Subgroups — C₃₁×#60826 #21517585

Order 7936.

2026 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3500	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3223	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3222	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3216	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3215	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3152	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#497	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3140	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3135	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3044	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3043	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3011	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3009	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2923	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
17	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
18	C₂×C₃₁×#137	C₂²	1	2	yes	—
19	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
20	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
21	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
22	C₃₁×#557	—	2	2	no	—
23	C₃₁×#556	—	2	2	no	—
24	C₃₁×#552	—	2	4	no	—
25	C₃₁×#548	—	2	2	no	—
26	C₃₁×#546	—	2	4	no	—
27	C₃₁×#546	—	2	2	no	—
28	C₃₁×#541	C₂²	1	4	yes	complemented
29	C₃₁×#536	C₂²	1	2	yes	—
30	C₃₁×#536	C₂²	1	1	yes	characteristic
31	C₃₁×#536	C₂²	1	2	yes	—
32	C₃₁×#535	C₂²	1	2	yes	—
33	C₃₁×#535	C₂²	1	1	yes	characteristic
34	C₃₁×#533	C₂²	1	4	yes	complemented
35	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#532	C₂²	1	1	yes	characteristic
37	C₃₁×#532	C₂²	1	2	yes	—
38	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
40	C₂×C₃₁×#124	C₂²	1	2	yes	—
41	C₃₁×#519	C₂²	1	2	yes	complemented
42	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
43	C₃₁×#497	C₂²	1	4	yes	complemented
44	C₃₁×#497	C₂²	1	4	yes	complemented
45	C₃₁×#497	C₂²	1	2	yes	complemented
46	C₃₁×#497	C₂²	1	2	yes	complemented
47	C₃₁×#494	C₂²	1	2	yes	complemented
48	C₃₁×#492	C₂²	1	2	yes	complemented
49	C₃₁×#491	C₂²	1	2	yes	complemented
50	C₃₁×#490	C₂²	1	2	yes	complemented
51	C₃₁×#489	C₂²	1	2	yes	complemented
52	C₃₁×#489	C₂²	1	2	yes	complemented
53	C₃₁×#489	C₂²	1	4	yes	complemented
54	C₃₁×#488	C₂²	1	4	yes	complemented
55	C₃₁×#464	C₂²	1	8	yes	complemented
56	C₃₁×#464	C₂²	1	8	yes	complemented
57	C₃₁×#462	C₂²	1	8	yes	complemented
58	C₃₁×#460	C₂²	1	8	yes	complemented
59	C₃₁×#452	C₂²	1	8	yes	—
60	C₃₁×#452	C₂²	1	8	yes	complemented
61	C₃₁×#451	C₂²	1	8	yes	complemented
62	C₃₁×#450	C₂²	1	8	yes	—
63	C₃₁×#433	C₂²	1	4	yes	complemented
64	C₃₁×#432	C₂²	1	4	yes	complemented
65	C₃₁×#424	C₂²	1	2	yes	complemented
66	C₃₁×#419	C₂²	1	2	yes	complemented
67	C₃₁×#418	C₂²	1	2	yes	—
68	C₃₁×#416	C₂²	1	2	yes	—
69	C₃₁×#416	C₂²	1	2	yes	complemented
70	C₃₁×#408	C₂²	1	2	yes	—
71	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic, complemented
73	C₃₁×2₋¹⁺⁴	—	4	4	no	—
74	C₃₁×H(5,𝔽₂)	—	4	4	no	—
75	C₂×#41×C₃₁	—	2	1	no	—
76	C₂×#41×C₃₁	—	2	2	no	—
77	C₂×#41×C₃₁	—	2	1	no	—
78	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
79	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
80	C₂×#41×C₃₁	C₂³	1	2	yes	—
81	C₂×#41×C₃₁	C₂³	1	2	yes	—
