Subgroups — C₃₁×#62549 #21519308

Order 7936.

1740 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3517	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3515	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3374	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3372	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3368	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3332	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3331	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3330	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3317	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3315	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3309	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3307	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3233	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3232	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3212	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3212	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3183	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3168	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3142	C₂	1	2	yes	maximal, complemented
22	C₃₁×#3131	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2965	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#557	C₂²	1	1	yes	characteristic
25	C₃₁×#557	C₂²	1	1	yes	characteristic
26	C₃₁×#554	C₂²	1	1	yes	characteristic
27	C₃₁×#554	C₂²	1	1	yes	characteristic
28	C₃₁×#553	—	2	1	no	—
29	C₃₁×#553	—	2	2	no	—
30	C₃₁×#553	C₂²	1	2	yes	—
31	C₃₁×#552	—	2	2	no	—
32	C₃₁×#552	—	2	1	no	—
33	C₃₁×#552	C₂²	1	2	yes	—
34	C₃₁×#550	—	2	1	no	—
35	C₃₁×#550	C₂²	1	1	yes	characteristic
36	C₃₁×#550	C₂²	1	2	yes	—
37	C₃₁×#550	C₂²	1	1	yes	characteristic
38	C₃₁×#547	—	2	1	no	—
39	C₃₁×#547	C₂²	1	1	yes	characteristic
40	C₃₁×#547	C₂²	1	2	yes	—
41	C₃₁×#547	C₂²	1	1	yes	characteristic
42	C₃₁×#541	—	2	1	no	—
43	C₃₁×#540	—	2	1	no	—
44	C₃₁×#540	—	2	2	no	—
45	C₃₁×#539	—	2	2	no	—
46	C₃₁×#533	C₂²	1	1	yes	characteristic
47	C₃₁×#532	C₂²	1	1	yes	characteristic
48	C₃₁×#532	C₂²	1	2	yes	—
49	C₃₁×#529	C₂²	1	1	yes	characteristic
50	C₃₁×#529	C₂²	1	1	yes	characteristic
51	C₃₁×#529	C₂²	1	2	yes	—
52	C₃₁×#529	C₂²	1	2	yes	—
53	C₂×C₃₁×#125	C₂²	1	2	yes	—
54	C₃₁×#520	—	2	1	no	—
55	C₃₁×#520	—	2	1	no	—
56	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
57	C₃₁×#499	C₂²	1	1	yes	characteristic
58	C₃₁×#499	C₂²	1	2	yes	—
59	C₃₁×#495	C₂²	1	1	yes	characteristic
60	C₃₁×#495	C₂²	1	2	yes	—
61	C₃₁×#491	C₂²	1	2	yes	—
62	C₃₁×#491	C₂²	1	2	yes	—
63	C₃₁×#490	C₂²	1	2	yes	—
64	C₃₁×#490	C₂²	1	2	yes	—
65	C₃₁×#488	C₂²	1	2	yes	—
66	C₃₁×#488	C₂²	1	2	yes	—
67	C₃₁×#488	C₂²	1	1	yes	characteristic
68	C₃₁×#488	C₂²	1	2	yes	—
69	C₃₁×#488	C₂²	1	2	yes	—
70	C₃₁×#488	C₂²	1	1	yes	characteristic
71	C₃₁×#487	C₂²	1	1	yes	characteristic
72	C₃₁×#487	C₂²	1	1	yes	characteristic
73	C₃₁×#486	C₂²	1	1	yes	characteristic
74	C₃₁×#486	C₂²	1	1	yes	characteristic
75	C₃₁×#485	C₂²	1	2	yes	—
76	C₃₁×#484	C₂²	1	2	yes	—
77	C₃₁×#483	C₂²	1	2	yes	—
78	C₃₁×#482	C₂²	1	2	yes	—
79	C₃₁×#481	C₂²	1	2	yes	—
80	C₃₁×#480	C₂²	1	2	yes	—
81	C₃₁×#479	C₂²	1	2	yes	—
82	C₃₁×#479	C₂²	1	2	yes	—
83	C₃₁×#478	C₂²	1	2	yes	—
84	C₃₁×#478	C₂²	1	2	yes	—
85	C₃₁×#477	C₂²	1	1	yes	characteristic
86	C₃₁×#476	C₂²	1	1	yes	characteristic
87	C₃₁×#475	C₂²	1	1	yes	characteristic
88	C₃₁×#474	C₂²	1	1	yes	characteristic
89	C₃₁×#470	C₂²	1	2	yes	—
90	C₃₁×#469	C₂²	1	2	yes	—
91	C₃₁×#468	C₂²	1	2	yes	—
92	C₃₁×#468	C₂²	1	2	yes	—
93	C₃₁×#467	C₂²	1	1	yes	characteristic
94	C₃₁×#466	C₂²	1	1	yes	characteristic
95	C₃₁×#465	C₂²	1	1	yes	characteristic
96	C₃₁×#465	C₂²	1	1	yes	characteristic
97	C₃₁×#462	C₂²	1	1	yes	characteristic
98	C₃₁×#462	C₂²	1	2	yes	—
99	C₃₁×#461	C₂²	1	2	yes	—
100	C₃₁×#461	C₂²	1	1	yes	characteristic
101	C₃₁×#460	C₂²	1	1	yes	characteristic
102	C₃₁×#460	C₂²	1	2	yes	—
103	C₃₁×#459	C₂²	1	1	yes	characteristic
104	C₃₁×#459	C₂²	1	2	yes	—
105	C₃₁×#452	C₂²	1	2	yes	—
106	C₃₁×#452	C₂²	1	2	yes	—
107	C₃₁×#452	C₂²	1	2	yes	—
108	C₃₁×#449	C₂²	1	2	yes	—
109	C₃₁×#449	C₂²	1	2	yes	—
110	C₃₁×#449	C₂²	1	2	yes	—
111	C₃₁×#446	C₂²	1	1	yes	characteristic
112	C₃₁×#446	C₂²	1	1	yes	characteristic
113	C₃₁×#442	C₂²	1	2	yes	—
114	C₃₁×#441	C₂²	1	2	yes	—
115	C₃₁×#440	C₂²	1	2	yes	—
116	C₃₁×#440	C₂²	1	2	yes	—
117	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
