—
256	#13133137	C₂³	1	2	yes	—
257	#13133137	C₂³	1	2	yes	—
258	#13133137	C₂³	1	2	yes	—
259	#13133128	C₂³	1	1	yes	characteristic
260	#13133128	C₂³	1	1	yes	characteristic
261	#13133127	C₂³	1	1	yes	characteristic
262	#13133127	C₂³	1	1	yes	characteristic
263	C₄×#88322	C₂³	1	1	yes	characteristic
264	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
265	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
266	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
267	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
268	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
269	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
270	#125×C₅₃	C₂³	1	2	yes	—
271	#125×C₅₃	C₂³	1	2	yes	—
272	C₂²⋊Q₈×C₅₃	—	2	2	no	—
273	C₂²⋊Q₈×C₅₃	—	2	2	no	—
274	C₂²⋊Q₈×C₅₃	—	2	2	no	—
275	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
276	C₄×D₄×C₅₃	C₂³	1	2	yes	—
277	C₄×D₄×C₅₃	C₂³	1	2	yes	—
278	C₄×D₄×C₅₃	C₂³	1	2	yes	—
279	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
280	#107×C₅₃	C₂³	1	1	yes	characteristic
281	#107×C₅₃	C₂³	1	1	yes	characteristic
282	#107×C₅₃	C₂³	1	1	yes	characteristic
283	#107×C₅₃	C₂³	1	2	yes	—
284	#106×C₅₃	C₂³	1	2	yes	—
285	#106×C₅₃	C₂³	1	2	yes	—
286	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
287	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
288	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
289	#102×C₅₃	C₂³	1	2	yes	—
290	#102×C₅₃	C₂³	1	2	yes	—
291	#102×C₅₃	C₂³	1	2	yes	—
292	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
293	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
294	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
295	C₂³×D₅₃	—	2	2	no	—
296	C₂×Q₈×C₅₃	—	2	2	no	—
297	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
298	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₅₃	—	2	2	no	—
300	C₂²×C₄×C₅₃	—	2	2	no	—
301	C₂²×C₄×C₅₃	—	2	2	no	—
302	C₂×C₂²⋊D₅₃	—	2	2	no	—
303	C₂²×Dic₅₃	—	2	2	no	—
304	C₂²×Dic₅₃	—	2	2	no	—
305	C₂²×Dic₅₃	—	2	2	no	—
306	Q₈×D₅₃	—	8	4	no	—
307	D₄×D₅₃	—	2	4	no	—
308	D₄×D₅₃	C₂×Q₈	1	8	yes	complemented
309	C₂×D₂₁₂	C₂⁴	1	2	yes	—
310	C₂×C₄×D₅₃	—	2	2	no	—
311	C₂×C₄×D₅₃	—	2	2	no	—
312	C₂×C₄×D₅₃	—	2	2	no	—
313	C₂×C₄×D₅₃	—	2	2	no	—
314	C₂×C₄×D₅₃	—	2	2	no	—
315	C₂×C₄×D₅₃	—	2	2	no	—
316	C₂×C₄×D₅₃	—	2	2	no	—
317	C₂×C₄×D₅₃	—	8	4	no	—
318	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
319	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
320	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
321	C₂×Dic₁₀₆	—	2	2	no	—
322	C₂×Dic₁₀₆	—	2	2	no	—
323	C₂×Dic₁₀₆	—	2	2	no	—
324	C₂×Dic₁₀₆	—	2	2	no	—
325	C₂×Dic₁₀₆	—	2	2	no	—
326	C₂×Dic₁₀₆	—	8	4	no	—
327	C₂×Dic₁₀₆	C₂×D₄	1	1	yes	characteristic
328	C₂×Dic₁₀₆	C₂×D₄	1	1	yes	characteristic
329	C₂×Dic₁₀₆	C₂×D₄	1	1	yes	characteristic
330	D₈×C₅₃	C₂×Q₈	1	4	yes	complemented
331	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
332	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
333	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
334	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
335	C₄⋊C₄×C₅₃	—	2	2	no	—
336	C₄⋊C₄×C₅₃	—	2	2	no	—
337	C₄⋊C₄×C₅₃	—	2	2	no	—
338	C₄⋊C₄×C₅₃	—	2	2	no	—
339	C₄⋊C₄×C₅₃	—	2	2	no	—
340	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
