Subgroups — #28264754

Order 13568.

1682 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288522	C₂	1	2	yes	maximal
2	#20287682	C₂	1	2	yes	maximal, complemented
3	#20287678	C₂	1	2	yes	maximal, complemented
4	#20287650	C₂	1	2	yes	maximal, complemented
5	#20287642	C₂	1	2	yes	maximal, complemented
6	#20287607	C₂	1	1	yes	maximal, characteristic, complemented
7	#20287606	C₂	1	1	yes	maximal, characteristic, complemented
8	#20287606	C₂	1	1	yes	maximal, characteristic, complemented
9	#20287603	C₂	1	1	yes	maximal, characteristic, complemented
10	#20287603	C₂	1	1	yes	maximal, characteristic, complemented
11	Q₁₆×Dic₁₀₆	C₂	1	1	yes	maximal, characteristic, complemented
12	#20287598	C₂	1	1	yes	maximal, characteristic, complemented
13	#20285252	C₂	1	1	yes	maximal, characteristic
14	#20285248	C₂	1	1	yes	maximal, characteristic
15	#20285228	C₂	1	1	yes	maximal, characteristic
16	#20284554	C₂	1	2	yes	maximal
17	#20284550	C₂	1	2	yes	maximal
18	#20284518	C₂	1	2	yes	maximal
19	#20283644	C₂	1	1	yes	maximal, characteristic
20	#20283578	C₂	1	1	yes	maximal, characteristic
21	#20283578	C₂	1	1	yes	maximal, characteristic
22	C₄×Q₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic
23	C₅₃×#3383	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₁₆×D₅₃	C₂²	1	1	yes	characteristic
25	Q₈×Dic₁₀₆	C₂²	1	2	yes	—
26	#16811353	—	2	2	no	—
27	#16811353	C₂²	1	2	yes	—
28	#16811351	—	2	2	no	—
29	#16811351	C₂²	1	2	yes	—
30	#16811350	—	2	2	no	—
31	#16811350	—	2	2	no	—
32	#16811350	C₂²	1	2	yes	—
33	#16811350	C₂²	1	2	yes	—
34	#16811349	C₂²	1	2	yes	—
35	#16811349	C₂²	1	2	yes	—
36	#16811253	—	2	2	no	—
37	#16811253	C₂²	1	2	yes	—
38	#16811250	—	2	2	no	—
39	#16811250	C₂²	1	2	yes	—
40	#16811179	—	2	2	no	—
41	#16811179	C₂²	1	2	yes	—
42	#16811177	—	2	2	no	—
43	#16811177	C₂²	1	1	yes	characteristic
44	#16811099	C₂²	1	2	yes	—
45	#16811099	C₂²	1	2	yes	—
46	C₄×Q₈×D₅₃	C₂²	1	2	yes	—
47	#16811033	C₂²	1	2	yes	—
48	#16811031	C₂²	1	2	yes	—
49	#16811030	C₂²	1	2	yes	—
50	#16811029	C₂²	1	2	yes	—
51	#16811028	C₂²	1	1	yes	characteristic
52	#16811027	C₂²	1	1	yes	characteristic
53	#16811027	C₂²	1	1	yes	characteristic
54	#16811027	C₂²	1	1	yes	characteristic
55	#16811027	C₂²	1	1	yes	characteristic
56	#16811025	C₂²	1	1	yes	characteristic
57	#16811025	C₂²	1	1	yes	characteristic
58	#16811024	C₂²	1	1	yes	characteristic
59	#16811024	C₂²	1	1	yes	characteristic
60	#16811022	C₂²	1	2	yes	—
61	#16811020	C₂²	1	2	yes	—
62	#16810933	C₂²	1	2	yes	—
63	#16810933	C₂²	1	2	yes	—
64	#16810931	C₂²	1	2	yes	—
65	#16810931	C₂²	1	2	yes	—
66	#16810930	C₂²	1	2	yes	—
67	#16810930	C₂²	1	2	yes	—
68	#16810928	C₂²	1	2	yes	—
69	#16810928	C₂²	1	2	yes	—
70	#16810927	C₂²	1	2	yes	—
71	#16810927	C₂²	1	2	yes	—
72	#16810918	C₂²	1	2	yes	—
73	#16810917	C₂²	1	2	yes	—
74	#16810917	C₂²	1	2	yes	—
75	#16810916	C₂²	1	2	yes	—
76	#16810916	C₂²	1	2	yes	—
77	#16810915	C₂²	1	2	yes	—
78	#16810909	C₂²	1	2	yes	—
79	#16810907	C₂²	1	2	yes	—
80	#16810907	C₂²	1	2	yes	—
81	#16810906	C₂²	1	2	yes	—
82	#16810906	C₂²	1	2	yes	—
83	#16810754	C₂²	1	1	yes	characteristic
84	#16810752	C₂²	1	1	yes	characteristic
85	#16810752	C₂²	1	1	yes	characteristic
86	#16810750	C₂²	1	1	yes	characteristic
87	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic
88	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic
89	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic
90	#16810728	C₂²	1	2	yes	—
91	#16810728	C₂²	1	2	yes	—
92	#16810727	C₂²	1	2	yes	—
93	#16810727	C₂²	1	2	yes	—
94	C₄×Dic₂₁₂	C₂²	1	1	yes	characteristic