121	C₃₁×#436	C₂²	1	1	yes	characteristic
122	C₃₁×#436	C₂²	1	1	yes	characteristic
123	C₃₁×#435	C₂²	1	2	yes	—
124	C₃₁×#435	C₂²	1	2	yes	—
125	C₃₁×#431	C₂²	1	2	yes	—
126	C₃₁×#431	C₂²	1	1	yes	characteristic
127	C₃₁×#417	C₂²	1	2	yes	—
128	C₃₁×#417	C₂²	1	2	yes	—
129	C₃₁×#417	C₂²	1	2	yes	—
130	C₃₁×#417	C₂²	1	2	yes	—
131	C₃₁×#416	C₂²	1	2	yes	—
132	C₃₁×#416	C₂²	1	2	yes	—
133	C₄×M₁₆×C₃₁	C₂²	1	2	yes	—
134	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
137	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
138	C₂×#41×C₃₁	C₂³	1	2	yes	—
139	C₂×#41×C₃₁	C₂³	1	2	yes	—
140	C₂×#41×C₃₁	C₂³	1	2	yes	—
141	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×D₈×C₃₁	C₂³	1	2	yes	—
149	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
153	C₃₁×C₄⋊Q₈	—	2	1	no	—
154	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
156	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₃₁×#127	—	2	1	no	—
159	C₃₁×#127	—	2	2	no	—
160	C₃₁×#127	C₂³	1	1	yes	characteristic
161	C₃₁×#127	C₂³	1	2	yes	—
162	C₃₁×#126	—	2	2	no	—
163	C₃₁×#126	—	2	2	no	—
164	C₃₁×#126	—	2	2	no	—
165	C₃₁×#126	—	2	1	no	—
166	C₃₁×#126	—	2	2	no	—
167	C₃₁×#126	—	2	1	no	—
168	C₃₁×#125	—	2	2	no	—
169	C₃₁×#125	—	2	1	no	—
170	C₃₁×#125	—	2	2	no	—
171	C₃₁×#125	—	2	2	no	—
172	C₃₁×#125	—	2	1	no	—
173	C₃₁×#125	—	2	2	no	—
174	C₃₁×#125	—	2	2	no	—
175	C₃₁×#125	C₂³	1	2	yes	—
176	C₃₁×#125	C₂³	1	2	yes	—
177	C₃₁×#125	C₂³	1	1	yes	characteristic
178	C₃₁×#125	C₂³	1	2	yes	—
179	C₃₁×#125	C₂³	1	1	yes	characteristic
180	C₃₁×#124	C₂³	1	2	yes	—
181	C₃₁×#124	C₂³	1	1	yes	characteristic
182	C₃₁×#124	C₂³	1	1	yes	characteristic
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	—	2	1	no	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	1	no	—
187	C₃₁×#123	—	2	2	no	—
188	C₃₁×#123	—	2	2	no	—
189	C₃₁×#123	—	2	2	no	—
190	C₃₁×#123	—	2	2	no	—
191	C₃₁×#123	—	2	2	no	—
192	C₃₁×#123	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	—	2	1	no	—
194	C₃₁×C₂²⋊Q₈	—	2	1	no	—
195	C₃₁×C₂²⋊Q₈	—	2	1	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	—	2	1	no	—
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
200	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
202	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	—	2	1	no	—
205	C₃₁×#121	—	2	2	no	—
206	C₃₁×#121	—	2	2	no	—
207	C₃₁×#121	—	2	1	no	—
208	C₃₁×#121	—	2	1	no	—
209	C₃₁×#121	—	2	2	no	—
210	C₃₁×#121	—	2	1	no	—
211	C₃₁×#121	—	2	2	no	—
212	C₃₁×#121	—	2	2	no	—
213	C₃₁×#121	—	2	2	no	—
214	C₃₁×#121	—	2	2	no	—
215	C₃₁×#121	C₂³	1	1	yes	characteristic
216	C₃₁×#121	C₂³	1	2	yes	—
217	C₃₁×#121	C₂³	1	1	yes	characteristic
218	C₃₁×#121	C₂³	1	2	yes	—
219	C₄×Q₈×C₃₁	—	2	1	no	—
220	C₄×Q₈×C₃₁	—	2	1	no	—
221	C₄×Q₈×C₃₁	—	2	1	no	—
222	C₄×Q₈×C₃₁	—	2	1	no	—
223	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
224	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
227	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
228	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
229	C₄×D₄×C₃₁	—	2	1	no	—
230	C₄×D₄×C₃₁	—	2	2	no	—
231	C₄×D₄×C₃₁	—	2	1	no	—
232	C₄×D₄×C₃₁	—	2	1	no	—
233	C₄×D₄×C₃₁	—	2	2	no	—
234	C₄×D₄×C₃₁	—	2	1	no	—
235	C₄×D₄×C₃₁	—	2	2	no	—
236	C₄×D₄×C₃₁	—	2	2	no	—
237	C₄×D₄×C₃₁	—	2	1	no	—
238	C₄×D₄×C₃₁	—	2	2	no	—
239	C₄×D₄×C₃₁	—	2	2	no	—
240	C₄×D₄×C₃₁	—	2	1	no	—
241	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
242	C₄×D₄×C₃₁	D₄	1	2	yes	—
243	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₃₁	C₂³	1	2	yes	—
246	C₄×D₄×C₃₁	C₂³	1	2	yes	—
247	C₄×D₄×C₃₁	C₂³	1	2	yes	—
248	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
249	C₃₁×#117	—	2	2	no	—
250	C₃₁×#117	—	2	1	no	—
251	C₃₁×#117	—	2	2	no	—
252	C₃₁×#117	—	2	1	no	—
253	C₃₁×#117	—	2	2	no	—
254	C₃₁×#117	D₄	1	1	yes	characteristic
255	C₃₁×#117	D₄	1	2	yes	—
256	C₃₁×#117	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
258	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
259	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
260	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
261	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
262	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
264	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
265	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
266	C₃₁×#107	C₂³	1	1	yes	characteristic
267	C₃₁×#107	C₂³	1	1	yes	characteristic