341	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
342	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
343	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
344	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
345	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
346	C₂²⋊C₄×C₅₃	—	2	2	no	—
347	C₂²⋊C₄×C₅₃	—	2	2	no	—
348	C₂²⋊C₄×C₅₃	—	2	2	no	—
349	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
350	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
351	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
352	C₂²⋊Dic₅₃	—	2	2	no	—
353	C₂²⋊Dic₅₃	—	2	2	no	—
354	C₂²⋊Dic₅₃	—	2	2	no	—
355	#11719922	C₂×Q₈	1	8	yes	complemented
356	#11719921	—	2	2	no	—
357	#11719921	—	2	2	no	—
358	#11719921	—	2	2	no	—
359	#11719921	—	2	2	no	—
360	#11719921	—	2	2	no	—
361	#11719921	—	2	2	no	—
362	#11719921	—	2	2	no	—
363	#11719921	—	2	2	no	—
364	#11719921	C₂×D₄	1	1	yes	characteristic
365	#11719921	C₂×D₄	1	1	yes	characteristic
366	#11719921	C₂×D₄	1	1	yes	characteristic
367	#11719921	C₂×D₄	1	1	yes	characteristic
368	C₄⋊Dic₅₃	—	2	2	no	—
369	C₄⋊Dic₅₃	—	2	2	no	—
370	C₄⋊Dic₅₃	—	2	2	no	—
371	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
372	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
373	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
374	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
375	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
376	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
377	#11719919	—	2	2	no	—
378	#11719919	—	2	2	no	—
379	#11719919	—	2	2	no	—
380	#11719919	—	2	2	no	—
381	#11719919	—	2	2	no	—
382	#11719919	—	2	2	no	—
383	#11719919	—	2	2	no	—
384	#11719919	—	2	2	no	—
385	#11719919	—	2	2	no	—
386	#11719919	—	2	2	no	—
387	#11719919	—	2	2	no	—
388	#11719919	C₂×D₄	1	1	yes	characteristic
389	#11719919	C₂×D₄	1	1	yes	characteristic
390	#11719919	C₂×D₄	1	1	yes	characteristic
391	#11719919	C₂×D₄	1	1	yes	characteristic
392	#11719919	C₂×D₄	1	1	yes	characteristic
393	#11719919	C₂×D₄	1	1	yes	characteristic
394	#11719919	C₂×D₄	1	1	yes	characteristic
395	#11719919	C₂×D₄	1	1	yes	characteristic
396	#11719919	C₂×D₄	1	1	yes	characteristic
397	#11719919	C₂×D₄	1	1	yes	characteristic
398	C₄×Dic₅₃	—	2	2	no	—
399	C₄×Dic₅₃	—	2	2	no	—
400	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
401	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
402	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
403	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
404	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
405	C₂×#88322	C₂⁴	1	1	yes	characteristic
406	C₂×#88322	C₂⁴	1	1	yes	characteristic
407	C₂×#88322	C₂⁴	1	1	yes	characteristic
408	C₂×#88322	C₂⁴	1	1	yes	characteristic
409	D₄₂₄	C₂×Q₈	1	4	yes	complemented
410	#11719912	—	2	2	no	—
411	#11719912	—	2	2	no	—
412	C₈×D₅₃	—	2	2	no	—
413	C₈×D₅₃	C₂×Q₈	1	4	yes	complemented
414	C₂³×C₅₃	—	2	2	no	—
415	C₂²×D₅₃	—	2	2	no	—
416	C₂²×D₅₃	—	2	8	no	—
417	C₂²×D₅₃	—	8	2	no	—
418	C₂²×D₅₃	—	8	2	no	—
419	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
420	Q₈×C₅₃	—	4	1	no	—
421	Q₈×C₅₃	—	8	2	no	—
422	D₄×C₅₃	—	2	2	no	—
423	D₄×C₅₃	C₂²×Q₈	1	4	yes	—
424	C₂×C₄×C₅₃	—	2	2	no	—
425	C₂×C₄×C₅₃	—	2	2	no	—