82	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
83	C₂²×Q₈×C₃₁	—	2	1	no	—
84	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
85	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
86	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
87	C₂²×D₄×C₃₁	—	2	2	no	—
88	C₂²×D₄×C₃₁	—	2	1	no	—
89	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
91	C₃₁×#137	—	4	4	no	—
92	C₃₁×#137	—	4	4	no	—
93	C₂×Q₁₆×C₃₁	—	4	4	no	—
94	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
95	C₂×Q₁₆×C₃₁	C₂³	1	8	yes	—
96	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
97	C₂×SD₁₆×C₃₁	—	4	4	no	—
98	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₃₁	C₂³	1	8	yes	—
100	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
101	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
102	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
103	C₃₁×C₄⋊Q₈	—	2	2	no	—
104	C₃₁×C₄⋊Q₈	—	2	2	no	—
105	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
106	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
107	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
108	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
109	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
110	C₃₁×#127	C₂³	1	2	yes	—
111	C₃₁×#127	C₂³	1	1	yes	characteristic
112	C₃₁×#126	—	2	8	no	—
113	C₃₁×#125	—	2	8	no	—
114	C₃₁×#125	—	2	4	no	—
115	C₃₁×#125	C₂³	1	2	yes	—
116	C₃₁×#124	—	2	2	no	—
117	C₃₁×#124	—	2	4	no	—
118	C₃₁×#124	—	2	2	no	—
119	C₃₁×#124	C₂³	1	2	yes	—
120	C₃₁×#124	C₂³	1	2	yes	—
121	C₃₁×#124	C₂³	1	2	yes	—
122	C₃₁×#124	C₂³	1	1	yes	characteristic
123	C₃₁×#124	C₂³	1	2	yes	—
124	C₃₁×#124	C₂³	1	1	yes	characteristic
125	C₃₁×#123	—	2	4	no	—
126	C₃₁×#123	—	2	2	no	—
127	C₃₁×#123	—	2	4	no	—
128	C₃₁×C₂²⋊Q₈	—	2	2	no	—
129	C₃₁×C₂²⋊Q₈	—	2	4	no	—
130	C₃₁×C₂²⋊Q₈	—	2	2	no	—
131	C₃₁×C₂²⋊Q₈	—	2	4	no	—
132	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
133	C₃₁×#121	—	2	2	no	—
134	C₃₁×#121	—	2	4	no	—
135	C₃₁×#121	—	2	2	no	—
136	C₃₁×#121	—	2	4	no	—
137	C₃₁×#120	—	2	2	no	—
138	C₃₁×#120	—	2	4	no	—
139	C₄×Q₈×C₃₁	—	2	4	no	—
140	C₄×Q₈×C₃₁	—	2	4	no	—
141	C₄×Q₈×C₃₁	—	2	2	no	—
142	C₄×Q₈×C₃₁	D₄	1	2	yes	—
143	C₄×Q₈×C₃₁	C₂³	1	8	yes	—
144	C₄×D₄×C₃₁	—	2	4	no	—
145	C₄×D₄×C₃₁	—	2	2	no	—
146	C₄×D₄×C₃₁	D₄	1	4	yes	—
147	C₄×D₄×C₃₁	D₄	1	2	yes	—
148	C₃₁×#117	—	2	4	no	—
149	C₃₁×#117	—	2	4	no	—
150	C₃₁×#117	C₂³	1	2	yes	—
151	C₃₁×#117	C₂³	1	1	yes	characteristic
152	C₃₁×#117	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
154	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
155	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
156	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
158	C₃₁×C₄⋊C₈	C₂³	1	8	yes	—
159	C₃₁×#103	C₂³	1	4	yes	—
160	C₃₁×#103	C₂³	1	4	yes	—
161	C₃₁×#103	C₂³	1	8	yes	—
162	C₃₁×#102	C₂³	1	4	yes	—
163	C₃₁×#102	C₂³	1	4	yes	—
164	C₃₁×#102	C₂³	1	8	yes	—
165	C₃₁×C₂²⋊C₈	C₂³	1	8	yes	—
166	C₃₁×#97	C₂³	1	2	yes	—
167	C₃₁×#97	C₂³	1	2	yes	—
168	C₃₁×#97	C₂³	1	2	yes	—
169	C₄×C₈×C₃₁	C₂³	1	2	yes	—
170	C₂⁴×C₃₁	—	2	2	no	—
171	C₂⁴×C₃₁	—	2	1	no	—
172	#41×C₃₁	—	2	4	no	—
173	#41×C₃₁	—	2	4	no	—
174	#41×C₃₁	—	2	4	no	—
175	#41×C₃₁	—	4	4	no	—
176	#41×C₃₁	—	4	4	no	—
177	#41×C₃₁	—	4	8	no	—
178	#41×C₃₁	—	4	4	no	—
179	#41×C₃₁	—	4	4	no	—
180	C₂×Q₈×C₃₁	—	2	2	no	—
181	C₂×Q₈×C₃₁	—	2	2	no	—