268	C₃₁×#107	C₂³	1	2	yes	—
269	C₃₁×#107	C₂³	1	2	yes	—
270	C₃₁×#106	C₂³	1	1	yes	characteristic
271	C₃₁×#106	C₂³	1	1	yes	characteristic
272	C₃₁×#106	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
275	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
276	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₃₁×#103	C₂³	1	2	yes	—
279	C₃₁×#103	C₂³	1	2	yes	—
280	C₃₁×#103	C₂³	1	2	yes	—
281	C₃₁×#103	C₂³	1	2	yes	—
282	C₃₁×#103	C₂³	1	1	yes	characteristic
283	C₃₁×#103	C₂³	1	1	yes	characteristic
284	C₃₁×#103	C₂³	1	2	yes	—
285	C₃₁×#103	C₂³	1	2	yes	—
286	C₃₁×#103	C₂³	1	2	yes	—
287	C₃₁×#103	C₂³	1	2	yes	—
288	C₃₁×#103	C₂³	1	1	yes	characteristic
289	C₃₁×#103	C₂³	1	1	yes	characteristic
290	C₃₁×#102	C₂³	1	2	yes	—
291	C₃₁×#102	C₂³	1	2	yes	—
292	C₃₁×#102	C₂³	1	2	yes	—
293	C₃₁×#102	C₂³	1	2	yes	—
294	C₃₁×#102	C₂³	1	1	yes	characteristic
295	C₃₁×#102	C₂³	1	1	yes	characteristic
296	C₃₁×#102	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	1	yes	characteristic
302	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
303	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₃₁×#97	C₂³	1	2	yes	—
306	C₃₁×#97	C₂³	1	2	yes	—
307	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	2	yes	—
312	#41×C₃₁	—	4	2	no	—
313	#41×C₃₁	—	4	2	no	—
314	#41×C₃₁	—	4	2	no	—
315	#41×C₃₁	—	4	2	no	—
316	#41×C₃₁	—	4	2	no	—
317	#41×C₃₁	—	4	2	no	—
318	#41×C₃₁	—	4	2	no	—
319	#41×C₃₁	—	4	4	no	—
320	#41×C₃₁	—	4	4	no	—
321	C₂×Q₈×C₃₁	—	2	1	no	—
322	C₂×Q₈×C₃₁	—	2	1	no	—
323	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
325	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
327	C₂×D₄×C₃₁	—	2	2	no	—
328	C₂×D₄×C₃₁	—	2	1	no	—
329	C₂×D₄×C₃₁	—	2	1	no	—
330	C₂×D₄×C₃₁	—	2	2	no	—
331	C₂×D₄×C₃₁	—	2	2	no	—
332	C₂×D₄×C₃₁	—	2	2	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	1	no	—
336	C₂×D₄×C₃₁	—	2	2	no	—
337	C₂×D₄×C₃₁	—	2	1	no	—
338	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
339	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
340	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
341	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
342	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₃₁	—	2	2	no	—
344	C₂²×C₄×C₃₁	—	2	2	no	—
345	C₂²×C₄×C₃₁	—	2	2	no	—
346	C₂²×C₄×C₃₁	—	2	1	no	—
347	C₂²×C₄×C₃₁	—	2	1	no	—
348	C₂²×C₄×C₃₁	—	2	2	no	—
349	C₂²×C₄×C₃₁	—	2	2	no	—
350	C₂²×C₄×C₃₁	—	2	2	no	—
351	C₂²×C₄×C₃₁	—	2	2	no	—
352	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
353	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
354	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
355	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
357	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
358	Q₁₆×C₃₁	—	4	1	no	—
359	Q₁₆×C₃₁	—	4	2	no	—
360	SD₁₆×C₃₁	—	4	1	no	—
361	SD₁₆×C₃₁	—	4	1	no	—
362	SD₁₆×C₃₁	—	4	2	no	—
363	SD₁₆×C₃₁	—	4	2	no	—
364	D₈×C₃₁	—	4	1	no	—
365	D₈×C₃₁	—	4	2	no	—
366	M₁₆×C₃₁	—	4	2	no	—
367	M₁₆×C₃₁	—	4	2	no	—
368	C₂×C₈×C₃₁	—	4	1	no	—
369	C₂×C₈×C₃₁	—	4	1	no	—
370	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
375	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
376	C₄⋊C₄×C₃₁	—	2	2	no	—
377	C₄⋊C₄×C₃₁	—	2	1	no	—
378	C₄⋊C₄×C₃₁	—	2	2	no	—
379	C₄⋊C₄×C₃₁	—	2	1	no	—
380	C₄⋊C₄×C₃₁	—	2	1	no	—
381	C₄⋊C₄×C₃₁	—	2	2	no	—
382	C₄⋊C₄×C₃₁	—	2	2	no	—
383	C₄⋊C₄×C₃₁	—	2	1	no	—
384	C₄⋊C₄×C₃₁	—	2	1	no	—
385	C₄⋊C₄×C₃₁	—	2	2	no	—
386	C₄⋊C₄×C₃₁	—	2	2	no	—
387	C₄⋊C₄×C₃₁	—	2	2	no	—
388	C₄⋊C₄×C₃₁	—	2	2	no	—
389	C₄⋊C₄×C₃₁	—	2	2	no	—
390	C₄⋊C₄×C₃₁	—	2	2	no	—
391	C₄⋊C₄×C₃₁	—	2	1	no	—
392	C₄⋊C₄×C₃₁	—	2	1	no	—
393	C₄⋊C₄×C₃₁	—	2	2	no	—
394	C₄⋊C₄×C₃₁	—	2	1	no	—
395	C₄⋊C₄×C₃₁	—	2	2	no	—
396	C₄⋊C₄×C₃₁	—	2	1	no	—
397	C₄⋊C₄×C₃₁	—	2	1	no	—
398	C₄⋊C₄×C₃₁	—	2	2	no	—
399	C₄⋊C₄×C₃₁	—	2	1	no	—
400	C₄⋊C₄×C₃₁	—	2	1	no	—
401	C₄⋊C₄×C₃₁	—	2	2	no	—
402	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
403	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
409	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
412	C₂²⋊C₄×C₃₁	—	2	2	no	—
413	C₂²⋊C₄×C₃₁	—	2	2	no	—
414	C₂²⋊C₄×C₃₁	—	2	1	no	—
415	C₂²⋊C₄×C₃₁	—	2	2	no	—
416	C₂²⋊C₄×C₃₁	—	2	1	no	—
417	C₂²⋊C₄×C₃₁	—	2	1	no	—
418	C₂²⋊C₄×C₃₁	—	2	1	no	—
419	C₂²⋊C₄×C₃₁	—	2	2	no	—
420	C₂²⋊C₄×C₃₁	—	2	1	no	—
421	C₂²⋊C₄×C₃₁	—	2	2	no	—
422	C₂²⋊C₄×C₃₁	—	2	1	no	—
423	C₂²⋊C₄×C₃₁	—	2	1	no	—
424	C₂²⋊C₄×C₃₁	—	2	2	no	—
425	C₂²⋊C₄×C₃₁	—	2	1	no	—
426	C₂²⋊C₄×C₃₁	—	2	2	no	—
