Subgroups — C₃₁×#33221 #21489980

Order 7936.

706 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3080	C₂	1	2	yes	maximal
3	C₄×C₃₁×#131	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1998	C₂	1	2	yes	maximal, complemented
5	C₃₁×#1952	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1951	C₂	1	2	yes	maximal, complemented
7	C₃₁×#1848	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1816	C₂	1	2	yes	maximal
9	C₃₁×#1815	C₂	1	2	yes	maximal
10	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
11	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
12	C₂×C₃₁×#125	C₂²	1	2	yes	—
13	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
14	C₃₁×#499	—	2	1	no	—
15	C₃₁×#499	—	2	1	no	—
16	C₃₁×#499	—	2	1	no	—
17	C₃₁×#499	—	2	1	no	—
18	C₃₁×#479	—	2	4	no	—
19	C₃₁×#478	—	2	4	no	—
20	C₂×C₃₁×#108	C₂²	1	2	yes	—
21	C₂×C₃₁×#108	C₂²	1	2	yes	—
22	C₃₁×#428	C₂²	1	4	yes	—
23	C₂×C₃₁×#107	C₂²	1	2	yes	—
24	C₂×C₃₁×#106	C₂²	1	2	yes	—
25	C₃₁×#423	C₂²	1	2	yes	—
26	C₃₁×#417	C₂²	1	4	yes	—
27	C₃₁×#405	—	2	1	no	—
28	C₃₁×#405	—	2	1	no	—
29	C₃₁×#405	C₂²	1	1	yes	characteristic
30	C₃₁×#405	C₂²	1	1	yes	characteristic
31	C₄×M₁₆×C₃₁	—	2	1	no	—
32	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₃₁	—	2	1	no	—
34	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
35	C₃₁×#343	C₂²	1	4	yes	—
36	C₃₁×#343	C₂²	1	4	yes	—
37	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
38	C₃₁×#131	—	2	2	no	—
39	C₃₁×#131	—	2	2	no	—
40	C₃₁×#131	Q₈	1	4	yes	—
41	C₃₁×#131	Q₈	1	4	yes	—
42	C₂×M₁₆×C₃₁	—	2	1	no	—
43	C₂×M₁₆×C₃₁	—	2	1	no	—
44	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
45	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₃₁	—	2	1	no	—
48	C₂²×C₈×C₃₁	—	2	1	no	—
49	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
51	C₃₁×#125	—	2	4	no	—
52	C₃₁×#125	—	2	2	no	—
53	C₃₁×#125	—	2	2	no	—
54	C₄×Q₈×C₃₁	D₄	1	2	yes	—
55	C₄×D₄×C₃₁	—	2	2	no	—
56	C₄×D₄×C₃₁	D₄	1	2	yes	—
57	C₃₁×#117	—	2	1	no	—
58	C₃₁×#117	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
60	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
61	C₂×C₄²×C₃₁	—	2	1	no	—
62	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
63	C₃₁×#108	—	2	4	no	—
64	C₃₁×#108	—	2	4	no	—
65	C₃₁×#107	—	2	2	no	—
66	C₃₁×#107	—	2	2	no	—
67	C₃₁×#107	—	2	4	no	—
68	C₃₁×#106	—	2	2	no	—
69	C₃₁×#106	—	2	2	no	—
70	C₃₁×#106	—	2	4	no	—
71	C₃₁×C₄⋊C₈	—	2	4	no	—
72	C₃₁×#103	—	2	4	no	—
73	C₃₁×#102	—	2	4	no	—
74	C₃₁×#97	—	2	1	no	—
75	C₃₁×#97	—	2	1	no	—
76	C₃₁×#97	—	2	1	no	—
77	C₄×C₈×C₃₁	—	2	1	no	—
78	C₄×C₈×C₃₁	—	2	1	no	—
79	C₄×C₈×C₃₁	—	2	1	no	—
80	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
81	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
82	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
83	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
84	#41×C₃₁	—	2	1	no	—
85	#41×C₃₁	—	2	1	no	—
86	#41×C₃₁	C₂×Q₈	1	2	yes	—
87	#41×C₃₁	C₂×Q₈	1	2	yes	—
88	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
89	C₂×D₄×C₃₁	—	2	1	no	—
90	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₃₁	—	2	1	no	—