95	C₄×Dic₂₁₂	C₂²	1	1	yes	characteristic
96	C₄×Dic₂₁₂	C₂²	1	1	yes	characteristic
97	Q₁₆×Dic₅₃	C₂²	1	1	yes	characteristic
98	Q₁₆×Dic₅₃	C₂²	1	1	yes	characteristic
99	Q₁₆×Dic₅₃	C₂²	1	1	yes	characteristic
100	#16810717	C₂²	1	1	yes	characteristic
101	#16810717	C₂²	1	1	yes	characteristic
102	#16810717	C₂²	1	1	yes	characteristic
103	C₄×#11719925	C₂²	1	2	yes	—
104	#16810715	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	#16810630	C₂²	1	2	yes	—
115	#16810630	C₂²	1	2	yes	—
116	#103×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×#557	C₂²	1	2	yes	—
121	C₅₃×#500	C₂²	1	1	yes	characteristic
122	C₅₃×#499	C₂²	1	1	yes	characteristic
123	C₅₃×#499	C₂²	1	1	yes	characteristic
124	C₅₃×#479	C₂²	1	2	yes	—
125	C₅₃×#479	C₂²	1	2	yes	—
126	C₅₃×#475	C₂²	1	2	yes	—
127	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic
128	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
129	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
130	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
131	C₂×Q₈×D₅₃	C₂³	1	2	yes	—
132	C₂×Dic₂₁₂	C₂³	1	1	yes	characteristic
133	C₂×#11719925	C₂³	1	2	yes	—
134	Q₁₆×D₅₃	Q₈	1	8	yes	complemented
135	C₂×#11719912	C₂³	1	1	yes	characteristic
136	C₂×#11719912	C₂³	1	1	yes	characteristic
137	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
138	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
139	#13133217	—	2	2	no	—
140	#13133217	C₂³	1	2	yes	—
141	#13133216	—	2	2	no	—
142	#13133216	—	2	2	no	—
143	#13133216	—	2	2	no	—
144	#13133216	—	2	2	no	—
145	#13133216	—	2	2	no	—
146	#13133216	—	2	2	no	—
147	#13133216	—	2	2	no	—
148	#13133216	—	2	2	no	—
149	#13133216	D₄	1	1	yes	characteristic
150	#13133216	C₂³	1	2	yes	—
151	#13133216	C₂³	1	2	yes	—
152	#13133216	C₂³	1	2	yes	—
153	#13133216	C₂³	1	2	yes	—
154	#13133215	—	2	2	no	—
155	#13133215	—	2	2	no	—
156	#13133215	—	2	2	no	—
157	#13133215	—	2	2	no	—
158	#13133215	D₄	1	1	yes	characteristic
159	#13133209	—	2	2	no	—
160	#13133209	—	2	2	no	—
161	#13133209	C₂³	1	2	yes	—
162	#13133209	C₂³	1	2	yes	—
163	#13133208	—	2	2	no	—
164	#13133208	—	2	2	no	—
165	#13133208	C₂³	1	2	yes	—
166	#13133208	C₂³	1	2	yes	—
167	#13133207	—	2	2	no	—
168	#13133207	—	2	2	no	—
169	#13133207	—	2	2	no	—
170	#13133207	—	2	2	no	—
171	#13133207	—	2	2	no	—
172	#13133207	—	2	2	no	—
173	#13133207	—	2	2	no	—
174	#13133207	—	2	2	no	—
175	#13133207	D₄	1	1	yes	characteristic
176	#13133207	D₄	1	1	yes	characteristic
177	#13133197	—	2	2	no	—
178	#13133197	D₄	1	1	yes	characteristic
179	#13133195	—	2	2	no	—
180	#13133195	—	2	2	no	—
181	#13133195	—	2	2	no	—
182	#13133195	—	2	2	no	—
183	#13133195	D₄	1	1	yes	characteristic
184	#13133195	D₄	1	1	yes	characteristic
185	#13133193	—	2	2	no	—
186	#13133193	D₄	1	1	yes	characteristic
187	Q₈×Dic₅₃	C₂³	1	2	yes	—
188	Q₈×Dic₅₃	C₂³	1	2	yes	—
189	Q₈×Dic₅₃	C₂³	1	2	yes	—
190	C₄×Dic₁₀₆	—	2	2	no	—
191	C₄×Dic₁₀₆	—	2	2	no	—
192	C₄×Dic₁₀₆	—	2	2	no	—
193	C₄×Dic₁₀₆	—	2	2	no	—
194	C₄×Dic₁₀₆	—	2	2	no	—
195	C₄×Dic₁₀₆	—	2	2	no	—
196	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
197	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
198	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
199	C₄×Dic₁₀₆	C₂³	1	2	yes	—
200	C₄×Dic₁₀₆	C₂³	1	2	yes	—
201	C₄×Dic₁₀₆	C₂³	1	2	yes	—
202	#13133182	—	2	2	no	—
203	#13133182	—	2	2	no	—
204	#13133182	—	2	2	no	—
205	#13133182	—	2	2	no	—
206	#13133182	—	2	2	no	—
207	#13133182	—	2	2	no	—
208	#13133182	—	2	2	no	—
209	#13133182	—	2	2	no	—
210	#13133182	—	2	2	no	—
211	#13133182	C₂³	1	2	yes	—