427	C₂²⋊C₄×C₃₁	—	2	2	no	—
428	C₂²⋊C₄×C₃₁	—	2	1	no	—
429	C₂²⋊C₄×C₃₁	—	2	2	no	—
430	C₂²⋊C₄×C₃₁	—	2	1	no	—
431	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
434	C₄²×C₃₁	—	2	2	no	—
435	C₄²×C₃₁	—	2	2	no	—
436	C₄²×C₃₁	—	2	2	no	—
437	C₄²×C₃₁	—	2	1	no	—
438	C₄²×C₃₁	—	2	1	no	—
439	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₃₁	C₂×D₄	1	2	yes	—
441	C₄²×C₃₁	C₂×D₄	1	2	yes	—
442	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
444	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
445	C₄²×C₃₁	C₂⁴	1	2	yes	—
446	#62549	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
447	C₂³×C₃₁	—	2	1	no	—
448	C₂³×C₃₁	—	2	2	no	—
449	C₂³×C₃₁	—	2	1	no	—
450	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
451	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
452	Q₈×C₃₁	—	2	2	no	—
453	Q₈×C₃₁	—	2	1	no	—
454	Q₈×C₃₁	—	2	1	no	—
455	Q₈×C₃₁	—	2	2	no	—
456	Q₈×C₃₁	—	2	1	no	—
457	Q₈×C₃₁	—	2	1	no	—
458	Q₈×C₃₁	—	2	2	no	—
459	Q₈×C₃₁	—	4	2	no	—
460	Q₈×C₃₁	—	8	1	no	—
461	D₄×C₃₁	—	2	2	no	—
462	D₄×C₃₁	—	2	1	no	—
463	D₄×C₃₁	—	2	1	no	—
464	D₄×C₃₁	—	2	2	no	—
465	D₄×C₃₁	—	2	1	no	—
466	D₄×C₃₁	—	2	1	no	—
467	D₄×C₃₁	—	2	2	no	—
468	D₄×C₃₁	—	4	2	no	—
469	D₄×C₃₁	—	4	4	no	—
470	D₄×C₃₁	—	4	4	no	—
471	D₄×C₃₁	—	4	2	no	—
472	D₄×C₃₁	—	8	2	no	—
473	D₄×C₃₁	—	8	1	no	—
474	D₄×C₃₁	—	8	1	no	—
475	D₄×C₃₁	—	8	2	no	—
476	D₄×C₃₁	—	8	1	no	—
477	D₄×C₃₁	—	8	2	no	—
478	D₄×C₃₁	—	8	2	no	—
479	D₄×C₃₁	—	8	2	no	—
480	C₂×C₄×C₃₁	—	2	2	no	—
481	C₂×C₄×C₃₁	—	2	1	no	—
482	C₂×C₄×C₃₁	—	2	1	no	—
483	C₂×C₄×C₃₁	—	2	2	no	—
484	C₂×C₄×C₃₁	—	2	2	no	—
485	C₂×C₄×C₃₁	—	2	1	no	—
486	C₂×C₄×C₃₁	—	2	1	no	—
487	C₂×C₄×C₃₁	—	2	2	no	—
488	C₂×C₄×C₃₁	—	2	2	no	—
489	C₂×C₄×C₃₁	—	2	2	no	—
490	C₂×C₄×C₃₁	—	2	1	no	—
491	C₂×C₄×C₃₁	—	2	1	no	—
492	C₂×C₄×C₃₁	—	2	1	no	—
493	C₂×C₄×C₃₁	—	2	1	no	—
494	C₂×C₄×C₃₁	—	4	2	no	—
495	C₂×C₄×C₃₁	—	4	1	no	—
496	C₂×C₄×C₃₁	—	4	2	no	—
497	C₂×C₄×C₃₁	—	4	4	no	—
498	C₂×C₄×C₃₁	—	4	4	no	—
499	C₂×C₄×C₃₁	—	4	2	no	—
500	C₂×C₄×C₃₁	—	4	2	no	—
501	C₂×C₄×C₃₁	—	8	2	no	—
502	C₂×C₄×C₃₁	—	8	2	no	—
503	C₂×C₄×C₃₁	—	8	2	no	—
504	C₂×C₄×C₃₁	—	8	2	no	—
505	C₂×C₄×C₃₁	—	8	2	no	—
506	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
508	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
512	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
515	C₈×C₃₁	—	2	1	no	—
516	C₈×C₃₁	—	2	1	no	—
517	C₈×C₃₁	—	2	1	no	—
518	C₈×C₃₁	—	2	1	no	—
519	C₈×C₃₁	—	2	2	no	—
520	C₈×C₃₁	—	2	2	no	—
521	#3517	C₂×C₃₁	1	1	yes	characteristic, complemented
522	#3515	C₂×C₃₁	1	1	yes	characteristic, complemented
523	#3374	C₂×C₃₁	1	1	yes	characteristic, complemented
524	#3372	C₂×C₃₁	1	1	yes	characteristic, complemented
525	#3368	C₂×C₃₁	1	1	yes	characteristic, complemented
526	#3366	C₂×C₃₁	1	1	yes	characteristic, complemented
527	#3333	C₂×C₃₁	1	1	yes	characteristic, complemented
528	#3332	C₂×C₃₁	1	1	yes	characteristic, complemented
529	#3331	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#3330	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3317	C₂×C₃₁	1	2	yes	complemented
532	#3315	C₂×C₃₁	1	2	yes	complemented
533	#3309	C₂×C₃₁	1	2	yes	complemented
534	#3307	C₂×C₃₁	1	2	yes	complemented
535	#3233	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3232	C₂×C₃₁	1	2	yes	complemented
537	#3212	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#3212	C₂×C₃₁	1	2	yes	complemented
539	#3183	C₂×C₃₁	1	2	yes	complemented
540	#3168	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3142	C₂×C₃₁	1	2	yes	complemented
542	#3131	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#2965	C₂×C₃₁	1	1	yes	characteristic, complemented
544	C₂²×C₃₁	—	2	2	no	—
545	C₂²×C₃₁	—	2	1	no	—
546	C₂²×C₃₁	—	2	1	no	—
547	C₂²×C₃₁	—	2	2	no	—
548	C₂²×C₃₁	—	2	1	no	—
549	C₂²×C₃₁	—	2	2	no	—
550	C₂²×C₃₁	—	4	1	no	—
551	C₂²×C₃₁	—	4	1	no	—
552	C₂²×C₃₁	—	4	2	no	—
553	C₂²×C₃₁	—	4	2	no	—
554	C₂²×C₃₁	—	4	1	no	—
555	C₂²×C₃₁	—	4	1	no	—
556	C₂²×C₃₁	—	4	2	no	—
557	C₂²×C₃₁	—	4	1	no	—
558	C₂²×C₃₁	—	4	1	no	—
559	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
560	C₄×C₃₁	—	2	1	no	—
561	C₄×C₃₁	—	2	2	no	—
562	C₄×C₃₁	—	2	1	no	—
563	C₄×C₃₁	—	2	1	no	—
564	C₄×C₃₁	—	2	2	no	—
565	C₄×C₃₁	—	2	1	no	—
566	C₄×C₃₁	—	2	2	no	—
567	C₄×C₃₁	—	4	1	no	—
568	C₄×C₃₁	—	4	2	no	—
569	C₄×C₃₁	—	4	1	no	—
570	C₄×C₃₁	—	4	2	no	—
571	C₄×C₃₁	—	4	1	no	—
572	C₄×C₃₁	—	4	1	no	—
573	C₄×C₃₁	—	4	1	no	—
574	C₄×C₃₁	—	4	1	no	—