182	C₂×Q₈×C₃₁	—	2	2	no	—
183	C₂×Q₈×C₃₁	—	2	1	no	—
184	C₂×Q₈×C₃₁	—	2	4	no	—
185	C₂×Q₈×C₃₁	—	2	4	no	—
186	C₂×Q₈×C₃₁	—	2	4	no	—
187	C₂×Q₈×C₃₁	—	4	4	no	—
188	C₂×Q₈×C₃₁	—	4	4	no	—
189	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
190	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
191	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
192	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
193	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
194	C₂×D₄×C₃₁	—	2	2	no	—
195	C₂×D₄×C₃₁	—	2	1	no	—
196	C₂×D₄×C₃₁	—	2	2	no	—
197	C₂×D₄×C₃₁	—	2	1	no	—
198	C₂×D₄×C₃₁	—	2	2	no	—
199	C₂×D₄×C₃₁	—	2	1	no	—
200	C₂×D₄×C₃₁	—	2	4	no	—
201	C₂×D₄×C₃₁	—	2	2	no	—
202	C₂×D₄×C₃₁	—	2	4	no	—
203	C₂×D₄×C₃₁	—	4	4	no	—
204	C₂×D₄×C₃₁	—	4	8	no	—
205	C₂×D₄×C₃₁	—	4	4	no	—
206	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
207	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
208	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
209	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
210	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₃₁	—	2	2	no	—
212	C₂²×C₄×C₃₁	—	2	1	no	—
213	C₂²×C₄×C₃₁	—	2	2	no	—
214	C₂²×C₄×C₃₁	—	2	2	no	—
215	C₂²×C₄×C₃₁	—	2	1	no	—
216	C₂²×C₄×C₃₁	—	2	2	no	—
217	C₂²×C₄×C₃₁	—	2	1	no	—
218	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
219	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
220	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
222	Q₁₆×C₃₁	—	4	8	no	—
223	Q₁₆×C₃₁	—	4	4	no	—
224	Q₁₆×C₃₁	—	4	4	no	—
225	SD₁₆×C₃₁	—	4	8	no	—
226	SD₁₆×C₃₁	—	4	4	no	—
227	SD₁₆×C₃₁	—	4	4	no	—
228	M₁₆×C₃₁	—	2	4	no	—
229	C₂×C₈×C₃₁	—	2	4	no	—
230	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
231	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
232	C₄⋊C₄×C₃₁	—	2	4	no	—
233	C₄⋊C₄×C₃₁	—	2	4	no	—
234	C₄⋊C₄×C₃₁	—	2	2	no	—
235	C₄⋊C₄×C₃₁	—	2	8	no	—
236	C₄⋊C₄×C₃₁	—	2	4	no	—
237	C₄⋊C₄×C₃₁	—	2	2	no	—
238	C₄⋊C₄×C₃₁	—	2	4	no	—
239	C₄⋊C₄×C₃₁	—	2	8	no	—
240	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
241	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
242	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
243	C₂²⋊C₄×C₃₁	—	2	2	no	—
244	C₂²⋊C₄×C₃₁	—	2	8	no	—
245	C₂²⋊C₄×C₃₁	—	2	4	no	—
246	C₂²⋊C₄×C₃₁	—	2	2	no	—
247	C₂²⋊C₄×C₃₁	—	2	4	no	—
248	C₂²⋊C₄×C₃₁	—	2	4	no	—
249	C₂²⋊C₄×C₃₁	—	2	4	no	—
250	C₂²⋊C₄×C₃₁	—	2	2	no	—
251	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
252	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
253	C₄²×C₃₁	—	2	8	no	—
254	C₄²×C₃₁	—	2	2	no	—
255	C₄²×C₃₁	C₂×D₄	1	4	yes	—
256	C₄²×C₃₁	C₂×D₄	1	2	yes	—
257	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
258	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
259	C₄²×C₃₁	C₂⁴	1	2	yes	—
260	#60826	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
261	C₂³×C₃₁	—	2	2	no	—
262	C₂³×C₃₁	—	2	1	no	—
263	C₂³×C₃₁	—	2	1	no	—
264	C₂³×C₃₁	—	4	4	no	—
265	C₂³×C₃₁	—	4	2	no	—
266	C₂³×C₃₁	—	8	2	no	—
267	C₂³×C₃₁	—	8	4	no	—
268	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
269	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
270	Q₈×C₃₁	—	2	2	no	—
271	Q₈×C₃₁	—	2	4	no	—
272	Q₈×C₃₁	—	2	4	no	—
273	Q₈×C₃₁	—	2	4	no	—
274	Q₈×C₃₁	—	2	2	no	—
275	Q₈×C₃₁	—	2	2	no	—
276	Q₈×C₃₁	—	4	4	no	—
277	Q₈×C₃₁	—	4	4	no	—
278	Q₈×C₃₁	—	4	4	no	—