212	#13133182	C₂³	1	2	yes	—
213	#13133182	C₂³	1	2	yes	—
214	#13133175	—	2	2	no	—
215	#13133175	—	2	2	no	—
216	#13133175	C₂³	1	2	yes	—
217	#13133175	C₂³	1	2	yes	—
218	#13133174	—	2	2	no	—
219	#13133174	—	2	2	no	—
220	#13133174	C₂³	1	1	yes	characteristic
221	#13133174	C₂³	1	1	yes	characteristic
222	C₄⋊C₄×D₅₃	—	2	2	no	—
223	C₄⋊C₄×D₅₃	C₂³	1	2	yes	—
224	C₄²×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	#13133142	C₂³	1	2	yes	—
251	#13133142	C₂³	1	2	yes	—
252	#13133142	C₂³	1	2	yes	—
253	#13133141	C₂³	1	2	yes	—
254	#13133141	C₂³	1	2	yes	—
255	#13133141	C₂³	1	2	yes	—
256	#13133140	C₂³	1	2	yes	—
257	#13133140	C₂³	1	2	yes	—
258	#13133140	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×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
269	C₄⋊Q₈×C₅₃	—	2	2	no	—
270	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
271	#125×C₅₃	—	2	2	no	—
272	#125×C₅₃	—	2	2	no	—
273	#125×C₅₃	C₂³	1	2	yes	—
274	#125×C₅₃	C₂³	1	2	yes	—
275	C₄×Q₈×C₅₃	—	2	2	no	—
276	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
277	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
278	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
279	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
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	#103×C₅₃	C₂³	1	2	yes	—
290	#103×C₅₃	C₂³	1	2	yes	—
291	#103×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	C₂×Q₈×C₅₃	—	2	2	no	—
296	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
297	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
298	Q₈×D₅₃	—	2	4	no	—
299	Q₈×D₅₃	C₂×Q₈	1	8	yes	—
300	C₂×C₄×D₅₃	—	2	2	no	—
301	C₂×C₄×D₅₃	—	2	2	no	—
302	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
303	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
304	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
305	C₂×Dic₁₀₆	—	2	2	no	—
306	C₂×Dic₁₀₆	—	2	2	no	—
307	C₂×Dic₁₀₆	—	2	2	no	—
308	C₂×Dic₁₀₆	—	2	2	no	—
309	C₂×Dic₁₀₆	—	2	2	no	—
310	C₂×Dic₁₀₆	—	2	2	no	—
311	C₂×Dic₁₀₆	C₂×D₄	1	1	yes	characteristic
312	C₂×Dic₁₀₆	C₂×D₄	1	1	yes	characteristic
313	C₂×Dic₁₀₆	C₂×D₄	1	1	yes	characteristic
314	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
315	Q₁₆×C₅₃	C₂×Q₈	1	4	yes	—
316	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
317	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
318	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
319	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
320	C₄⋊C₄×C₅₃	—	2	2	no	—
321	C₄⋊C₄×C₅₃	—	2	2	no	—
322	C₄⋊C₄×C₅₃	—	2	2	no	—
323	C₄⋊C₄×C₅₃	—	2	2	no	—
324	C₄⋊C₄×C₅₃	—	2	2	no	—
325	C₄⋊C₄×C₅₃	—	2	2	no	—
326	C₄⋊C₄×C₅₃	—	2	2	no	—
327	C₄⋊C₄×C₅₃	—	2	2	no	—
328	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
329	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
330	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
331	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
332	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
333	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
334	C₄²×C₅₃	—	2	2	no	—
335	C₄²×C₅₃	—	2	2	no	—
336	C₄²×C₅₃	—	2	2	no	—
337	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
338	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
339	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
340	#11719925	C₂×Q₈	1	8	yes	—
341	#11719921	—	2	2	no	—
342	#11719921	—	2	2	no	—
343	#11719921	C₂×D₄	1	1	yes	characteristic
344	#11719921	C₂×D₄	1	1	yes	characteristic
345	#11719921	C₂×D₄	1	1	yes	characteristic
346	#11719921	C₂×D₄	1	1	yes	characteristic
347	C₄⋊Dic₅₃	—	2	2	no	—