426	C₂×C₄×C₅₃	—	2	2	no	—
427	C₂×C₄×C₅₃	—	8	2	no	—
428	C₂×C₄×C₅₃	—	8	2	no	—
429	C₂×C₄×C₅₃	—	8	2	no	—
430	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
431	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
432	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
434	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
435	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
436	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
437	C₂²⋊D₅₃	—	2	8	no	—
438	C₂×Dic₅₃	—	2	2	no	—
439	C₂×Dic₅₃	—	2	2	no	—
440	C₂×Dic₅₃	—	2	2	no	—
441	C₂×Dic₅₃	—	4	4	no	—
442	C₂×Dic₅₃	—	8	2	no	—
443	C₂×Dic₅₃	—	8	2	no	—
444	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
445	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
446	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
447	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
448	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
449	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
450	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
451	D₂₁₂	—	2	2	no	—
452	D₂₁₂	C₂²×Q₈	1	4	yes	—
453	C₄×D₅₃	—	2	2	no	—
454	C₄×D₅₃	—	4	1	no	—
455	C₄×D₅₃	—	4	4	no	—
456	C₄×D₅₃	—	8	2	no	—
457	C₄×D₅₃	—	8	2	no	—
458	C₄×D₅₃	—	8	2	no	—
459	C₄×D₅₃	—	8	2	no	—
460	C₄×D₅₃	—	8	2	no	—
461	C₄×D₅₃	—	8	2	no	—
462	C₄×D₅₃	C₂²×Q₈	1	2	yes	—
463	C₄×D₅₃	2₋¹⁺⁴	1	2	yes	—
464	Dic₁₀₆	—	2	2	no	—
465	Dic₁₀₆	—	2	2	no	—
466	Dic₁₀₆	—	4	1	no	—
467	Dic₁₀₆	—	4	4	no	—
468	Dic₁₀₆	—	8	2	no	—
469	Dic₁₀₆	—	8	2	no	—
470	Dic₁₀₆	—	8	2	no	—
471	Dic₁₀₆	—	8	2	no	—
472	C₈×C₅₃	—	2	1	no	—
473	C₈×C₅₃	—	2	1	no	—
474	C₈×C₅₃	—	2	1	no	—
475	C₈×C₅₃	C₂²×Q₈	1	2	yes	—
476	#88322	—	2	1	no	—
477	#88322	—	2	1	no	—
478	#88322	—	2	1	no	—
479	#88322	C₂²×Q₈	1	2	yes	—
480	#61370	—	53	1	no	maximal, Sylow
481	C₂²×C₅₃	—	2	4	no	—
482	C₂²×C₅₃	—	4	2	no	—
483	C₂²×C₅₃	—	4	2	no	—
484	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
485	C₂×D₅₃	—	2	1	no	—
486	C₂×D₅₃	—	2	1	no	—
487	C₂×D₅₃	—	2	4	no	—
488	C₂×D₅₃	—	4	2	no	—
489	C₂×D₅₃	—	4	2	no	—
490	C₂×D₅₃	—	8	8	no	—
491	C₂×D₅₃	D₄×Q₈	1	2	yes	—
492	C₄×C₅₃	—	2	1	no	—
493	C₄×C₅₃	—	2	1	no	—
494	C₄×C₅₃	—	2	1	no	—
495	C₄×C₅₃	—	2	1	no	—
496	C₄×C₅₃	—	2	1	no	—
497	C₄×C₅₃	—	2	1	no	—
498	C₄×C₅₃	—	4	2	no	—
499	C₄×C₅₃	—	4	2	no	—
500	C₄×C₅₃	—	4	2	no	—
501	C₄×C₅₃	C₂³×Q₈	1	1	yes	characteristic
502	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
503	Dic₅₃	—	2	1	no	—
504	Dic₅₃	—	2	1	no	—
505	Dic₅₃	—	2	1	no	—
506	Dic₅₃	—	2	1	no	—
507	Dic₅₃	—	2	1	no	—
508	Dic₅₃	—	4	2	no	—
509	Dic₅₃	—	4	2	no	—
510	Dic₅₃	—	4	2	no	—
511	Dic₅₃	D₄×Q₈	1	2	yes	—
512	Dic₅₃	#576	1	2	yes	—
513	#3501	—	53	2	no	—
514	#3389	—	53	2	no	—
515	#3389	—	53	2	no	—
516	#3384	—	53	2	no	—
517	#3384	—	53	2	no	—
518	#3380	—	53	1	no	—
519	#3380	—	53	1	no	—
520	#3380	—	53	1	no	—
521	#3380	—	53	1	no	—
522	#3380	—	53	1	no	—
523	#3380	D₅₃	1	1	yes	characteristic, complemented
524	Q₈×D₈	—	53	1	no	—
525	Q₈×D₈	—	53	1	no	—
526	#3164	—	53	1	no	—
527	#3164	—	53	1	no	—
528	#3160	—	53	1	no	—
529	#3081	—	53	2	no	—
530	#3081	—	53	2	no	—
531	#3077	—	53	2	no	—
532	#2960	—	53	1	no	—
533	#2948	—	53	1	no	—
534	#2948	—	53	1	no	—
535	C₂×C₄×D₈	—	53	1	no	—
536	C₂×C₅₃	—	4	4	no	—
537	C₂×C₅₃	C₂×D₄×Q₈	1	1	yes	characteristic