92	C₂²×C₄×C₃₁	—	2	2	no	—
93	C₂²×C₄×C₃₁	—	2	4	no	—
94	C₂²×C₄×C₃₁	#41	1	2	yes	—
95	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
96	M₁₆×C₃₁	—	2	1	no	—
97	M₁₆×C₃₁	—	2	1	no	—
98	M₁₆×C₃₁	—	2	4	no	—
99	M₁₆×C₃₁	—	2	4	no	—
100	M₁₆×C₃₁	—	2	4	no	—
101	M₁₆×C₃₁	—	2	4	no	—
102	M₁₆×C₃₁	C₂×Q₈	1	2	yes	—
103	M₁₆×C₃₁	C₂×Q₈	1	2	yes	—
104	C₂×C₈×C₃₁	—	2	1	no	—
105	C₂×C₈×C₃₁	—	2	1	no	—
106	C₂×C₈×C₃₁	—	2	4	no	—
107	C₂×C₈×C₃₁	—	2	4	no	—
108	C₂×C₈×C₃₁	—	2	4	no	—
109	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
110	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₃₁	C₂×Q₈	1	2	yes	—
114	C₂×C₈×C₃₁	C₂×Q₈	1	2	yes	—
115	C₂×C₈×C₃₁	#41	1	2	yes	—
116	C₂×C₈×C₃₁	#41	1	2	yes	—
117	C₄⋊C₄×C₃₁	—	2	2	no	—
118	C₄⋊C₄×C₃₁	—	2	4	no	—
119	C₄⋊C₄×C₃₁	—	2	4	no	—
120	C₄⋊C₄×C₃₁	—	4	4	no	—
121	C₄⋊C₄×C₃₁	—	4	4	no	—
122	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
123	C₂²⋊C₄×C₃₁	—	2	1	no	—
124	C₂²⋊C₄×C₃₁	—	2	2	no	—
125	C₄²×C₃₁	—	2	2	no	—
126	C₄²×C₃₁	—	2	1	no	—
127	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₃₁	C₂×D₄	1	2	yes	—
130	#33221	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂³×C₃₁	—	2	1	no	—
132	C₂³×C₃₁	C₂×#41	1	1	yes	characteristic
133	Q₈×C₃₁	—	2	1	no	—
134	Q₈×C₃₁	C₄⋊Q₈	1	2	yes	—
135	D₄×C₃₁	—	2	2	no	—
136	D₄×C₃₁	—	2	2	no	—
137	D₄×C₃₁	—	2	1	no	—
138	D₄×C₃₁	C₄⋊Q₈	1	2	yes	—
139	C₂×C₄×C₃₁	—	2	1	no	—
140	C₂×C₄×C₃₁	—	2	2	no	—
141	C₂×C₄×C₃₁	—	2	2	no	—
142	C₂×C₄×C₃₁	—	2	2	no	—
143	C₂×C₄×C₃₁	—	4	2	no	—
144	C₂×C₄×C₃₁	—	4	4	no	—
145	C₂×C₄×C₃₁	—	4	4	no	—
146	C₂×C₄×C₃₁	—	8	4	no	—
147	C₂×C₄×C₃₁	#121	1	2	yes	—
148	C₂×C₄×C₃₁	#121	1	2	yes	—
149	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
150	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₃₁	C₂²×Q₈	1	1	yes	characteristic
152	C₂×C₄×C₃₁	C₂²×Q₈	1	1	yes	characteristic
153	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
154	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
155	C₈×C₃₁	—	2	2	no	—
156	C₈×C₃₁	—	2	2	no	—
157	C₈×C₃₁	—	4	4	no	—
158	C₈×C₃₁	C₂²⋊Q₈	1	2	yes	—
159	C₈×C₃₁	C₂²⋊Q₈	1	2	yes	—
160	C₈×C₃₁	C₂²⋊Q₈	1	2	yes	—
161	C₈×C₃₁	C₂²⋊Q₈	1	2	yes	—
162	C₂×#499	C₂×C₃₁	1	1	yes	characteristic, complemented
163	#3080	C₂×C₃₁	1	2	yes	—
164	C₄×#131	C₂×C₃₁	1	1	yes	characteristic
165	#1998	C₂×C₃₁	1	2	yes	complemented
166	#1952	C₂×C₃₁	1	2	yes	complemented
167	#1951	C₂×C₃₁	1	2	yes	complemented
168	#1848	C₂×C₃₁	1	1	yes	characteristic, complemented
169	#1816	C₂×C₃₁	1	2	yes	—
170	#1815	C₂×C₃₁	1	2	yes	—
171	C₂²×C₃₁	—	2	2	no	—
172	C₂²×C₃₁	—	2	2	no	—
173	C₂²×C₃₁	—	4	2	no	—
174	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
175	C₂²×C₃₁	#533	1	1	yes	characteristic
176	C₂²×C₃₁	#533	1	1	yes	characteristic
177	C₄×C₃₁	—	2	2	no	—
178	C₄×C₃₁	—	2	2	no	—
179	C₄×C₃₁	—	2	2	no	—
180	C₄×C₃₁	—	4	2	no	—
181	C₄×C₃₁	—	8	4	no	—
182	C₄×C₃₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
183	C₄×C₃₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
184	C₄×C₃₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
185	C₄×C₃₁	#532	1	1	yes	characteristic
186	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