348	C₄⋊Dic₅₃	—	2	2	no	—
349	C₄⋊Dic₅₃	—	2	2	no	—
350	C₄⋊Dic₅₃	—	2	2	no	—
351	C₄⋊Dic₅₃	—	2	2	no	—
352	C₄⋊Dic₅₃	—	2	2	no	—
353	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
354	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
355	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
356	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
357	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
358	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
359	#11719919	—	2	2	no	—
360	#11719919	—	2	2	no	—
361	#11719919	—	2	2	no	—
362	#11719919	—	2	2	no	—
363	#11719919	—	2	2	no	—
364	#11719919	—	2	2	no	—
365	#11719919	—	2	2	no	—
366	#11719919	—	2	2	no	—
367	#11719919	—	2	2	no	—
368	#11719919	—	2	2	no	—
369	#11719919	—	2	2	no	—
370	#11719919	—	2	2	no	—
371	#11719919	—	2	2	no	—
372	#11719919	—	2	2	no	—
373	#11719919	—	2	2	no	—
374	#11719919	—	2	2	no	—
375	#11719919	—	2	2	no	—
376	#11719919	C₂×D₄	1	1	yes	characteristic
377	#11719919	C₂×D₄	1	1	yes	characteristic
378	#11719919	C₂×D₄	1	1	yes	characteristic
379	#11719919	C₂×D₄	1	1	yes	characteristic
380	#11719919	C₂×D₄	1	1	yes	characteristic
381	#11719919	C₂×D₄	1	1	yes	characteristic
382	#11719919	C₂×D₄	1	1	yes	characteristic
383	#11719919	C₂×D₄	1	1	yes	characteristic
384	#11719919	C₂×D₄	1	1	yes	characteristic
385	#11719919	C₂×D₄	1	1	yes	characteristic
386	C₄×Dic₅₃	—	2	2	no	—
387	C₄×Dic₅₃	—	2	2	no	—
388	C₄×Dic₅₃	—	2	2	no	—
389	C₄×Dic₅₃	—	2	2	no	—
390	C₄×Dic₅₃	—	2	2	no	—
391	C₄×Dic₅₃	—	2	2	no	—
392	C₄×Dic₅₃	—	2	2	no	—
393	C₄×Dic₅₃	—	2	2	no	—
394	C₄×Dic₅₃	—	2	2	no	—
395	C₄×Dic₅₃	—	2	2	no	—
396	C₄×Dic₅₃	—	2	2	no	—
397	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
398	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
399	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
400	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
401	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
402	C₂×#88322	C₂⁴	1	1	yes	characteristic
403	C₂×#88322	C₂⁴	1	1	yes	characteristic
404	C₂×#88322	C₂⁴	1	1	yes	characteristic
405	C₂×#88322	C₂⁴	1	1	yes	characteristic
406	Dic₂₁₂	C₂×Q₈	1	4	yes	—
407	#11719912	—	2	2	no	—
408	#11719912	—	2	2	no	—
409	C₈×D₅₃	—	2	2	no	—
410	C₈×D₅₃	C₂×Q₈	1	4	yes	—
411	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
412	Q₈×C₅₃	—	2	2	no	—
413	Q₈×C₅₃	—	4	1	no	—
414	Q₈×C₅₃	—	8	2	no	—
415	Q₈×C₅₃	C₂²×Q₈	1	4	yes	—
416	C₂×C₄×C₅₃	—	2	2	no	—
417	C₂×C₄×C₅₃	—	2	2	no	—
418	C₂×C₄×C₅₃	—	2	2	no	—
419	C₂×C₄×C₅₃	—	2	2	no	—
420	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
427	C₂×Dic₅₃	—	2	2	no	—
428	C₂×Dic₅₃	—	2	2	no	—
429	C₂×Dic₅₃	—	2	2	no	—
430	C₂×Dic₅₃	—	2	2	no	—
431	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
432	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
433	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
434	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
435	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
436	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
437	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
438	C₄×D₅₃	—	2	8	no	—
439	C₄×D₅₃	—	2	2	no	—
440	C₄×D₅₃	—	4	1	no	—
441	C₄×D₅₃	—	8	2	no	—
442	C₄×D₅₃	C₂²×Q₈	1	2	yes	—
443	C₄×D₅₃	2₋¹⁺⁴	1	2	yes	—
444	Dic₁₀₆	—	2	2	no	—
445	Dic₁₀₆	—	2	8	no	—
446	Dic₁₀₆	—	2	2	no	—
447	Dic₁₀₆	—	2	2	no	—
448	Dic₁₀₆	—	4	1	no	—
449	Dic₁₀₆	—	4	4	no	—
450	Dic₁₀₆	—	8	2	no	—
451	Dic₁₀₆	—	8	2	no	—
452	Dic₁₀₆	—	8	2	no	—
453	Dic₁₀₆	—	8	2	no	—
454	Dic₁₀₆	C₂²×Q₈	1	4	yes	—
455	C₈×C₅₃	—	2	1	no	—
456	C₈×C₅₃	—	2	1	no	—
457	C₈×C₅₃	—	2	1	no	—