538	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
539	C₂×C₅₃	#3584	1	1	yes	characteristic
540	D₅₃	—	2	2	no	—
541	D₅₃	—	4	4	no	—
542	C₂²×D₈	—	53	1	no	—
543	#554	—	53	2	no	—
544	#554	—	53	2	no	—
545	#554	—	53	2	no	—
546	#554	—	53	2	no	—
547	#554	—	53	2	no	—
548	#554	—	106	2	no	—
549	#554	—	106	2	no	—
550	#554	—	106	2	no	—
551	#554	C₂×D₅₃	1	2	yes	complemented
552	D₄×Q₈	—	53	2	no	—
553	D₄×Q₈	—	53	2	no	—
554	D₄×Q₈	—	106	2	no	—
555	#544	—	53	2	no	—
556	#544	—	53	2	no	—
557	#543	—	106	2	no	—
558	#543	—	106	2	no	—
559	#533	—	53	1	no	—
560	#533	—	53	2	no	—
561	C₂×C₂²⋊Q₈	—	106	2	no	—
562	C₂×C₂²⋊Q₈	—	106	2	no	—
563	#518	—	53	2	no	—
564	#518	—	53	2	no	—
565	C₂×C₄×D₄	—	53	2	no	—
566	#501	—	53	2	no	—
567	#501	—	53	2	no	—
568	#501	—	53	2	no	—
569	#501	—	53	2	no	—
570	#500	—	53	1	no	—
571	#500	—	53	1	no	—
572	#500	—	53	1	no	—
573	#500	—	53	1	no	—
574	#500	—	53	1	no	—
575	#500	C₂×D₅₃	1	1	yes	characteristic, complemented
576	#499	—	53	2	no	—
577	#499	—	53	1	no	—
578	#499	—	53	1	no	—
579	#499	—	53	1	no	—
580	#499	—	53	1	no	—
581	#499	C₂×D₅₃	1	1	yes	characteristic, complemented
582	#499	C₂×D₅₃	1	1	yes	characteristic, complemented
583	#498	—	53	2	no	—
584	#478	—	53	2	no	—
585	#478	—	53	2	no	—
586	#478	—	53	2	no	—
587	#478	—	53	2	no	—
588	#478	—	53	2	no	—
589	#478	—	53	2	no	—
590	#478	—	53	2	no	—
591	#478	—	53	2	no	—
592	#478	—	53	2	no	—
593	#478	—	53	2	no	—
594	#478	C₂×D₅₃	1	2	yes	complemented
595	#478	C₂×D₅₃	1	2	yes	complemented
596	#476	—	53	2	no	—
597	#476	—	53	2	no	—
598	#476	—	53	2	no	—
599	#476	—	53	2	no	—
600	#476	—	53	2	no	—
601	#476	C₂×D₅₃	1	2	yes	complemented
602	#474	—	53	2	no	—
603	#474	—	53	2	no	—
604	#474	—	53	2	no	—
605	#474	—	53	2	no	—
606	#474	—	53	2	no	—
607	#474	—	53	2	no	—
608	#446	—	53	1	no	—
609	#446	—	53	1	no	—
610	#446	—	53	1	no	—
611	#446	—	53	1	no	—
612	C₈×Q₈	—	53	1	no	—
613	C₈×Q₈	—	53	1	no	—
614	C₈×Q₈	—	53	1	no	—
615	C₈×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
616	#442	—	53	2	no	—
617	#442	—	53	2	no	—
618	#442	—	53	2	no	—
619	#442	—	53	2	no	—
620	C₄×D₈	—	53	1	no	—
621	C₄×D₈	—	53	1	no	—
622	C₄×D₈	—	53	1	no	—
623	C₄×D₈	—	53	2	no	—
624	C₄×D₈	—	53	1	no	—
625	C₄×D₈	—	53	1	no	—
626	C₄×D₈	—	53	1	no	—
627	C₄×D₈	—	53	2	no	—
628	C₄×D₈	—	53	1	no	—
629	C₄×D₈	—	53	1	no	—
630	C₄×D₈	—	53	1	no	—
631	C₄×D₈	C₂×D₅₃	1	1	yes	characteristic
632	C₄×D₈	C₂×D₅₃	1	1	yes	characteristic
633	C₄×D₈	C₂×D₅₃	1	1	yes	characteristic
634	#428	—	53	2	no	—
635	#428	—	53	2	no	—
636	#427	—	53	1	no	—
637	#427	—	53	1	no	—
638	#427	—	53	2	no	—
639	C₂×#107	—	53	1	no	—
640	#424	—	53	1	no	—
641	#424	—	53	1	no	—
642	#423	—	53	1	no	—
643	#418	—	53	2	no	—
644	#418	—	53	2	no	—
645	C₂×#102	—	53	2	no	—
646	#405	—	53	1	no	—
647	#405	—	53	1	no	—
648	C₂×C₄×C₈	—	53	1	no	—
649	C₅₃	#61370	1	1	yes	characteristic, complemented, Sylow
650	C₂²×Q₈	—	106	2	no	—
651	C₂²×Q₈	—	106	2	no	—
652	C₂²×D₄	—	53	2	no	—
653	C₂³×C₄	—	106	2	no	—
654	C₂×D₈	—	53	2	no	—
655	C₂×D₈	—	53	8	no	—
656	C₂×D₈	—	53	1	no	—
657	C₂×D₈	C₂²×D₅₃	1	1	yes	characteristic
658	C₂×M₁₆	—	53	1	no	—
659	C₂×M₁₆	—	53	1	no	—
660	C₂²×C₈	—	53	1	no	—
661	C₂²×C₈	—	53	1	no	—
662	C₄⋊Q₈	—	53	1	no	—
663	C₄⋊Q₈	—	53	1	no	—
664	C₄⋊Q₈	—	53	2	no	—
665	C₄⋊Q₈	—	53	2	no	—
666	C₄⋊Q₈	—	53	2	no	—