187	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
188	C₂×#125	C₂²×C₃₁	1	2	yes	—
189	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
190	#499	—	2	1	no	—
191	#499	—	2	1	no	—
192	#499	—	2	1	no	—
193	#499	—	2	1	no	—
194	#479	—	2	4	no	—
195	#478	—	2	4	no	—
196	C₂×#108	C₂²×C₃₁	1	2	yes	—
197	C₂×#108	C₂²×C₃₁	1	2	yes	—
198	#428	C₂²×C₃₁	1	4	yes	—
199	C₂×#107	C₂²×C₃₁	1	2	yes	—
200	C₂×#106	C₂²×C₃₁	1	2	yes	—
201	#423	C₂²×C₃₁	1	2	yes	—
202	#417	C₂²×C₃₁	1	4	yes	—
203	#405	—	2	1	no	—
204	#405	—	2	1	no	—
205	#405	C₂²×C₃₁	1	1	yes	characteristic
206	#405	C₂²×C₃₁	1	1	yes	characteristic
207	C₄×M₁₆	—	2	1	no	—
208	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
209	C₂×C₄×C₈	—	2	1	no	—
210	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
211	#343	C₂²×C₃₁	1	4	yes	—
212	#343	C₂²×C₃₁	1	4	yes	—
213	C₂×C₃₁	—	2	1	no	—
214	C₂×C₃₁	—	2	1	no	—
215	C₂×C₃₁	—	4	2	no	—
216	C₂×C₃₁	#2857	1	1	yes	characteristic
217	C₂×C₃₁	#3067	1	2	yes	—
218	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
219	#131	—	2	2	no	—
220	#131	—	2	2	no	—
221	#131	Q₈×C₃₁	1	4	yes	—
222	#131	Q₈×C₃₁	1	4	yes	—
223	C₂×M₁₆	—	2	1	no	—
224	C₂×M₁₆	—	2	1	no	—
225	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
226	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
227	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
228	C₂²×C₈	—	2	1	no	—
229	C₂²×C₈	—	2	1	no	—
230	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
231	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
232	#125	—	2	4	no	—
233	#125	—	2	2	no	—
234	#125	—	2	2	no	—
235	C₄×Q₈	D₄×C₃₁	1	2	yes	—
236	C₄×D₄	—	2	2	no	—
237	C₄×D₄	D₄×C₃₁	1	2	yes	—
238	#117	—	2	1	no	—
239	#117	C₂³×C₃₁	1	1	yes	characteristic
240	C₂×C₄⋊C₄	—	2	4	no	—
241	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
242	C₂×C₄²	—	2	1	no	—
243	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
244	#108	—	2	4	no	—
245	#108	—	2	4	no	—
246	#107	—	2	2	no	—
247	#107	—	2	2	no	—
248	#107	—	2	4	no	—
249	#106	—	2	2	no	—
250	#106	—	2	2	no	—
251	#106	—	2	4	no	—
252	C₄⋊C₈	—	2	4	no	—
253	#103	—	2	4	no	—
254	#102	—	2	4	no	—
255	#97	—	2	1	no	—
256	#97	—	2	1	no	—
257	#97	—	2	1	no	—
258	C₄×C₈	—	2	1	no	—
259	C₄×C₈	—	2	1	no	—
260	C₄×C₈	—	2	1	no	—
261	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
262	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
263	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
264	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
265	C₃₁	#33221	1	1	yes	characteristic, direct product factor, Sylow
266	#41	—	2	1	no	—
267	#41	—	2	1	no	—
268	#41	C₂×Q₈×C₃₁	1	2	yes	—
269	#41	C₂×Q₈×C₃₁	1	2	yes	—
270	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
271	C₂×D₄	—	2	1	no	—
272	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	#41×C₃₁	1	2	yes	—
277	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
278	M₁₆	—	2	1	no	—
279	M₁₆	—	2	1	no	—
280	M₁₆	—	2	4	no	—
281	M₁₆	—	2	4	no	—
282	M₁₆	—	2	4	no	—
283	M₁₆	—	2	4	no	—
284	M₁₆	C₂×Q₈×C₃₁	1	2	yes	—
285	M₁₆	C₂×Q₈×C₃₁	1	2	yes	—
286	C₂×C₈	—	2	1	no	—