279	Q₈×C₃₁	—	4	2	no	—
280	D₄×C₃₁	—	2	4	no	—
281	D₄×C₃₁	—	2	2	no	—
282	D₄×C₃₁	—	2	4	no	—
283	D₄×C₃₁	—	2	2	no	—
284	D₄×C₃₁	—	2	2	no	—
285	D₄×C₃₁	—	4	4	no	—
286	D₄×C₃₁	—	4	4	no	—
287	D₄×C₃₁	—	4	4	no	—
288	D₄×C₃₁	—	4	2	no	—
289	D₄×C₃₁	—	4	2	no	—
290	D₄×C₃₁	—	4	2	no	—
291	D₄×C₃₁	—	8	4	no	—
292	D₄×C₃₁	—	8	2	no	—
293	C₂×C₄×C₃₁	—	2	4	no	—
294	C₂×C₄×C₃₁	—	2	4	no	—
295	C₂×C₄×C₃₁	—	2	4	no	—
296	C₂×C₄×C₃₁	—	2	2	no	—
297	C₂×C₄×C₃₁	—	2	1	no	—
298	C₂×C₄×C₃₁	—	2	1	no	—
299	C₂×C₄×C₃₁	—	4	2	no	—
300	C₂×C₄×C₃₁	—	4	4	no	—
301	C₂×C₄×C₃₁	—	4	4	no	—
302	C₂×C₄×C₃₁	—	4	4	no	—
303	C₂×C₄×C₃₁	—	4	4	no	—
304	C₂×C₄×C₃₁	—	4	4	no	—
305	C₂×C₄×C₃₁	—	4	2	no	—
306	C₂×C₄×C₃₁	—	4	2	no	—
307	C₂×C₄×C₃₁	—	4	2	no	—
308	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
309	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
310	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
311	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
312	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
313	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
314	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
315	C₈×C₃₁	—	2	4	no	—
316	C₈×C₃₁	—	2	4	no	—
317	#3509	C₂×C₃₁	1	1	yes	characteristic, complemented
318	#3500	C₂×C₃₁	1	1	yes	characteristic
319	#3223	C₂×C₃₁	1	4	yes	complemented
320	#3222	C₂×C₃₁	1	4	yes	complemented
321	#3216	C₂×C₃₁	1	4	yes	complemented
322	#3215	C₂×C₃₁	1	4	yes	complemented
323	#3152	C₂×C₃₁	1	1	yes	characteristic, complemented
324	C₂×#497	C₂×C₃₁	1	1	yes	characteristic, complemented
325	#3140	C₂×C₃₁	1	1	yes	characteristic, complemented
326	#3135	C₂×C₃₁	1	1	yes	characteristic, complemented
327	#3044	C₂×C₃₁	1	2	yes	complemented
328	#3043	C₂×C₃₁	1	2	yes	complemented
329	#3011	C₂×C₃₁	1	2	yes	complemented
330	#3009	C₂×C₃₁	1	2	yes	complemented
331	#2923	C₂×C₃₁	1	1	yes	characteristic, complemented
332	C₂²×C₃₁	—	2	2	no	—
333	C₂²×C₃₁	—	2	4	no	—
334	C₂²×C₃₁	—	2	2	no	—
335	C₂²×C₃₁	—	4	2	no	—
336	C₂²×C₃₁	—	4	4	no	—
337	C₂²×C₃₁	—	4	2	no	—
338	C₂²×C₃₁	—	4	1	no	—
339	C₂²×C₃₁	—	4	2	no	—
340	C₂²×C₃₁	—	4	1	no	—
341	C₂²×C₃₁	—	16	2	no	—
342	C₂²×C₃₁	—	16	4	no	—
343	C₂²×C₃₁	#535	1	2	yes	—
344	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
345	C₄×C₃₁	—	2	2	no	—
346	C₄×C₃₁	—	2	4	no	—
347	C₄×C₃₁	—	2	2	no	—
348	C₄×C₃₁	—	2	2	no	—
349	C₄×C₃₁	—	4	4	no	—
350	C₄×C₃₁	—	4	1	no	—
351	C₄×C₃₁	—	4	2	no	—
352	C₄×C₃₁	—	4	1	no	—
353	C₄×C₃₁	—	4	4	no	—
354	C₄×C₃₁	#535	1	2	yes	—
355	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
356	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	1	yes	characteristic
357	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	1	yes	characteristic
358	C₂×#137	C₂²×C₃₁	1	2	yes	—
359	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
360	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
361	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
362	#557	—	2	2	no	—
363	#556	—	2	2	no	—
364	#552	—	2	4	no	—
365	#548	—	2	2	no	—
366	#546	—	2	4	no	—
367	#546	—	2	2	no	—
368	#541	C₂²×C₃₁	1	4	yes	complemented
369	#536	C₂²×C₃₁	1	2	yes	—
370	#536	C₂²×C₃₁	1	1	yes	characteristic
371	#536	C₂²×C₃₁	1	2	yes	—
372	#535	C₂²×C₃₁	1	2	yes	—
373	#535	C₂²×C₃₁	1	1	yes	characteristic
374	#533	C₂²×C₃₁	1	4	yes	complemented
375	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