667	C₄⋊Q₈	—	53	2	no	—
668	C₄⋊Q₈	—	53	2	no	—
669	C₄⋊Q₈	—	106	2	no	—
670	C₄⋊Q₈	—	106	2	no	—
671	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	—
672	#125	—	53	1	no	—
673	#125	—	53	1	no	—
674	#125	—	53	2	no	—
675	#125	—	53	2	no	—
676	#125	—	53	2	no	—
677	#125	—	53	2	no	—
678	#125	—	106	2	no	—
679	#125	—	106	2	no	—
680	#125	C₂²×D₅₃	1	2	yes	—
681	#125	C₂²×D₅₃	1	2	yes	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	—	2	2	no	—
685	C₂²⋊Q₈	—	53	1	no	—
686	C₂²⋊Q₈	—	53	1	no	—
687	C₂²⋊Q₈	—	53	1	no	—
688	C₂²⋊Q₈	—	53	1	no	—
689	C₂²⋊Q₈	—	106	2	no	—
690	C₂²⋊Q₈	—	106	2	no	—
691	C₂²⋊Q₈	—	106	2	no	—
692	C₂²⋊Q₈	—	106	2	no	—
693	C₂²⋊Q₈	—	106	2	no	—
694	C₂²⋊Q₈	—	106	2	no	—
695	C₂²⋊Q₈	—	106	2	no	—
696	C₂²⋊Q₈	—	106	2	no	—
697	C₂²⋊Q₈	—	106	2	no	—
698	C₂²⋊Q₈	—	106	2	no	—
699	C₂²⋊Q₈	—	106	2	no	—
700	C₂²⋊Q₈	—	106	2	no	—
701	C₂²⋊Q₈	—	106	2	no	—
702	C₂²⋊Q₈	—	106	2	no	—
703	C₂²⋊Q₈	—	106	2	no	—
704	C₂²⋊Q₈	—	106	2	no	—
705	C₂²⋊Q₈	—	106	2	no	—
706	C₂²⋊Q₈	—	106	2	no	—
707	C₂²⋊Q₈	—	106	2	no	—
708	C₂²⋊Q₈	—	106	2	no	—
709	C₂²⋊Q₈	—	106	2	no	—
710	C₂²⋊Q₈	—	106	2	no	—
711	C₂²⋊Q₈	—	106	2	no	—
712	C₂²⋊Q₈	—	106	2	no	—
713	C₂²⋊Q₈	—	106	2	no	—
714	C₂²⋊Q₈	—	106	2	no	—
715	C₂²⋊Q₈	—	106	2	no	—
716	C₄×Q₈	—	53	1	no	—
717	C₄×Q₈	—	53	1	no	—
718	C₄×Q₈	—	53	1	no	—
719	C₄×Q₈	—	106	2	no	—
720	C₄×Q₈	—	106	2	no	—
721	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
722	C₄×D₄	—	53	2	no	—
723	C₄×D₄	—	53	2	no	—
724	C₄×D₄	—	53	2	no	—
725	C₄×D₄	—	53	2	no	—
726	C₄×D₄	—	53	2	no	—
727	C₄×D₄	—	53	2	no	—
728	C₄×D₄	—	53	2	no	—
729	C₄×D₄	—	53	2	no	—
730	C₄×D₄	—	53	2	no	—
731	C₄×D₄	—	106	2	no	—
732	C₄×D₄	—	106	2	no	—
733	C₄×D₄	—	106	2	no	—
734	C₄×D₄	—	106	2	no	—
735	C₄×D₄	—	106	2	no	—
736	C₄×D₄	—	106	2	no	—
737	C₄×D₄	C₂²×D₅₃	1	2	yes	—
738	C₄×D₄	C₂²×D₅₃	1	2	yes	—
739	C₄×D₄	C₂²×D₅₃	1	2	yes	—
740	#117	—	53	1	no	—
741	#117	—	53	1	no	—
742	#117	—	53	2	no	—
743	#117	—	53	2	no	—
744	C₂×C₄⋊C₄	—	2	2	no	—
745	C₂×C₄⋊C₄	—	53	2	no	—
746	C₂×C₄⋊C₄	—	106	2	no	—
747	C₂×C₄⋊C₄	—	106	2	no	—
748	C₂×C₄⋊C₄	—	106	2	no	—
749	C₂×C₄⋊C₄	—	106	2	no	—
750	C₂×C₄⋊C₄	—	106	2	no	—
751	C₂×C₂²⋊C₄	—	106	2	no	—
752	C₂×C₂²⋊C₄	—	106	2	no	—
753	C₂×C₂²⋊C₄	—	106	2	no	—
754	C₂×C₂²⋊C₄	—	106	2	no	—
755	C₂×C₂²⋊C₄	—	106	2	no	—
756	C₂×C₄²	—	53	1	no	—
757	#107	—	53	1	no	—
758	#107	—	53	1	no	—
759	#107	—	53	1	no	—
760	#107	—	53	2	no	—
761	#107	—	53	2	no	—
762	#107	—	53	2	no	—
763	#107	—	53	2	no	—
764	#107	—	53	2	no	—
765	#107	—	53	2	no	—
766	#107	C₂²×D₅₃	1	1	yes	characteristic
767	#107	C₂²×D₅₃	1	1	yes	characteristic
768	#107	C₂²×D₅₃	1	1	yes	characteristic
769	#107	C₂²×D₅₃	1	2	yes	—
770	#106	—	53	2	no	—
771	#106	—	53	2	no	—
772	#106	—	53	2	no	—
773	#106	—	53	2	no	—
774	#106	—	53	2	no	—
775	#106	—	53	2	no	—
776	#106	C₂²×D₅₃	1	2	yes	—
777	#106	C₂²×D₅₃	1	2	yes	—
778	C₄⋊C₈	—	53	1	no	—
779	C₄⋊C₈	—	53	1	no	—
780	C₄⋊C₈	—	53	1	no	—
781	C₄⋊C₈	—	53	1	no	—
782	C₄⋊C₈	—	53	1	no	—
783	C₄⋊C₈	—	53	1	no	—
784	C₄⋊C₈	—	53	1	no	—
785	C₄⋊C₈	—	53	1	no	—
786	C₄⋊C₈	—	53	1	no	—
787	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
788	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
789	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
790	#102	—	53	2	no	—
791	#102	—	53	2	no	—