458	C₈×C₅₃	C₂²×Q₈	1	2	yes	—
459	#88322	—	2	1	no	—
460	#88322	—	2	1	no	—
461	#88322	—	2	1	no	—
462	#88322	C₂²×Q₈	1	2	yes	—
463	#61372	—	53	1	no	maximal, Sylow
464	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
465	C₂×D₅₃	—	2	1	no	—
466	C₂×D₅₃	—	2	1	no	—
467	C₂×D₅₃	D₄×Q₈	1	2	yes	—
468	C₄×C₅₃	—	2	1	no	—
469	C₄×C₅₃	—	2	1	no	—
470	C₄×C₅₃	—	2	1	no	—
471	C₄×C₅₃	—	2	4	no	—
472	C₄×C₅₃	—	2	1	no	—
473	C₄×C₅₃	—	2	1	no	—
474	C₄×C₅₃	—	2	1	no	—
475	C₄×C₅₃	—	4	2	no	—
476	C₄×C₅₃	—	4	2	no	—
477	C₄×C₅₃	—	4	2	no	—
478	C₄×C₅₃	C₂³×Q₈	1	1	yes	characteristic
479	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
480	Dic₅₃	—	2	1	no	—
481	Dic₅₃	—	2	1	no	—
482	Dic₅₃	—	2	1	no	—
483	Dic₅₃	—	2	4	no	—
484	Dic₅₃	—	2	1	no	—
485	Dic₅₃	—	2	1	no	—
486	Dic₅₃	—	4	2	no	—
487	Dic₅₃	—	4	2	no	—
488	Dic₅₃	—	4	2	no	—
489	Dic₅₃	D₄×Q₈	1	2	yes	—
490	Dic₅₃	#578	1	2	yes	—
491	#3502	—	53	2	no	—
492	#3390	—	53	2	no	—
493	#3390	—	53	2	no	—
494	#3387	—	53	2	no	—
495	#3387	—	53	2	no	—
496	#3383	—	53	1	no	—
497	#3383	—	53	1	no	—
498	#3383	—	53	1	no	—
499	#3383	—	53	1	no	—
500	#3383	—	53	1	no	—
501	#3383	D₅₃	1	1	yes	characteristic, complemented
502	Q₈×Q₁₆	—	53	1	no	—
503	Q₈×Q₁₆	—	53	1	no	—
504	#3164	—	53	1	no	—
505	#3164	—	53	1	no	—
506	#3160	—	53	1	no	—
507	#3082	—	53	2	no	—
508	#3082	—	53	2	no	—
509	#3078	—	53	2	no	—
510	#2960	—	53	1	no	—
511	#2950	—	53	1	no	—
512	#2950	—	53	1	no	—
513	C₂×C₄×Q₁₆	—	53	1	no	—
514	C₂×C₅₃	C₂×D₄×Q₈	1	1	yes	characteristic
515	C₂×C₅₃	C₂×#578	1	1	yes	characteristic
516	C₂×C₅₃	#3584	1	1	yes	characteristic
517	D₅₃	—	2	2	no	—
518	C₂²×Q₁₆	—	53	1	no	—
519	Q₈²	—	53	2	no	—
520	Q₈²	—	53	2	no	—
521	Q₈²	—	106	2	no	—
522	#557	—	53	2	no	—
523	#557	—	53	2	no	—
524	#557	—	53	2	no	—
525	#557	—	53	2	no	—
526	#557	—	53	2	no	—
527	#557	—	106	2	no	—
528	#557	—	106	2	no	—
529	#557	—	106	2	no	—
530	#557	C₂×D₅₃	1	2	yes	—
531	#544	—	53	2	no	—
532	#544	—	53	2	no	—
533	#544	—	106	2	no	—
534	#544	—	106	2	no	—
535	#533	—	53	1	no	—
536	#533	—	53	2	no	—
537	#533	—	106	2	no	—
538	#533	—	106	2	no	—
539	#519	—	53	2	no	—
540	#519	—	53	2	no	—
541	C₂×C₄×Q₈	—	53	2	no	—
542	#501	—	53	2	no	—
543	#501	—	53	2	no	—
544	#501	—	53	2	no	—
545	#501	—	53	2	no	—
546	#500	—	53	1	no	—
547	#500	—	53	1	no	—
548	#500	—	53	1	no	—
549	#500	—	53	1	no	—
550	#500	—	53	1	no	—
551	#500	C₂×D₅₃	1	1	yes	characteristic
552	#499	—	53	2	no	—
553	#499	—	53	1	no	—
554	#499	—	53	1	no	—
555	#499	—	53	1	no	—
556	#499	—	53	1	no	—
557	#499	C₂×D₅₃	1	1	yes	characteristic
558	#499	C₂×D₅₃	1	1	yes	characteristic
559	#498	—	53	2	no	—
560	#479	—	53	2	no	—
561	#479	—	53	2	no	—
562	#479	—	53	2	no	—
563	#479	—	53	2	no	—
564	#479	—	53	2	no	—
565	#479	—	53	2	no	—
566	#479	—	53	2	no	—
567	#479	—	53	2	no	—
568	#479	—	53	2	no	—
569	#479	—	53	2	no	—
570	#479	C₂×D₅₃	1	2	yes	—
571	#479	C₂×D₅₃	1	2	yes	—
572	#477	—	53	2	no	—
573	#477	—	53	2	no	—
574	#477	—	53	2	no	—
575	#477	—	53	2	no	—
576	#477	—	53	2	no	—
577	#477	—	53	2	no	—
578	#475	—	53	2	no	—
579	#475	—	53	2	no	—
580	#475	—	53	2	no	—
581	#475	—	53	2	no	—
582	#475	—	53	2	no	—
583	#475	C₂×D₅₃	1	2	yes	—
584	#446	—	53	1	no	—
585	#446	—	53	1	no	—
586	#446	—	53	1	no	—
587	#446	—	53	1	no	—
588	C₈×Q₈	—	53	1	no	—
589	C₈×Q₈	—	53	1	no	—
590	C₈×Q₈	—	53	1	no	—
591	C₈×Q₈	C₂×D₅₃	1	1	yes	characteristic
592	#441	—	53	2	no	—
593	#441	—	53	2	no	—
594	#441	—	53	2	no	—
595	#441	—	53	2	no	—
596	C₄×Q₁₆	—	53	1	no	—
597	C₄×Q₁₆	—	53	1	no	—
598	C₄×Q₁₆	—	53	1	no	—
599	C₄×Q₁₆	—	53	2	no	—
600	C₄×Q₁₆	—	53	1	no	—
601	C₄×Q₁₆	—	53	1	no	—
602	C₄×Q₁₆	—	53	1	no	—