575	C₄×C₃₁	—	4	2	no	—
576	C₄×C₃₁	#575	1	2	yes	—
577	C₄×C₃₁	#585	1	1	yes	characteristic
578	C₄×C₃₁	#585	1	1	yes	characteristic
579	#557	C₂²×C₃₁	1	1	yes	characteristic
580	#557	C₂²×C₃₁	1	1	yes	characteristic
581	#554	C₂²×C₃₁	1	1	yes	characteristic
582	#554	C₂²×C₃₁	1	1	yes	characteristic
583	#553	—	2	1	no	—
584	#553	—	2	2	no	—
585	#553	C₂²×C₃₁	1	2	yes	—
586	#552	—	2	2	no	—
587	#552	—	2	1	no	—
588	#552	C₂²×C₃₁	1	2	yes	—
589	#550	—	2	1	no	—
590	#550	C₂²×C₃₁	1	1	yes	characteristic
591	#550	C₂²×C₃₁	1	2	yes	—
592	#550	C₂²×C₃₁	1	1	yes	characteristic
593	#547	—	2	1	no	—
594	#547	C₂²×C₃₁	1	1	yes	characteristic
595	#547	C₂²×C₃₁	1	2	yes	—
596	#547	C₂²×C₃₁	1	1	yes	characteristic
597	#541	—	2	1	no	—
598	#540	—	2	1	no	—
599	#540	—	2	2	no	—
600	#539	—	2	2	no	—
601	#533	C₂²×C₃₁	1	1	yes	characteristic
602	#532	C₂²×C₃₁	1	1	yes	characteristic
603	#532	C₂²×C₃₁	1	2	yes	—
604	#529	C₂²×C₃₁	1	1	yes	characteristic
605	#529	C₂²×C₃₁	1	1	yes	characteristic
606	#529	C₂²×C₃₁	1	2	yes	—
607	#529	C₂²×C₃₁	1	2	yes	—
608	C₂×#125	C₂²×C₃₁	1	2	yes	—
609	#520	—	2	1	no	—
610	#520	—	2	1	no	—
611	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
612	#499	C₂²×C₃₁	1	1	yes	characteristic
613	#499	C₂²×C₃₁	1	2	yes	—
614	#495	C₂²×C₃₁	1	1	yes	characteristic
615	#495	C₂²×C₃₁	1	2	yes	—
616	#491	C₂²×C₃₁	1	2	yes	—
617	#491	C₂²×C₃₁	1	2	yes	—
618	#490	C₂²×C₃₁	1	2	yes	—
619	#490	C₂²×C₃₁	1	2	yes	—
620	#488	C₂²×C₃₁	1	2	yes	—
621	#488	C₂²×C₃₁	1	2	yes	—
622	#488	C₂²×C₃₁	1	1	yes	characteristic
623	#488	C₂²×C₃₁	1	2	yes	—
624	#488	C₂²×C₃₁	1	2	yes	—
625	#488	C₂²×C₃₁	1	1	yes	characteristic
626	#487	C₂²×C₃₁	1	1	yes	characteristic
627	#487	C₂²×C₃₁	1	1	yes	characteristic
628	#486	C₂²×C₃₁	1	1	yes	characteristic
629	#486	C₂²×C₃₁	1	1	yes	characteristic
630	#485	C₂²×C₃₁	1	2	yes	—
631	#484	C₂²×C₃₁	1	2	yes	—
632	#483	C₂²×C₃₁	1	2	yes	—
633	#482	C₂²×C₃₁	1	2	yes	—
634	#481	C₂²×C₃₁	1	2	yes	—
635	#480	C₂²×C₃₁	1	2	yes	—
636	#479	C₂²×C₃₁	1	2	yes	—
637	#479	C₂²×C₃₁	1	2	yes	—
638	#478	C₂²×C₃₁	1	2	yes	—
639	#478	C₂²×C₃₁	1	2	yes	—
640	#477	C₂²×C₃₁	1	1	yes	characteristic
641	#476	C₂²×C₃₁	1	1	yes	characteristic
642	#475	C₂²×C₃₁	1	1	yes	characteristic
643	#474	C₂²×C₃₁	1	1	yes	characteristic
644	#470	C₂²×C₃₁	1	2	yes	—
645	#469	C₂²×C₃₁	1	2	yes	—
646	#468	C₂²×C₃₁	1	2	yes	—
647	#468	C₂²×C₃₁	1	2	yes	—
648	#467	C₂²×C₃₁	1	1	yes	characteristic
649	#466	C₂²×C₃₁	1	1	yes	characteristic
650	#465	C₂²×C₃₁	1	1	yes	characteristic
651	#465	C₂²×C₃₁	1	1	yes	characteristic
652	#462	C₂²×C₃₁	1	1	yes	characteristic
653	#462	C₂²×C₃₁	1	2	yes	—
654	#461	C₂²×C₃₁	1	1	yes	characteristic
655	#461	C₂²×C₃₁	1	2	yes	—
656	#460	C₂²×C₃₁	1	1	yes	characteristic
657	#460	C₂²×C₃₁	1	2	yes	—
658	#459	C₂²×C₃₁	1	1	yes	characteristic
659	#459	C₂²×C₃₁	1	2	yes	—
660	#452	C₂²×C₃₁	1	2	yes	—
661	#452	C₂²×C₃₁	1	2	yes	—
662	#452	C₂²×C₃₁	1	2	yes	—
663	#449	C₂²×C₃₁	1	2	yes	—
664	#449	C₂²×C₃₁	1	2	yes	—
665	#449	C₂²×C₃₁	1	2	yes	—
666	#446	C₂²×C₃₁	1	1	yes	characteristic
667	#446	C₂²×C₃₁	1	1	yes	characteristic
668	#442	C₂²×C₃₁	1	2	yes	—
669	#441	C₂²×C₃₁	1	2	yes	—
670	#440	C₂²×C₃₁	1	2	yes	—
671	#440	C₂²×C₃₁	1	2	yes	—
672	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
673	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
674	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
675	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
676	#436	C₂²×C₃₁	1	1	yes	characteristic
677	#436	C₂²×C₃₁	1	1	yes	characteristic
678	#435	C₂²×C₃₁	1	2	yes	—
679	#435	C₂²×C₃₁	1	2	yes	—
680	#431	C₂²×C₃₁	1	2	yes	—
681	#431	C₂²×C₃₁	1	1	yes	characteristic
682	#417	C₂²×C₃₁	1	2	yes	—
683	#417	C₂²×C₃₁	1	2	yes	—
684	#417	C₂²×C₃₁	1	2	yes	—
685	#417	C₂²×C₃₁	1	2	yes	—
686	#416	C₂²×C₃₁	1	2	yes	—
687	#416	C₂²×C₃₁	1	2	yes	—
688	C₄×M₁₆	C₂²×C₃₁	1	2	yes	—
689	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
690	C₂×C₃₁	—	4	2	no	—
691	C₂×C₃₁	—	4	1	no	—
692	C₂×C₃₁	—	8	1	no	—
693	C₂×C₃₁	—	8	2	no	—
694	C₂×C₃₁	—	8	1	no	—
695	C₂×C₃₁	#3500	1	1	yes	characteristic
696	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
697	C₂×C₃₁	#3584	1	1	yes	characteristic
698	C₂×#41	—	2	1	no	—
699	C₂×#41	—	2	1	no	—
700	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
701	C₂×#41	C₂³×C₃₁	1	2	yes	—
702	C₂×#41	C₂³×C₃₁	1	2	yes	—
703	C₂×#41	C₂³×C₃₁	1	2	yes	—
704	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