792	#102	—	53	2	no	—
793	#102	—	53	2	no	—
794	#102	—	53	2	no	—
795	#102	—	53	2	no	—
796	#102	—	53	2	no	—
797	#102	—	53	2	no	—
798	#102	—	53	2	no	—
799	#102	C₂²×D₅₃	1	2	yes	—
800	#102	C₂²×D₅₃	1	2	yes	—
801	#102	C₂²×D₅₃	1	2	yes	—
802	#97	—	53	1	no	—
803	#97	—	53	1	no	—
804	#97	—	53	1	no	—
805	#97	—	53	1	no	—
806	C₄×C₈	—	53	1	no	—
807	C₄×C₈	—	53	1	no	—
808	C₄×C₈	—	53	1	no	—
809	C₄×C₈	—	53	1	no	—
810	C₄×C₈	—	53	1	no	—
811	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
812	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
813	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
814	C₂⁴	—	106	2	no	—
815	C₂×Q₈	—	2	2	no	—
816	C₂×Q₈	—	53	1	no	—
817	C₂×Q₈	—	53	1	no	—
818	C₂×Q₈	—	53	1	no	—
819	C₂×Q₈	—	106	2	no	—
820	C₂×Q₈	—	106	2	no	—
821	C₂×Q₈	—	106	2	no	—
822	C₂×Q₈	—	106	2	no	—
823	C₂×Q₈	—	106	2	no	—
824	C₂×Q₈	—	424	4	no	—
825	C₂×Q₈	—	424	4	no	—
826	C₂×Q₈	D₄×D₅₃	1	1	yes	characteristic
827	C₂×D₄	—	53	8	no	—
828	C₂×D₄	—	53	2	no	—
829	C₂×D₄	—	106	4	no	—
830	C₂×D₄	—	106	2	no	—
831	C₂×D₄	C₂³×D₅₃	1	2	yes	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	53	1	no	—
836	C₂²×C₄	—	53	1	no	—
837	C₂²×C₄	—	53	1	no	—
838	C₂²×C₄	—	106	2	no	—
839	C₂²×C₄	—	106	2	no	—
840	C₂²×C₄	—	106	2	no	—
841	C₂²×C₄	—	106	2	no	—
842	C₂²×C₄	—	106	2	no	—
843	C₂²×C₄	—	106	2	no	—
844	C₂²×C₄	—	106	2	no	—
845	C₂²×C₄	—	106	2	no	—
846	C₂²×C₄	—	106	2	no	—
847	C₂²×C₄	—	106	2	no	—
848	C₂²×C₄	—	424	4	no	—
849	D₈	—	53	8	no	—
850	D₈	—	53	4	no	—
851	D₈	Q₈×D₅₃	1	4	yes	complemented
852	M₁₆	—	106	2	no	—
853	M₁₆	—	106	2	no	—
854	C₂×C₈	—	53	1	no	—
855	C₂×C₈	—	53	4	no	—
856	C₂×C₈	—	53	1	no	—
857	C₂×C₈	—	53	1	no	—
858	C₂×C₈	—	53	1	no	—
859	C₂×C₈	—	106	2	no	—
860	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
861	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
862	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
863	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	53	1	no	—
870	C₄⋊C₄	—	53	1	no	—
871	C₄⋊C₄	—	53	1	no	—
872	C₄⋊C₄	—	53	1	no	—
873	C₄⋊C₄	—	53	1	no	—
874	C₄⋊C₄	—	53	1	no	—
875	C₄⋊C₄	—	53	1	no	—
876	C₄⋊C₄	—	53	1	no	—
877	C₄⋊C₄	—	53	1	no	—
878	C₄⋊C₄	—	53	1	no	—
879	C₄⋊C₄	—	53	1	no	—
880	C₄⋊C₄	—	53	1	no	—
881	C₄⋊C₄	—	53	1	no	—
882	C₄⋊C₄	—	53	2	no	—
883	C₄⋊C₄	—	53	2	no	—
884	C₄⋊C₄	—	53	2	no	—
885	C₄⋊C₄	—	106	2	no	—
886	C₄⋊C₄	—	106	2	no	—
887	C₄⋊C₄	—	106	2	no	—
888	C₄⋊C₄	—	106	2	no	—
889	C₄⋊C₄	—	106	2	no	—
890	C₄⋊C₄	—	106	2	no	—
891	C₄⋊C₄	—	106	2	no	—
892	C₄⋊C₄	—	106	2	no	—
893	C₄⋊C₄	—	106	2	no	—
894	C₄⋊C₄	—	106	2	no	—
895	C₄⋊C₄	—	106	2	no	—
896	C₄⋊C₄	—	106	2	no	—
897	C₄⋊C₄	—	106	2	no	—
898	C₄⋊C₄	—	106	2	no	—
899	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
900	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
901	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
902	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
903	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
904	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	53	1	no	—
909	C₂²⋊C₄	—	53	1	no	—
910	C₂²⋊C₄	—	53	1	no	—
911	C₂²⋊C₄	—	53	1	no	—
912	C₂²⋊C₄	—	106	2	no	—
913	C₂²⋊C₄	—	106	2	no	—
914	C₂²⋊C₄	—	106	2	no	—
915	C₂²⋊C₄	—	106	2	no	—
916	C₂²⋊C₄	—	106	2	no	—
917	C₂²⋊C₄	—	106	2	no	—
918	C₂²⋊C₄	—	106	2	no	—
919	C₂²⋊C₄	—	106	2	no	—