603	C₄×Q₁₆	—	53	2	no	—
604	C₄×Q₁₆	—	53	1	no	—
605	C₄×Q₁₆	—	53	1	no	—
606	C₄×Q₁₆	—	53	1	no	—
607	C₄×Q₁₆	C₂×D₅₃	1	1	yes	characteristic
608	C₄×Q₁₆	C₂×D₅₃	1	1	yes	characteristic
609	C₄×Q₁₆	C₂×D₅₃	1	1	yes	characteristic
610	#428	—	53	2	no	—
611	#428	—	53	2	no	—
612	#427	—	53	1	no	—
613	#427	—	53	1	no	—
614	#427	—	53	2	no	—
615	C₂×#107	—	53	1	no	—
616	#424	—	53	1	no	—
617	#424	—	53	1	no	—
618	#423	—	53	1	no	—
619	#419	—	53	2	no	—
620	#419	—	53	2	no	—
621	C₂×#103	—	53	2	no	—
622	#405	—	53	1	no	—
623	#405	—	53	1	no	—
624	C₂×C₄×C₈	—	53	1	no	—
625	C₅₃	#61372	1	1	yes	characteristic, complemented, Sylow
626	C₂²×Q₈	—	53	2	no	—
627	C₂×Q₁₆	—	53	2	no	—
628	C₂×Q₁₆	—	53	8	no	—
629	C₂×Q₁₆	—	53	1	no	—
630	C₂×Q₁₆	C₂²×D₅₃	1	1	yes	characteristic
631	C₂×M₁₆	—	53	1	no	—
632	C₂×M₁₆	—	53	1	no	—
633	C₂²×C₈	—	53	1	no	—
634	C₂²×C₈	—	53	1	no	—
635	C₄⋊Q₈	—	2	2	no	—
636	C₄⋊Q₈	—	53	1	no	—
637	C₄⋊Q₈	—	53	1	no	—
638	C₄⋊Q₈	—	53	2	no	—
639	C₄⋊Q₈	—	53	2	no	—
640	C₄⋊Q₈	—	53	2	no	—
641	C₄⋊Q₈	—	53	2	no	—
642	C₄⋊Q₈	—	53	2	no	—
643	C₄⋊Q₈	—	106	2	no	—
644	C₄⋊Q₈	—	106	2	no	—
645	C₄⋊Q₈	—	106	2	no	—
646	C₄⋊Q₈	—	106	2	no	—
647	C₄⋊Q₈	—	106	2	no	—
648	C₄⋊Q₈	—	106	2	no	—
649	C₄⋊Q₈	—	106	2	no	—
650	C₄⋊Q₈	—	106	2	no	—
651	C₄⋊Q₈	—	106	2	no	—
652	C₄⋊Q₈	—	106	2	no	—
653	C₄⋊Q₈	—	106	2	no	—
654	C₄⋊Q₈	—	106	2	no	—
655	C₄⋊Q₈	—	106	2	no	—
656	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	—
657	#125	—	2	2	no	—
658	#125	—	2	2	no	—
659	#125	—	53	1	no	—
660	#125	—	53	1	no	—
661	#125	—	53	2	no	—
662	#125	—	53	2	no	—
663	#125	—	53	2	no	—
664	#125	—	53	2	no	—
665	#125	—	106	2	no	—
666	#125	—	106	2	no	—
667	#125	—	106	2	no	—
668	#125	—	106	2	no	—
669	#125	—	106	2	no	—
670	#125	—	106	2	no	—
671	#125	—	106	2	no	—
672	#125	—	106	2	no	—
673	#125	—	106	2	no	—
674	#125	—	106	2	no	—
675	#125	—	106	2	no	—
676	#125	—	106	2	no	—
677	#125	C₂²×D₅₃	1	2	yes	—
678	#125	C₂²×D₅₃	1	2	yes	—
679	C₂²⋊Q₈	—	53	1	no	—
680	C₂²⋊Q₈	—	53	1	no	—
681	C₂²⋊Q₈	—	53	1	no	—
682	C₂²⋊Q₈	—	53	1	no	—
683	C₂²⋊Q₈	—	106	2	no	—
684	C₂²⋊Q₈	—	106	2	no	—
685	C₂²⋊Q₈	—	106	2	no	—
686	C₂²⋊Q₈	—	106	2	no	—
687	C₂²⋊Q₈	—	106	2	no	—
688	C₂²⋊Q₈	—	106	2	no	—
689	C₄×Q₈	—	2	2	no	—
690	C₄×Q₈	—	53	1	no	—
691	C₄×Q₈	—	53	1	no	—
692	C₄×Q₈	—	53	1	no	—
693	C₄×Q₈	—	53	2	no	—
694	C₄×Q₈	—	53	2	no	—
695	C₄×Q₈	—	53	2	no	—
696	C₄×Q₈	—	53	2	no	—
697	C₄×Q₈	—	53	2	no	—
698	C₄×Q₈	—	53	2	no	—
699	C₄×Q₈	—	53	2	no	—
700	C₄×Q₈	—	53	2	no	—
701	C₄×Q₈	—	53	2	no	—
702	C₄×Q₈	—	106	2	no	—
703	C₄×Q₈	—	106	2	no	—
704	C₄×Q₈	—	106	2	no	—
705	C₄×Q₈	—	106	2	no	—
706	C₄×Q₈	—	106	2	no	—
707	C₄×Q₈	—	106	2	no	—
708	C₄×Q₈	—	106	2	no	—
709	C₄×Q₈	—	106	2	no	—
710	C₄×Q₈	—	106	2	no	—
711	C₄×Q₈	—	106	2	no	—
712	C₄×Q₈	—	106	2	no	—
713	C₄×Q₈	—	106	2	no	—
714	C₄×Q₈	—	106	2	no	—
715	C₄×Q₈	—	106	2	no	—
716	C₄×Q₈	—	106	2	no	—
717	C₄×Q₈	C₂²×D₅₃	1	2	yes	—
718	C₄×Q₈	C₂²×D₅₃	1	2	yes	—
719	C₄×Q₈	C₂²×D₅₃	1	2	yes	—
720	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
721	#117	—	53	1	no	—
722	#117	—	53	1	no	—
723	#117	—	53	2	no	—
724	#117	—	53	2	no	—
725	#117	—	106	2	no	—
726	#117	—	106	2	no	—
727	#117	—	106	2	no	—
728	#117	—	106	2	no	—
729	C₂×C₄⋊C₄	—	53	2	no	—
730	C₂×C₄⋊C₄	—	106	2	no	—
731	C₂×C₄²	—	53	1	no	—
732	C₂×C₄²	—	106	2	no	—
733	#107	—	53	1	no	—
734	#107	—	53	1	no	—
735	#107	—	53	1	no	—
736	#107	—	53	2	no	—
737	#107	—	53	2	no	—
738	#107	—	53	2	no	—
739	#107	—	53	2	no	—
740	#107	—	53	2	no	—
741	#107	—	53	2	no	—
742	#107	C₂²×D₅₃	1	1	yes	characteristic
743	#107	C₂²×D₅₃	1	1	yes	characteristic
744	#107	C₂²×D₅₃	1	1	yes	characteristic