705	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
706	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
707	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
708	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
709	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
710	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
711	C₂×D₈	C₂³×C₃₁	1	2	yes	—
712	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
713	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
714	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
715	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
716	C₄⋊Q₈	—	2	1	no	—
717	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
718	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
719	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
720	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
721	#127	—	2	1	no	—
722	#127	—	2	2	no	—
723	#127	C₂³×C₃₁	1	1	yes	characteristic
724	#127	C₂³×C₃₁	1	2	yes	—
725	#126	—	2	2	no	—
726	#126	—	2	2	no	—
727	#126	—	2	2	no	—
728	#126	—	2	1	no	—
729	#126	—	2	2	no	—
730	#126	—	2	1	no	—
731	#125	—	2	2	no	—
732	#125	—	2	1	no	—
733	#125	—	2	2	no	—
734	#125	—	2	2	no	—
735	#125	—	2	1	no	—
736	#125	—	2	2	no	—
737	#125	—	2	2	no	—
738	#125	C₂³×C₃₁	1	1	yes	characteristic
739	#125	C₂³×C₃₁	1	2	yes	—
740	#125	C₂³×C₃₁	1	2	yes	—
741	#125	C₂³×C₃₁	1	2	yes	—
742	#125	C₂³×C₃₁	1	1	yes	characteristic
743	#124	C₂³×C₃₁	1	1	yes	characteristic
744	#124	C₂³×C₃₁	1	1	yes	characteristic
745	#124	C₂³×C₃₁	1	2	yes	—
746	#123	—	2	2	no	—
747	#123	—	2	1	no	—
748	#123	—	2	2	no	—
749	#123	—	2	1	no	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	C₂²⋊Q₈	—	2	1	no	—
757	C₂²⋊Q₈	—	2	1	no	—
758	C₂²⋊Q₈	—	2	1	no	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	—	2	1	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
763	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
764	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
765	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
766	#121	—	2	2	no	—
767	#121	—	2	1	no	—
768	#121	—	2	2	no	—
769	#121	—	2	2	no	—
770	#121	—	2	1	no	—
771	#121	—	2	1	no	—
772	#121	—	2	2	no	—
773	#121	—	2	1	no	—
774	#121	—	2	2	no	—
775	#121	—	2	2	no	—
776	#121	—	2	2	no	—
777	#121	—	2	2	no	—
778	#121	C₂³×C₃₁	1	2	yes	—
779	#121	C₂³×C₃₁	1	1	yes	characteristic
780	#121	C₂³×C₃₁	1	2	yes	—
781	#121	C₂³×C₃₁	1	1	yes	characteristic
782	C₄×Q₈	—	2	1	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	—	2	1	no	—
786	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
787	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
788	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
789	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
790	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
791	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
805	C₄×D₄	D₄×C₃₁	1	2	yes	—
806	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
807	C₄×D₄	C₂³×C₃₁	1	2	yes	—
808	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
809	C₄×D₄	C₂³×C₃₁	1	2	yes	—
810	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
811	C₄×D₄	C₂³×C₃₁	1	2	yes	—
812	#117	—	2	2	no	—
813	#117	—	2	1	no	—
814	#117	—	2	2	no	—
815	#117	—	2	1	no	—
816	#117	—	2	2	no	—
817	#117	D₄×C₃₁	1	1	yes	characteristic
818	#117	D₄×C₃₁	1	2	yes	—
819	#117	C₂³×C₃₁	1	2	yes	—
820	C₂×C₄⋊C₄	—	2	2	no	—
821	C₂×C₄⋊C₄	—	2	2	no	—
822	C₂×C₄⋊C₄	—	2	1	no	—
823	C₂×C₄⋊C₄	—	2	2	no	—
824	C₂×C₄⋊C₄	—	2	1	no	—
825	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
826	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
827	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
828	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
829	#107	C₂³×C₃₁	1	1	yes	characteristic
830	#107	C₂³×C₃₁	1	1	yes	characteristic
831	#107	C₂³×C₃₁	1	2	yes	—
832	#107	C₂³×C₃₁	1	2	yes	—
833	#106	C₂³×C₃₁	1	1	yes	characteristic
834	#106	C₂³×C₃₁	1	1	yes	characteristic
835	#106	C₂³×C₃₁	1	2	yes	—
836	#106	C₂³×C₃₁	1	2	yes	—
837	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
838	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
839	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
840	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
841	#103	C₂³×C₃₁	1	2	yes	—
842	#103	C₂³×C₃₁	1	2	yes	—
843	#103	C₂³×C₃₁	1	2	yes	—
844	#103	C₂³×C₃₁	1	2	yes	—
845	#103	C₂³×C₃₁	1	1	yes	characteristic