920	C₂²⋊C₄	—	106	2	no	—
921	C₂²⋊C₄	—	106	2	no	—
922	C₂²⋊C₄	—	106	2	no	—
923	C₄²	—	53	1	no	—
924	C₄²	—	53	1	no	—
925	C₄²	—	53	1	no	—
926	C₄²	—	53	1	no	—
927	C₄²	—	53	1	no	—
928	C₄²	—	106	2	no	—
929	C₄²	—	106	2	no	—
930	C₄²	C₂³×D₅₃	1	1	yes	characteristic
931	C₄²	C₂³×D₅₃	1	1	yes	characteristic
932	C₄²	C₂³×D₅₃	1	1	yes	characteristic
933	C₂³	—	2	2	no	—
934	C₂³	—	53	1	no	—
935	C₂³	—	106	8	no	—
936	C₂³	—	106	2	no	—
937	C₂³	—	424	2	no	—
938	C₂³	—	424	2	no	—
939	Q₈	—	4	1	no	—
940	Q₈	—	8	2	no	—
941	Q₈	—	106	2	no	—
942	Q₈	—	106	2	no	—
943	Q₈	—	424	2	no	—
944	Q₈	—	424	2	no	—
945	Q₈	—	424	2	no	—
946	Q₈	—	424	2	no	—
947	Q₈	—	212	1	no	—
948	Q₈	—	212	4	no	—
949	D₄	—	2	2	no	—
950	D₄	—	53	4	no	—
951	D₄	—	106	8	no	—
952	D₄	—	106	2	no	—
953	D₄	C₂×Q₈×D₅₃	1	4	yes	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	8	2	no	—
958	C₂×C₄	—	8	2	no	—
959	C₂×C₄	—	8	2	no	—
960	C₂×C₄	—	53	1	no	—
961	C₂×C₄	—	53	1	no	—
962	C₂×C₄	—	53	2	no	—
963	C₂×C₄	—	53	2	no	—
964	C₂×C₄	—	53	1	no	—
965	C₂×C₄	—	53	1	no	—
966	C₂×C₄	—	53	1	no	—
967	C₂×C₄	—	53	1	no	—
968	C₂×C₄	—	53	1	no	—
969	C₂×C₄	—	106	2	no	—
970	C₂×C₄	—	106	2	no	—
971	C₂×C₄	—	106	2	no	—
972	C₂×C₄	—	106	2	no	—
973	C₂×C₄	—	424	2	no	—
974	C₂×C₄	—	424	2	no	—
975	C₂×C₄	—	424	2	no	—
976	C₂×C₄	—	424	2	no	—
977	C₂×C₄	—	424	2	no	—
978	C₂×C₄	—	424	2	no	—
979	C₂×C₄	—	424	2	no	—
980	C₂×C₄	—	424	2	no	—
981	C₂×C₄	—	212	1	no	—
982	C₂×C₄	—	212	4	no	—
983	C₂×C₄	—	212	4	no	—
984	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
985	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
986	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
987	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
988	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
989	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
990	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
991	C₈	—	2	1	no	—
992	C₈	—	2	1	no	—
993	C₈	—	2	1	no	—
994	C₈	—	53	2	no	—
995	C₈	—	106	1	no	—
996	C₈	—	106	1	no	—
997	C₈	—	106	1	no	—
998	C₈	C₂×Q₈×D₅₃	1	2	yes	—
999	C₂²	—	2	4	no	—
1000	C₂²	—	4	2	no	—
1001	C₂²	—	4	2	no	—
1002	C₂²	—	53	2	no	—
1003	C₂²	—	106	1	no	—
1004	C₂²	—	106	1	no	—
1005	C₂²	—	106	4	no	—
1006	C₂²	—	424	8	no	—
1007	C₂²	—	212	2	no	—
1008	C₂²	—	212	2	no	—
1009	C₂²	C₂²×D₄×D₅₃	1	1	yes	characteristic
1010	C₄	—	2	1	no	—
1011	C₄	—	2	1	no	—
1012	C₄	—	2	1	no	—
1013	C₄	—	2	1	no	—
1014	C₄	—	2	1	no	—
1015	C₄	—	2	1	no	—
1016	C₄	—	4	2	no	—
1017	C₄	—	4	2	no	—
1018	C₄	—	4	2	no	—
1019	C₄	—	53	2	no	—
1020	C₄	—	53	2	no	—
1021	C₄	—	106	1	no	—
1022	C₄	—	106	1	no	—
1023	C₄	—	106	1	no	—
1024	C₄	—	106	1	no	—
1025	C₄	—	106	1	no	—
1026	C₄	—	212	2	no	—
1027	C₄	—	212	2	no	—
1028	C₄	—	212	2	no	—
1029	C₄	C₂²×Q₈×D₅₃	1	1	yes	characteristic
1030	C₄	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1031	C₂	—	4	4	no	—
1032	C₂	—	106	2	no	—
1033	C₂	—	212	4	no	—
1034	C₂	D₄×Q₈×D₅₃	1	1	yes	characteristic
1035	C₂	#576×D₅₃	1	1	yes	characteristic
1036	C₂	#20289484	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₅₃
commutator, cosocle	C₂×C₄×C₅₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₅₃
Fitting	C₅₃×#3380	C₂
socle	C₂²×C₅₃	C₂³×D₄
prime radical	C₂×D₈×D₅₃	C₂²
hypercenter	#3380	D₅₃
hypocenter	C₅₃	#61370