745	#107	C₂²×D₅₃	1	2	yes	—
746	#106	—	53	2	no	—
747	#106	—	53	2	no	—
748	#106	—	53	2	no	—
749	#106	—	53	2	no	—
750	#106	—	53	2	no	—
751	#106	—	53	2	no	—
752	#106	C₂²×D₅₃	1	2	yes	—
753	#106	C₂²×D₅₃	1	2	yes	—
754	C₄⋊C₈	—	53	1	no	—
755	C₄⋊C₈	—	53	1	no	—
756	C₄⋊C₈	—	53	1	no	—
757	C₄⋊C₈	—	53	1	no	—
758	C₄⋊C₈	—	53	1	no	—
759	C₄⋊C₈	—	53	1	no	—
760	C₄⋊C₈	—	53	1	no	—
761	C₄⋊C₈	—	53	1	no	—
762	C₄⋊C₈	—	53	1	no	—
763	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
764	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
765	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
766	#103	—	53	2	no	—
767	#103	—	53	2	no	—
768	#103	—	53	2	no	—
769	#103	—	53	2	no	—
770	#103	—	53	2	no	—
771	#103	—	53	2	no	—
772	#103	—	53	2	no	—
773	#103	—	53	2	no	—
774	#103	—	53	2	no	—
775	#103	C₂²×D₅₃	1	2	yes	—
776	#103	C₂²×D₅₃	1	2	yes	—
777	#103	C₂²×D₅₃	1	2	yes	—
778	#97	—	53	1	no	—
779	#97	—	53	1	no	—
780	#97	—	53	1	no	—
781	#97	—	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	C₂×Q₈	—	2	2	no	—
791	C₂×Q₈	—	53	1	no	—
792	C₂×Q₈	—	53	1	no	—
793	C₂×Q₈	—	53	1	no	—
794	C₂×Q₈	—	53	8	no	—
795	C₂×Q₈	—	53	2	no	—
796	C₂×Q₈	—	106	2	no	—
797	C₂×Q₈	—	106	2	no	—
798	C₂×Q₈	—	106	2	no	—
799	C₂×Q₈	—	106	2	no	—
800	C₂×Q₈	—	106	2	no	—
801	C₂×Q₈	—	106	4	no	—
802	C₂×Q₈	—	106	2	no	—
803	C₂×Q₈	D₄×D₅₃	1	1	yes	characteristic
804	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
805	C₂²×C₄	—	53	1	no	—
806	C₂²×C₄	—	53	1	no	—
807	C₂²×C₄	—	53	1	no	—
808	C₂²×C₄	—	106	2	no	—
809	C₂²×C₄	—	106	2	no	—
810	Q₁₆	—	53	8	no	—
811	Q₁₆	—	53	4	no	—
812	Q₁₆	Q₈×D₅₃	1	4	yes	—
813	M₁₆	—	106	2	no	—
814	M₁₆	—	106	2	no	—
815	C₂×C₈	—	53	1	no	—
816	C₂×C₈	—	53	4	no	—
817	C₂×C₈	—	53	1	no	—
818	C₂×C₈	—	53	1	no	—
819	C₂×C₈	—	53	1	no	—
820	C₂×C₈	—	106	2	no	—
821	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
822	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
823	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
824	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	53	1	no	—
834	C₄⋊C₄	—	53	1	no	—
835	C₄⋊C₄	—	53	1	no	—
836	C₄⋊C₄	—	53	1	no	—
837	C₄⋊C₄	—	53	1	no	—
838	C₄⋊C₄	—	53	1	no	—
839	C₄⋊C₄	—	53	1	no	—
840	C₄⋊C₄	—	53	1	no	—
841	C₄⋊C₄	—	53	1	no	—
842	C₄⋊C₄	—	53	1	no	—
843	C₄⋊C₄	—	53	1	no	—
844	C₄⋊C₄	—	53	1	no	—
845	C₄⋊C₄	—	53	1	no	—
846	C₄⋊C₄	—	53	2	no	—
847	C₄⋊C₄	—	53	2	no	—
848	C₄⋊C₄	—	53	2	no	—
849	C₄⋊C₄	—	106	2	no	—
850	C₄⋊C₄	—	106	2	no	—
851	C₄⋊C₄	—	106	2	no	—
852	C₄⋊C₄	—	106	2	no	—
853	C₄⋊C₄	—	106	2	no	—
854	C₄⋊C₄	—	106	2	no	—
855	C₄⋊C₄	—	106	2	no	—
856	C₄⋊C₄	—	106	2	no	—
857	C₄⋊C₄	—	106	2	no	—
858	C₄⋊C₄	—	106	2	no	—
859	C₄⋊C₄	—	106	2	no	—
860	C₄⋊C₄	—	106	2	no	—
861	C₄⋊C₄	—	106	2	no	—
862	C₄⋊C₄	—	106	2	no	—
863	C₄⋊C₄	—	106	2	no	—
864	C₄⋊C₄	—	106	2	no	—
865	C₄⋊C₄	—	106	2	no	—
866	C₄⋊C₄	—	106	2	no	—
867	C₄⋊C₄	—	106	2	no	—
868	C₄⋊C₄	—	106	2	no	—
869	C₄⋊C₄	—	106	2	no	—
870	C₄⋊C₄	—	106	2	no	—
871	C₄⋊C₄	—	106	2	no	—
872	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
873	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
874	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
875	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
876	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
877	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
878	C₂²⋊C₄	—	53	1	no	—
879	C₂²⋊C₄	—	53	1	no	—
880	C₂²⋊C₄	—	53	1	no	—
881	C₂²⋊C₄	—	53	1	no	—
882	C₂²⋊C₄	—	106	2	no	—
883	C₂²⋊C₄	—	106	2	no	—
884	C₄²	—	2	2	no	—
885	C₄²	—	2	2	no	—
886	C₄²	—	2	2	no	—
887	C₄²	—	53	1	no	—
888	C₄²	—	53	1	no	—
889	C₄²	—	53	1	no	—
890	C₄²	—	53	1	no	—