846	#103	C₂³×C₃₁	1	1	yes	characteristic
847	#103	C₂³×C₃₁	1	2	yes	—
848	#103	C₂³×C₃₁	1	2	yes	—
849	#103	C₂³×C₃₁	1	2	yes	—
850	#103	C₂³×C₃₁	1	2	yes	—
851	#103	C₂³×C₃₁	1	1	yes	characteristic
852	#103	C₂³×C₃₁	1	1	yes	characteristic
853	#102	C₂³×C₃₁	1	2	yes	—
854	#102	C₂³×C₃₁	1	2	yes	—
855	#102	C₂³×C₃₁	1	2	yes	—
856	#102	C₂³×C₃₁	1	2	yes	—
857	#102	C₂³×C₃₁	1	1	yes	characteristic
858	#102	C₂³×C₃₁	1	1	yes	characteristic
859	#102	C₂³×C₃₁	1	2	yes	—
860	#102	C₂³×C₃₁	1	2	yes	—
861	#102	C₂³×C₃₁	1	2	yes	—
862	#102	C₂³×C₃₁	1	2	yes	—
863	#102	C₂³×C₃₁	1	1	yes	characteristic
864	#102	C₂³×C₃₁	1	1	yes	characteristic
865	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
866	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
867	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
868	#97	C₂³×C₃₁	1	2	yes	—
869	#97	C₂³×C₃₁	1	2	yes	—
870	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
871	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
872	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
873	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
874	C₄×C₈	C₂³×C₃₁	1	2	yes	—
875	C₃₁	#62549	1	1	yes	characteristic, direct product factor, Sylow
876	#41	—	4	2	no	—
877	#41	—	4	2	no	—
878	#41	—	4	2	no	—
879	#41	—	4	2	no	—
880	#41	—	4	2	no	—
881	#41	—	4	2	no	—
882	#41	—	4	2	no	—
883	#41	—	4	4	no	—
884	#41	—	4	4	no	—
885	C₂×Q₈	—	2	1	no	—
886	C₂×Q₈	—	2	1	no	—
887	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
888	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
889	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
890	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
891	C₂×D₄	—	2	2	no	—
892	C₂×D₄	—	2	1	no	—
893	C₂×D₄	—	2	1	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	1	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
903	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
904	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
905	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
906	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
917	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
918	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
919	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
920	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
921	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
922	Q₁₆	—	4	1	no	—
923	Q₁₆	—	4	2	no	—
924	SD₁₆	—	4	1	no	—
925	SD₁₆	—	4	1	no	—
926	SD₁₆	—	4	2	no	—
927	SD₁₆	—	4	2	no	—
928	D₈	—	4	1	no	—
929	D₈	—	4	2	no	—
930	M₁₆	—	4	2	no	—
931	M₁₆	—	4	2	no	—
932	C₂×C₈	—	4	1	no	—
933	C₂×C₈	—	4	1	no	—
934	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
935	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
936	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
937	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
938	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
939	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
967	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
968	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
969	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
970	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
971	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
972	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
973	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
974	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
975	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
996	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
997	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	2	no	—
1000	C₄²	—	2	2	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	1	no	—
1003	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1004	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1005	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1006	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1007	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1008	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1009	C₄²	C₂⁴×C₃₁	1	2	yes	—
1010	C₂³	—	2	1	no	—
1011	C₂³	—	2	2	no	—
1012	C₂³	—	2	1	no	—
1013	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1014	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1015	Q₈	—	2	2	no	—
1016	Q₈	—	2	1	no	—
1017	Q₈	—	2	1	no	—