376	#532	C₂²×C₃₁	1	1	yes	characteristic
377	#532	C₂²×C₃₁	1	2	yes	—
378	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
379	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
380	C₂×#124	C₂²×C₃₁	1	2	yes	—
381	#519	C₂²×C₃₁	1	2	yes	complemented
382	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
383	#497	C₂²×C₃₁	1	4	yes	complemented
384	#497	C₂²×C₃₁	1	4	yes	complemented
385	#497	C₂²×C₃₁	1	2	yes	complemented
386	#497	C₂²×C₃₁	1	2	yes	complemented
387	#494	C₂²×C₃₁	1	2	yes	complemented
388	#492	C₂²×C₃₁	1	2	yes	complemented
389	#491	C₂²×C₃₁	1	2	yes	complemented
390	#490	C₂²×C₃₁	1	2	yes	complemented
391	#489	C₂²×C₃₁	1	2	yes	complemented
392	#489	C₂²×C₃₁	1	2	yes	complemented
393	#489	C₂²×C₃₁	1	4	yes	complemented
394	#488	C₂²×C₃₁	1	4	yes	complemented
395	#464	C₂²×C₃₁	1	8	yes	complemented
396	#464	C₂²×C₃₁	1	8	yes	complemented
397	#462	C₂²×C₃₁	1	8	yes	complemented
398	#460	C₂²×C₃₁	1	8	yes	complemented
399	#452	C₂²×C₃₁	1	8	yes	—
400	#452	C₂²×C₃₁	1	8	yes	complemented
401	#451	C₂²×C₃₁	1	8	yes	complemented
402	#450	C₂²×C₃₁	1	8	yes	—
403	#433	C₂²×C₃₁	1	4	yes	complemented
404	#432	C₂²×C₃₁	1	4	yes	complemented
405	#424	C₂²×C₃₁	1	2	yes	complemented
406	#419	C₂²×C₃₁	1	2	yes	complemented
407	#418	C₂²×C₃₁	1	2	yes	—
408	#416	C₂²×C₃₁	1	2	yes	—
409	#416	C₂²×C₃₁	1	2	yes	complemented
410	#408	C₂²×C₃₁	1	2	yes	—
411	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
412	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic, complemented
413	C₂×C₃₁	—	2	2	no	—
414	C₂×C₃₁	—	4	2	no	—
415	C₂×C₃₁	—	8	1	no	—
416	C₂×C₃₁	—	8	2	no	—
417	C₂×C₃₁	—	8	1	no	—
418	C₂×C₃₁	C₂×#535	1	1	yes	characteristic
419	C₂×C₃₁	#3586	1	2	yes	—
420	2₋¹⁺⁴	—	4	4	no	—
421	H(5,𝔽₂)	—	4	4	no	—
422	C₂×#41	—	2	1	no	—
423	C₂×#41	—	2	2	no	—
424	C₂×#41	—	2	1	no	—
425	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
426	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
427	C₂×#41	C₂³×C₃₁	1	2	yes	—
428	C₂×#41	C₂³×C₃₁	1	2	yes	—
429	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
430	C₂²×Q₈	—	2	1	no	—
431	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
432	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
433	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
434	C₂²×D₄	—	2	2	no	—
435	C₂²×D₄	—	2	1	no	—
436	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
437	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
438	#137	—	4	4	no	—
439	#137	—	4	4	no	—
440	C₂×Q₁₆	—	4	4	no	—
441	C₂×Q₁₆	C₂³×C₃₁	1	8	yes	—
442	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
443	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
444	C₂×SD₁₆	—	4	4	no	—
445	C₂×SD₁₆	C₂³×C₃₁	1	8	yes	—
446	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
447	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
448	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
449	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
450	C₄⋊Q₈	—	2	2	no	—
451	C₄⋊Q₈	—	2	2	no	—
452	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
453	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
454	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
455	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
456	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
457	#127	C₂³×C₃₁	1	2	yes	—