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #3380

Complements

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

N	H ≅ G/N	type
1. #20288514	C₂	semidirect
2. #20287673	C₂	semidirect
3. #20287669	C₂	semidirect
4. #20287617	C₂	semidirect
5. #20287609	C₂	semidirect
6. #20287583	C₂	semidirect
7. #20287582	C₂	semidirect
8. #20287582	C₂	semidirect
9. #20287579	C₂	semidirect
10. #20287579	C₂	semidirect
11. D₈×Dic₁₀₆	C₂	semidirect
12. #20287567	C₂	semidirect
13. #20285252	C₂	semidirect
14. #20285248	C₂	semidirect
15. #20285228	C₂	semidirect
16. #20284545	C₂	semidirect
17. #20284541	C₂	semidirect
18. #20284510	C₂	semidirect
19. #20283644	C₂	semidirect
23. C₅₃×#3380	C₂	semidirect
25. #16811333	C₂²	semidirect
26. #16811332	C₂²	semidirect
27. #16811332	C₂²	semidirect
28. #16811329	C₂²	semidirect
29. #16811329	C₂²	semidirect
33. D₄×Dic₁₀₆	C₂²	semidirect
34. #16811288	C₂²	semidirect
47. #16811033	C₂²	semidirect
48. #16811031	C₂²	semidirect
49. #16811030	C₂²	semidirect
50. #16811029	C₂²	semidirect
51. #16811028	C₂²	semidirect
52. #16811027	C₂²	semidirect
53. #16811027	C₂²	semidirect
54. #16811027	C₂²	semidirect
55. #16811027	C₂²	semidirect
56. #16811025	C₂²	semidirect
57. #16811025	C₂²	semidirect
58. #16811024	C₂²	semidirect
59. #16811024	C₂²	semidirect
60. #16811022	C₂²	semidirect
61. #16811020	C₂²	semidirect
62. #16810925	C₂²	semidirect
63. #16810925	C₂²	semidirect
64. #16810924	C₂²	semidirect
65. #16810924	C₂²	semidirect
66. #16810923	C₂²	semidirect
67. #16810923	C₂²	semidirect
68. #16810922	C₂²	semidirect
69. #16810922	C₂²	semidirect
70. #16810920	C₂²	semidirect
71. #16810920	C₂²	semidirect
72. #16810914	C₂²	semidirect
73. #16810912	C₂²	semidirect
74. #16810912	C₂²	semidirect
75. #16810911	C₂²	semidirect
76. #16810911	C₂²	semidirect
77. #16810903	C₂²	semidirect
78. #16810902	C₂²	semidirect
79. #16810902	C₂²	semidirect
80. #16810901	C₂²	semidirect
81. #16810901	C₂²	semidirect
82. #16810900	C₂²	semidirect
83. #16810754	C₂²	semidirect
84. #16810752	C₂²	semidirect
85. #16810752	C₂²	semidirect
86. #16810750	C₂²	semidirect
87. C₈×Dic₁₀₆	C₂²	semidirect
88. C₈×Dic₁₀₆	C₂²	semidirect
89. C₈×Dic₁₀₆	C₂²	semidirect
120. C₅₃×#554	C₂²	semidirect
121. C₅₃×#500	C₂²	semidirect
122. C₅₃×#499	C₂²	semidirect
123. C₅₃×#499	C₂²	semidirect
124. C₅₃×#478	C₂²	semidirect
125. C₅₃×#478	C₂²	semidirect
126. C₅₃×#476	C₂²	semidirect
127. C₈×Q₈×C₅₃	C₂²	semidirect
137. D₈×D₅₃	Q₈	semidirect
308. D₄×D₅₃	C₂×Q₈	semidirect
330. D₈×C₅₃	C₂×Q₈	semidirect
355. #11719922	C₂×Q₈	semidirect
409. D₄₂₄	C₂×Q₈	semidirect
413. C₈×D₅₃	C₂×Q₈	semidirect
523. #3380	D₅₃	semidirect
551. #554	C₂×D₅₃	semidirect
575. #500	C₂×D₅₃	semidirect
581. #499	C₂×D₅₃	semidirect
582. #499	C₂×D₅₃	semidirect
594. #478	C₂×D₅₃	semidirect
595. #478	C₂×D₅₃	semidirect
601. #476	C₂×D₅₃	semidirect
615. C₈×Q₈	C₂×D₅₃	semidirect
649. C₅₃	#61370	semidirect
851. D₈	Q₈×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20288514	2
#20287673	2
#20287669	2
#20287617	2
#20287609	2
#20287583	2
#20287582	2
#20287579	2
D₈×Dic₁₀₆	2
#20287567	2
#20285252	2
#20285248	2
#20285228	2
#20284545	2
#20284541	2
#20284510	2
#20283644	2
#20283562	2
C₄×D₈×D₅₃	2
C₅₃×#3380	2
#61370	53