287	C₂×C₈	—	2	1	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	—	2	4	no	—
291	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
292	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
293	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
294	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
295	C₂×C₈	C₂×Q₈×C₃₁	1	2	yes	—
296	C₂×C₈	C₂×Q₈×C₃₁	1	2	yes	—
297	C₂×C₈	#41×C₃₁	1	2	yes	—
298	C₂×C₈	#41×C₃₁	1	2	yes	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	4	no	—
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	—	4	4	no	—
303	C₄⋊C₄	—	4	4	no	—
304	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
305	C₂²⋊C₄	—	2	1	no	—
306	C₂²⋊C₄	—	2	2	no	—
307	C₄²	—	2	2	no	—
308	C₄²	—	2	1	no	—
309	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
310	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
311	C₄²	C₂×D₄×C₃₁	1	2	yes	—
312	C₂³	—	2	1	no	—
313	C₂³	C₂×#41×C₃₁	1	1	yes	characteristic
314	Q₈	—	2	1	no	—
315	Q₈	C₃₁×C₄⋊Q₈	1	2	yes	—
316	D₄	—	2	2	no	—
317	D₄	—	2	2	no	—
318	D₄	—	2	1	no	—
319	D₄	C₃₁×C₄⋊Q₈	1	2	yes	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	8	4	no	—
328	C₂×C₄	C₃₁×#121	1	2	yes	—
329	C₂×C₄	C₃₁×#121	1	2	yes	—
330	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
331	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
332	C₂×C₄	C₂²×Q₈×C₃₁	1	1	yes	characteristic
333	C₂×C₄	C₂²×Q₈×C₃₁	1	1	yes	characteristic
334	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
335	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
336	C₈	—	2	2	no	—
337	C₈	—	2	2	no	—
338	C₈	—	4	4	no	—
339	C₈	C₃₁×C₂²⋊Q₈	1	2	yes	—
340	C₈	C₃₁×C₂²⋊Q₈	1	2	yes	—
341	C₈	C₃₁×C₂²⋊Q₈	1	2	yes	—
342	C₈	C₃₁×C₂²⋊Q₈	1	2	yes	—
343	C₂²	—	2	2	no	—
344	C₂²	—	2	2	no	—
345	C₂²	—	4	2	no	—
346	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
347	C₂²	C₃₁×#533	1	1	yes	characteristic
348	C₂²	C₃₁×#533	1	1	yes	characteristic
349	C₄	—	2	2	no	—
350	C₄	—	2	2	no	—
351	C₄	—	2	2	no	—
352	C₄	—	4	2	no	—
353	C₄	—	8	4	no	—
354	C₄	C₂×C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
355	C₄	C₂×C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
356	C₄	C₂×C₃₁×C₄⋊Q₈	1	1	yes	characteristic
357	C₄	C₃₁×#532	1	1	yes	characteristic
358	C₂	—	2	1	no	—
359	C₂	—	2	1	no	—
360	C₂	—	4	2	no	—
361	C₂	C₃₁×#2857	1	1	yes	characteristic
362	C₂	C₃₁×#3067	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂×#41×C₃₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#499	C₂	semidirect
4. C₃₁×#1998	C₂	semidirect
5. C₃₁×#1952	C₂	semidirect
6. C₃₁×#1951	C₂	semidirect
7. C₃₁×#1848	C₂	semidirect
130. #33221	C₃₁	direct (N × H)
162. C₂×#499	C₂×C₃₁	semidirect
165. #1998	C₂×C₃₁	semidirect
166. #1952	C₂×C₃₁	semidirect
167. #1951	C₂×C₃₁	semidirect
168. #1848	C₂×C₃₁	semidirect
265. C₃₁	#33221	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#499	2
C₃₁×#3080	2
C₄×C₃₁×#131	2
C₃₁×#1998	2
C₃₁×#1952	2
C₃₁×#1951	2
C₃₁×#1848	2
C₃₁×#1816	2
C₃₁×#1815	2
#33221	31

Subgroups — C31×#33221 #21489980

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33221 #21489980