458	#127	C₂³×C₃₁	1	1	yes	characteristic
459	#126	—	2	8	no	—
460	#125	—	2	8	no	—
461	#125	—	2	4	no	—
462	#125	C₂³×C₃₁	1	2	yes	—
463	#124	—	2	2	no	—
464	#124	—	2	4	no	—
465	#124	—	2	2	no	—
466	#124	C₂³×C₃₁	1	2	yes	—
467	#124	C₂³×C₃₁	1	1	yes	characteristic
468	#124	C₂³×C₃₁	1	2	yes	—
469	#124	C₂³×C₃₁	1	2	yes	—
470	#124	C₂³×C₃₁	1	2	yes	—
471	#124	C₂³×C₃₁	1	1	yes	characteristic
472	#123	—	2	4	no	—
473	#123	—	2	2	no	—
474	#123	—	2	4	no	—
475	C₂²⋊Q₈	—	2	2	no	—
476	C₂²⋊Q₈	—	2	4	no	—
477	C₂²⋊Q₈	—	2	2	no	—
478	C₂²⋊Q₈	—	2	4	no	—
479	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
480	#121	—	2	2	no	—
481	#121	—	2	4	no	—
482	#121	—	2	2	no	—
483	#121	—	2	4	no	—
484	#120	—	2	2	no	—
485	#120	—	2	4	no	—
486	C₄×Q₈	—	2	4	no	—
487	C₄×Q₈	—	2	4	no	—
488	C₄×Q₈	—	2	2	no	—
489	C₄×Q₈	D₄×C₃₁	1	2	yes	—
490	C₄×Q₈	C₂³×C₃₁	1	8	yes	—
491	C₄×D₄	—	2	4	no	—
492	C₄×D₄	—	2	2	no	—
493	C₄×D₄	D₄×C₃₁	1	4	yes	—
494	C₄×D₄	D₄×C₃₁	1	2	yes	—
495	#117	—	2	4	no	—
496	#117	—	2	4	no	—
497	#117	C₂³×C₃₁	1	2	yes	—
498	#117	C₂³×C₃₁	1	1	yes	characteristic
499	#117	C₂³×C₃₁	1	2	yes	—
500	C₂×C₄⋊C₄	—	2	2	no	—
501	C₂×C₂²⋊C₄	—	2	2	no	—
502	C₂×C₂²⋊C₄	—	2	4	no	—
503	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
504	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
505	C₄⋊C₈	C₂³×C₃₁	1	8	yes	—
506	#103	C₂³×C₃₁	1	4	yes	—
507	#103	C₂³×C₃₁	1	4	yes	—
508	#103	C₂³×C₃₁	1	8	yes	—
509	#102	C₂³×C₃₁	1	4	yes	—
510	#102	C₂³×C₃₁	1	4	yes	—
511	#102	C₂³×C₃₁	1	8	yes	—
512	C₂²⋊C₈	C₂³×C₃₁	1	8	yes	—
513	#97	C₂³×C₃₁	1	2	yes	—
514	#97	C₂³×C₃₁	1	2	yes	—
515	#97	C₂³×C₃₁	1	2	yes	—
516	C₄×C₈	C₂³×C₃₁	1	2	yes	—
517	C₃₁	#60826	1	1	yes	characteristic, direct product factor, Sylow
518	C₂⁴	—	2	2	no	—
519	C₂⁴	—	2	1	no	—
520	#41	—	2	4	no	—
521	#41	—	2	4	no	—
522	#41	—	2	4	no	—
523	#41	—	4	4	no	—
524	#41	—	4	4	no	—
525	#41	—	4	8	no	—
526	#41	—	4	4	no	—
527	#41	—	4	4	no	—
528	C₂×Q₈	—	2	2	no	—
529	C₂×Q₈	—	2	2	no	—
530	C₂×Q₈	—	2	2	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	—	2	4	no	—
533	C₂×Q₈	—	2	4	no	—
534	C₂×Q₈	—	2	4	no	—
535	C₂×Q₈	—	4	4	no	—
536	C₂×Q₈	—	4	4	no	—
537	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
538	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
539	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
540	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
541	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
542	C₂×D₄	—	2	2	no	—
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	—	2	2	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	2	2	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	2	4	no	—
549	C₂×D₄	—	2	2	no	—
550	C₂×D₄	—	2	4	no	—
551	C₂×D₄	—	4	4	no	—
552	C₂×D₄	—	4	8	no	—
553	C₂×D₄	—	4	4	no	—
554	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
555	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
556	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
557	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
558	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
559	C₂²×C₄	—	2	2	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
567	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
568	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
570	Q₁₆	—	4	8	no	—
571	Q₁₆	—	4	4	no	—
572	Q₁₆	—	4	4	no	—
573	SD₁₆	—	4	8	no	—