1018	Q₈	—	2	2	no	—
1019	Q₈	—	2	1	no	—
1020	Q₈	—	2	1	no	—
1021	Q₈	—	2	2	no	—
1022	Q₈	—	4	2	no	—
1023	Q₈	—	8	1	no	—
1024	D₄	—	2	2	no	—
1025	D₄	—	2	1	no	—
1026	D₄	—	2	1	no	—
1027	D₄	—	2	2	no	—
1028	D₄	—	2	1	no	—
1029	D₄	—	2	1	no	—
1030	D₄	—	2	2	no	—
1031	D₄	—	4	2	no	—
1032	D₄	—	4	4	no	—
1033	D₄	—	4	4	no	—
1034	D₄	—	4	2	no	—
1035	D₄	—	8	2	no	—
1036	D₄	—	8	1	no	—
1037	D₄	—	8	1	no	—
1038	D₄	—	8	2	no	—
1039	D₄	—	8	1	no	—
1040	D₄	—	8	2	no	—
1041	D₄	—	8	2	no	—
1042	D₄	—	8	2	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	4	2	no	—
1058	C₂×C₄	—	4	1	no	—
1059	C₂×C₄	—	4	2	no	—
1060	C₂×C₄	—	4	4	no	—
1061	C₂×C₄	—	4	4	no	—
1062	C₂×C₄	—	4	2	no	—
1063	C₂×C₄	—	4	2	no	—
1064	C₂×C₄	—	8	2	no	—
1065	C₂×C₄	—	8	2	no	—
1066	C₂×C₄	—	8	2	no	—
1067	C₂×C₄	—	8	2	no	—
1068	C₂×C₄	—	8	2	no	—
1069	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1070	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1071	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1072	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1073	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1074	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1075	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1076	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1077	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1078	C₈	—	2	1	no	—
1079	C₈	—	2	1	no	—
1080	C₈	—	2	1	no	—
1081	C₈	—	2	1	no	—
1082	C₈	—	2	2	no	—
1083	C₈	—	2	2	no	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	2	2	no	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	2	2	no	—
1089	C₂²	—	2	1	no	—
1090	C₂²	—	4	2	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	2	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	4	1	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	4	2	no	—
1099	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1100	C₄	—	2	1	no	—
1101	C₄	—	2	2	no	—
1102	C₄	—	2	1	no	—
1103	C₄	—	2	2	no	—
1104	C₄	—	2	1	no	—
1105	C₄	—	2	2	no	—
1106	C₄	—	2	1	no	—
1107	C₄	—	4	2	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	2	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	2	no	—
1115	C₄	—	4	1	no	—
1116	C₄	C₃₁×#575	1	2	yes	—
1117	C₄	C₃₁×#585	1	1	yes	characteristic
1118	C₄	C₃₁×#585	1	1	yes	characteristic
1119	C₂	—	4	1	no	—
1120	C₂	—	4	2	no	—
1121	C₂	—	8	2	no	—
1122	C₂	—	8	1	no	—
1123	C₂	—	8	1	no	—
1124	C₂	C₃₁×#3500	1	1	yes	characteristic
1125	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1126	C₂	C₃₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3517	C₂	semidirect
2. C₃₁×#3515	C₂	semidirect
3. C₃₁×#3374	C₂	semidirect
4. C₃₁×#3372	C₂	semidirect
5. C₃₁×#3368	C₂	semidirect
6. C₃₁×#3366	C₂	semidirect
7. C₃₁×#3333	C₂	semidirect
8. C₃₁×#3332	C₂	semidirect
9. C₃₁×#3331	C₂	semidirect
10. C₃₁×#3330	C₂	semidirect
11. C₃₁×#3317	C₂	semidirect
12. C₃₁×#3315	C₂	semidirect
13. C₃₁×#3309	C₂	semidirect
14. C₃₁×#3307	C₂	semidirect
15. C₃₁×#3233	C₂	semidirect
16. C₃₁×#3232	C₂	semidirect
17. C₃₁×#3212	C₂	semidirect
18. C₃₁×#3212	C₂	semidirect
19. C₃₁×#3183	C₂	semidirect
20. C₃₁×#3168	C₂	semidirect
21. C₃₁×#3142	C₂	semidirect
22. C₃₁×#3131	C₂	semidirect
23. C₃₁×#2965	C₂	semidirect
446. #62549	C₃₁	direct (N × H)
521. #3517	C₂×C₃₁	semidirect
522. #3515	C₂×C₃₁	semidirect
523. #3374	C₂×C₃₁	semidirect
524. #3372	C₂×C₃₁	semidirect
525. #3368	C₂×C₃₁	semidirect
526. #3366	C₂×C₃₁	semidirect
527. #3333	C₂×C₃₁	semidirect
528. #3332	C₂×C₃₁	semidirect
529. #3331	C₂×C₃₁	semidirect
530. #3330	C₂×C₃₁	semidirect
531. #3317	C₂×C₃₁	semidirect
532. #3315	C₂×C₃₁	semidirect
533. #3309	C₂×C₃₁	semidirect
534. #3307	C₂×C₃₁	semidirect
535. #3233	C₂×C₃₁	semidirect
536. #3232	C₂×C₃₁	semidirect
537. #3212	C₂×C₃₁	semidirect
538. #3212	C₂×C₃₁	semidirect
539. #3183	C₂×C₃₁	semidirect
540. #3168	C₂×C₃₁	semidirect
541. #3142	C₂×C₃₁	semidirect
542. #3131	C₂×C₃₁	semidirect
543. #2965	C₂×C₃₁	semidirect
875. C₃₁	#62549	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#3517	2
C₃₁×#3515	2
C₃₁×#3374	2
C₃₁×#3372	2
C₃₁×#3368	2
C₃₁×#3366	2
C₃₁×#3333	2
C₃₁×#3332	2
C₃₁×#3331	2
C₃₁×#3330	2
C₃₁×#3317	2
C₃₁×#3315	2
C₃₁×#3309	2
C₃₁×#3307	2
C₃₁×#3233	2
C₃₁×#3232	2
C₃₁×#3212	2
C₃₁×#3183	2
C₃₁×#3168	2
C₃₁×#3142	2
C₃₁×#3131	2
C₃₁×#2965	2
#62549	31

Subgroups — C31×#62549 #21519308

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62549 #21519308