891	C₄²	—	53	1	no	—
892	C₄²	—	106	2	no	—
893	C₄²	—	106	2	no	—
894	C₄²	—	106	2	no	—
895	C₄²	—	106	2	no	—
896	C₄²	—	106	2	no	—
897	C₄²	—	106	2	no	—
898	C₄²	—	106	2	no	—
899	C₄²	—	106	2	no	—
900	C₄²	—	106	2	no	—
901	C₄²	—	106	2	no	—
902	C₄²	—	106	2	no	—
903	C₄²	C₂³×D₅₃	1	1	yes	characteristic
904	C₄²	C₂³×D₅₃	1	1	yes	characteristic
905	C₄²	C₂³×D₅₃	1	1	yes	characteristic
906	C₂³	—	53	1	no	—
907	Q₈	—	2	2	no	—
908	Q₈	—	4	1	no	—
909	Q₈	—	8	2	no	—
910	Q₈	—	53	4	no	—
911	Q₈	—	106	2	no	—
912	Q₈	—	106	2	no	—
913	Q₈	—	106	8	no	—
914	Q₈	—	106	2	no	—
915	Q₈	—	424	2	no	—
916	Q₈	—	424	2	no	—
917	Q₈	—	424	2	no	—
918	Q₈	—	424	2	no	—
919	Q₈	—	212	1	no	—
920	Q₈	—	212	4	no	—
921	Q₈	C₂×Q₈×D₅₃	1	4	yes	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	53	1	no	—
927	C₂×C₄	—	53	1	no	—
928	C₂×C₄	—	53	2	no	—
929	C₂×C₄	—	53	2	no	—
930	C₂×C₄	—	53	1	no	—
931	C₂×C₄	—	53	1	no	—
932	C₂×C₄	—	53	1	no	—
933	C₂×C₄	—	53	1	no	—
934	C₂×C₄	—	53	1	no	—
935	C₂×C₄	—	106	2	no	—
936	C₂×C₄	—	106	8	no	—
937	C₂×C₄	—	106	2	no	—
938	C₂×C₄	—	106	2	no	—
939	C₂×C₄	—	106	2	no	—
940	C₂×C₄	—	106	2	no	—
941	C₂×C₄	—	424	2	no	—
942	C₂×C₄	—	212	1	no	—
943	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
944	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
945	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
946	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
947	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
948	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
949	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
950	C₈	—	2	1	no	—
951	C₈	—	2	1	no	—
952	C₈	—	2	1	no	—
953	C₈	—	53	2	no	—
954	C₈	—	106	1	no	—
955	C₈	—	106	1	no	—
956	C₈	—	106	1	no	—
957	C₈	C₂×Q₈×D₅₃	1	2	yes	—
958	C₂²	—	53	2	no	—
959	C₂²	—	106	1	no	—
960	C₂²	—	106	1	no	—
961	C₂²	C₂²×D₄×D₅₃	1	1	yes	characteristic
962	C₄	—	2	4	no	—
963	C₄	—	2	1	no	—
964	C₄	—	2	1	no	—
965	C₄	—	2	1	no	—
966	C₄	—	2	1	no	—
967	C₄	—	2	1	no	—
968	C₄	—	2	1	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	2	no	—
972	C₄	—	53	2	no	—
973	C₄	—	53	2	no	—
974	C₄	—	106	4	no	—
975	C₄	—	106	1	no	—
976	C₄	—	106	1	no	—
977	C₄	—	106	1	no	—
978	C₄	—	106	1	no	—
979	C₄	—	106	1	no	—
980	C₄	—	212	2	no	—
981	C₄	—	212	2	no	—
982	C₄	—	212	2	no	—
983	C₄	C₂²×Q₈×D₅₃	1	1	yes	characteristic
984	C₄	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
985	C₂	—	106	2	no	—
986	C₂	D₄×Q₈×D₅₃	1	1	yes	characteristic
987	C₂	#578×D₅₃	1	1	yes	characteristic
988	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×#3383	C₂
socle	C₂²×C₅₃	C₂³×D₄
prime radical	C₂²×D₅₃	C₂²×D₄
hypercenter	#3383	D₅₃
hypocenter	C₅₃	#61372
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #3383

Complements

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

N	H ≅ G/N	type
2. #20287682	C₂	semidirect
3. #20287678	C₂	semidirect
4. #20287650	C₂	semidirect
5. #20287642	C₂	semidirect
6. #20287607	C₂	semidirect
7. #20287606	C₂	semidirect
8. #20287606	C₂	semidirect
9. #20287603	C₂	semidirect
10. #20287603	C₂	semidirect
11. Q₁₆×Dic₁₀₆	C₂	semidirect
12. #20287598	C₂	semidirect
23. C₅₃×#3383	C₂	semidirect
134. Q₁₆×D₅₃	Q₈	semidirect
501. #3383	D₅₃	semidirect
625. C₅₃	#61372	semidirect

Maximal subgroups

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

subgroup	index
#20288522	2
#20287682	2
#20287678	2
#20287650	2
#20287642	2
#20287607	2
#20287606	2
#20287603	2
Q₁₆×Dic₁₀₆	2
#20287598	2
#20285252	2
#20285248	2
#20285228	2
#20284554	2
#20284550	2
#20284518	2
#20283644	2
#20283578	2
C₄×Q₁₆×D₅₃	2
C₅₃×#3383	2
#61372	53