574	SD₁₆	—	4	4	no	—
575	SD₁₆	—	4	4	no	—
576	M₁₆	—	2	4	no	—
577	C₂×C₈	—	2	4	no	—
578	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
579	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
580	C₄⋊C₄	—	2	4	no	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	2	no	—
583	C₄⋊C₄	—	2	8	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	2	no	—
586	C₄⋊C₄	—	2	4	no	—
587	C₄⋊C₄	—	2	8	no	—
588	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
589	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
590	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
591	C₂²⋊C₄	—	2	2	no	—
592	C₂²⋊C₄	—	2	8	no	—
593	C₂²⋊C₄	—	2	4	no	—
594	C₂²⋊C₄	—	2	2	no	—
595	C₂²⋊C₄	—	2	4	no	—
596	C₂²⋊C₄	—	2	4	no	—
597	C₂²⋊C₄	—	2	4	no	—
598	C₂²⋊C₄	—	2	2	no	—
599	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
600	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
601	C₄²	—	2	8	no	—
602	C₄²	—	2	2	no	—
603	C₄²	C₂×D₄×C₃₁	1	4	yes	—
604	C₄²	C₂×D₄×C₃₁	1	2	yes	—
605	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
606	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
607	C₄²	C₂⁴×C₃₁	1	2	yes	—
608	C₂³	—	2	2	no	—
609	C₂³	—	2	1	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	4	4	no	—
612	C₂³	—	4	2	no	—
613	C₂³	—	8	2	no	—
614	C₂³	—	8	4	no	—
615	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
616	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
617	Q₈	—	2	2	no	—
618	Q₈	—	2	4	no	—
619	Q₈	—	2	4	no	—
620	Q₈	—	2	4	no	—
621	Q₈	—	2	2	no	—
622	Q₈	—	2	2	no	—
623	Q₈	—	4	4	no	—
624	Q₈	—	4	4	no	—
625	Q₈	—	4	4	no	—
626	Q₈	—	4	2	no	—
627	D₄	—	2	4	no	—
628	D₄	—	2	2	no	—
629	D₄	—	2	4	no	—
630	D₄	—	2	2	no	—
631	D₄	—	2	2	no	—
632	D₄	—	4	4	no	—
633	D₄	—	4	4	no	—
634	D₄	—	4	4	no	—
635	D₄	—	4	2	no	—
636	D₄	—	4	2	no	—
637	D₄	—	4	2	no	—
638	D₄	—	8	4	no	—
639	D₄	—	8	2	no	—
640	C₂×C₄	—	2	4	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	4	2	no	—
647	C₂×C₄	—	4	4	no	—
648	C₂×C₄	—	4	4	no	—
649	C₂×C₄	—	4	4	no	—
650	C₂×C₄	—	4	4	no	—
651	C₂×C₄	—	4	4	no	—
652	C₂×C₄	—	4	2	no	—
653	C₂×C₄	—	4	2	no	—
654	C₂×C₄	—	4	2	no	—
655	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
656	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
657	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
658	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
659	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
660	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
661	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
662	C₈	—	2	4	no	—
663	C₈	—	2	4	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	2	4	no	—
667	C₂²	—	4	1	no	—
668	C₂²	—	4	2	no	—
669	C₂²	—	4	1	no	—
670	C₂²	—	4	2	no	—
671	C₂²	—	4	4	no	—
672	C₂²	—	4	2	no	—
673	C₂²	—	16	2	no	—
674	C₂²	—	16	4	no	—
675	C₂²	C₃₁×#535	1	2	yes	—
676	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
677	C₄	—	2	2	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	4	no	—
680	C₄	—	2	2	no	—
681	C₄	—	4	1	no	—
682	C₄	—	4	2	no	—
683	C₄	—	4	1	no	—
684	C₄	—	4	4	no	—
685	C₄	—	4	4	no	—
686	C₄	C₃₁×#535	1	2	yes	—
687	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
688	C₂	—	2	2	no	—
689	C₂	—	4	2	no	—
690	C₂	—	8	2	no	—
691	C₂	—	8	1	no	—
692	C₂	—	8	1	no	—
693	C₂	C₂×C₃₁×#535	1	1	yes	characteristic
694	C₂	C₃₁×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3500	C₂
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×#3509	C₂	semidirect
3. C₃₁×#3223	C₂	semidirect
4. C₃₁×#3222	C₂	semidirect
5. C₃₁×#3216	C₂	semidirect
6. C₃₁×#3215	C₂	semidirect
7. C₃₁×#3152	C₂	semidirect
8. C₂×C₃₁×#497	C₂	semidirect
9. C₃₁×#3140	C₂	semidirect
10. C₃₁×#3135	C₂	semidirect
11. C₃₁×#3044	C₂	semidirect
12. C₃₁×#3043	C₂	semidirect
13. C₃₁×#3011	C₂	semidirect
14. C₃₁×#3009	C₂	semidirect
15. C₃₁×#2923	C₂	semidirect
19. C₂×C₃₁×#137	C₂²	semidirect
20. C₂²×Q₁₆×C₃₁	C₂²	semidirect
28. C₃₁×#541	C₂²	semidirect
34. C₃₁×#533	C₂²	semidirect
35. C₃₁×#533	C₂²	semidirect
38. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
41. C₃₁×#519	C₂²	semidirect
43. C₃₁×#497	C₂²	semidirect
44. C₃₁×#497	C₂²	semidirect
45. C₃₁×#497	C₂²	semidirect
46. C₃₁×#497	C₂²	semidirect
47. C₃₁×#494	C₂²	semidirect
48. C₃₁×#492	C₂²	semidirect
49. C₃₁×#491	C₂²	semidirect
50. C₃₁×#490	C₂²	semidirect
51. C₃₁×#489	C₂²	semidirect
52. C₃₁×#489	C₂²	semidirect
53. C₃₁×#489	C₂²	semidirect
54. C₃₁×#488	C₂²	semidirect
55. C₃₁×#464	C₂²	semidirect
56. C₃₁×#464	C₂²	semidirect
57. C₃₁×#462	C₂²	semidirect
58. C₃₁×#460	C₂²	semidirect
60. C₃₁×#452	C₂²	semidirect
61. C₃₁×#451	C₂²	semidirect
63. C₃₁×#433	C₂²	semidirect
64. C₃₁×#432	C₂²	semidirect
65. C₃₁×#424	C₂²	semidirect
66. C₃₁×#419	C₂²	semidirect
69. C₃₁×#416	C₂²	semidirect
71. C₄×M₁₆×C₃₁	C₂²	semidirect
72. C₂×C₃₁×#97	C₂²	semidirect
260. #60826	C₃₁	direct (N × H)
317. #3509	C₂×C₃₁	semidirect
319. #3223	C₂×C₃₁	semidirect
320. #3222	C₂×C₃₁	semidirect
321. #3216	C₂×C₃₁	semidirect
322. #3215	C₂×C₃₁	semidirect
323. #3152	C₂×C₃₁	semidirect
324. C₂×#497	C₂×C₃₁	semidirect
325. #3140	C₂×C₃₁	semidirect
326. #3135	C₂×C₃₁	semidirect
327. #3044	C₂×C₃₁	semidirect
328. #3043	C₂×C₃₁	semidirect
329. #3011	C₂×C₃₁	semidirect
330. #3009	C₂×C₃₁	semidirect
331. #2923	C₂×C₃₁	semidirect
359. C₂×#137	C₂²×C₃₁	semidirect
360. C₂²×Q₁₆	C₂²×C₃₁	semidirect
368. #541	C₂²×C₃₁	semidirect
374. #533	C₂²×C₃₁	semidirect
375. #533	C₂²×C₃₁	semidirect
378. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
381. #519	C₂²×C₃₁	semidirect
383. #497	C₂²×C₃₁	semidirect
384. #497	C₂²×C₃₁	semidirect
385. #497	C₂²×C₃₁	semidirect
386. #497	C₂²×C₃₁	semidirect
387. #494	C₂²×C₃₁	semidirect
388. #492	C₂²×C₃₁	semidirect
389. #491	C₂²×C₃₁	semidirect
390. #490	C₂²×C₃₁	semidirect
391. #489	C₂²×C₃₁	semidirect
392. #489	C₂²×C₃₁	semidirect
393. #489	C₂²×C₃₁	semidirect
394. #488	C₂²×C₃₁	semidirect
395. #464	C₂²×C₃₁	semidirect
396. #464	C₂²×C₃₁	semidirect
397. #462	C₂²×C₃₁	semidirect
398. #460	C₂²×C₃₁	semidirect
400. #452	C₂²×C₃₁	semidirect
401. #451	C₂²×C₃₁	semidirect
403. #433	C₂²×C₃₁	semidirect
404. #432	C₂²×C₃₁	semidirect
405. #424	C₂²×C₃₁	semidirect
406. #419	C₂²×C₃₁	semidirect
409. #416	C₂²×C₃₁	semidirect
411. C₄×M₁₆	C₂²×C₃₁	semidirect
412. C₂×#97	C₂²×C₃₁	semidirect
517. C₃₁	#60826	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×#3509	2
C₃₁×#3500	2
C₃₁×#3223	2
C₃₁×#3222	2
C₃₁×#3216	2
C₃₁×#3215	2
C₃₁×#3152	2
C₂×C₃₁×#497	2
C₃₁×#3140	2
C₃₁×#3135	2
C₃₁×#3044	2
C₃₁×#3043	2
C₃₁×#3011	2
C₃₁×#3009	2
C₃₁×#2923	2
#60826	31

Subgroups — C31×#60826 #21517585

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60826 #21517585