Subgroups — C₃₁×#20476 #21477235

Order 7936.

990 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#432	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₈×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2283	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1770	C₂	1	2	yes	maximal, complemented
5	C₈×C₄⋊C₄×C₃₁	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1752	C₂	1	2	yes	maximal
7	C₈×C₂²⋊C₄×C₃₁	C₂	1	2	yes	maximal
8	C₃₁×#1746	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1726	C₂	1	2	yes	maximal, complemented
10	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
13	C₃₁×#432	C₄	1	8	yes	complemented
14	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
16	C₂×C₃₁×#97	C₂²	1	4	yes	—
17	C₂×C₃₁×#97	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₃₁	C₄	1	8	yes	complemented
19	C₂×C₄×C₈×C₃₁	C₂²	1	4	yes	—
20	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
24	C₃₁×#383	C₄	1	2	yes	—
25	C₃₁×#382	C₄	1	2	yes	—
26	C₃₁×#381	C₄	1	2	yes	—
27	C₃₁×#380	C₄	1	2	yes	—
28	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
29	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
30	C₃₁×#376	C₂²	1	2	yes	—
31	C₃₁×#336	C₂²	1	4	yes	—
32	C₃₁×#336	C₂²	1	4	yes	—
33	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
36	C₂²×C₈×C₃₁	—	2	4	no	—
37	C₂²×C₈×C₃₁	—	2	4	no	—
38	C₂²×C₈×C₃₁	C₂×C₄	1	4	yes	—
39	C₂²×C₈×C₃₁	C₂×C₄	1	4	yes	—
40	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
43	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
46	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
47	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₃₁	C₂×C₄	1	4	yes	—
50	C₂×C₄²×C₃₁	C₂×C₄	1	4	yes	—
51	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
52	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
54	C₃₁×C₄⋊C₈	C₂×C₄	1	8	yes	—
55	C₃₁×C₂²⋊C₈	C₂×C₄	1	8	yes	—
56	C₃₁×#97	—	2	8	no	—
57	C₃₁×#97	C₂×C₄	1	8	yes	—
58	C₄×C₈×C₃₁	—	2	8	no	—
59	C₄×C₈×C₃₁	C₂×C₄	1	4	yes	—
60	C₄×C₈×C₃₁	C₂×C₄	1	4	yes	—
61	C₄×C₈×C₃₁	C₂×C₄	1	4	yes	—
62	C₄×C₈×C₃₁	C₂×C₄	1	4	yes	—
63	C₃₁×#95	C₂×C₄	1	4	yes	—
64	C₃₁×#95	C₂×C₄	1	4	yes	—
65	C₃₁×#95	C₂×C₄	1	4	yes	—
66	C₃₁×#95	C₂×C₄	1	4	yes	—
67	C₂⁴×C₃₁	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₃₁	—	2	4	no	—
69	C₂²×C₄×C₃₁	—	2	4	no	—
70	C₂²×C₄×C₃₁	—	2	2	no	—
71	C₂²×C₄×C₃₁	—	2	2	no	—
72	C₂²×C₄×C₃₁	C₄²	1	4	yes	—
73	C₂²×C₄×C₃₁	C₄²	1	4	yes	—
74	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
75	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
83	C₂×C₈×C₃₁	—	2	4	no	—
84	C₂×C₈×C₃₁	—	2	4	no	—
85	C₂×C₈×C₃₁	—	2	2	no	—
86	C₂×C₈×C₃₁	—	2	2	no	—
87	C₂×C₈×C₃₁	—	2	8	no	—
88	C₂×C₈×C₃₁	—	2	8	no	—
89	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
90	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
91	C₂×C₈×C₃₁	C₂²×C₄	1	8	yes	—
92	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
93	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
94	C₂×C₈×C₃₁	#41	1	4	yes	—
95	C₂×C₈×C₃₁	#41	1	4	yes	—
96	C₄⋊C₄×C₃₁	—	2	8	no	—
97	C₂²⋊C₄×C₃₁	—	2	8	no	—
98	C₄²×C₃₁	—	2	4	no	—
99	C₄²×C₃₁	—	2	4	no	—
100	C₄²×C₃₁	C₄²	1	4	yes	—
101	C₄²×C₃₁	C₄²	1	4	yes	—
102	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
103	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
104	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
105	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
106	#20476	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
107	C₂³×C₃₁	—	2	2	no	—
108	C₂³×C₃₁	—	2	2	no	—
109	C₂³×C₃₁	C₂×C₄²	1	2	yes	—
110	C₂³×C₃₁	#131	1	4	yes	—
111	C₂³×C₃₁	C₂³×C₄	1	1	yes	characteristic
112	C₂×C₄×C₃₁	—	2	2	no	—
113	C₂×C₄×C₃₁	—	2	2	no	—
114	C₂×C₄×C₃₁	—	2	2	no	—
115	C₂×C₄×C₃₁	—	2	2	no	—
116	C₂×C₄×C₃₁	—	2	8	no	—
117	C₂×C₄×C₃₁	—	2	2	no	—
118	C₂×C₄×C₃₁	—	2	2	no	—
119	C₂×C₄×C₃₁	—	2	4	no	—
120	C₂×C₄×C₃₁	—	2	8	no	—
121	C₂×C₄×C₃₁	—	2	8	no	—
122	C₂×C₄×C₃₁	—	2	8	no	—
123	C₂×C₄×C₃₁	—	2	8	no	—
124	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
125	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
126	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
127	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
128	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
129	C₂×C₄×C₃₁	#131	1	4	yes	—
130	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
131	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
132	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
133	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
134	C₈×C₃₁	—	2	2	no	—
135	C₈×C₃₁	—	2	2	no	—
136	C₈×C₃₁	—	2	8	no	—
137	C₈×C₃₁	#117	1	4	yes	—
138	C₈×C₃₁	#117	1	4	yes	—
139	C₂×#432	C₂×C₃₁	1	1	yes	characteristic
140	C₂²×C₄×C₈	C₂×C₃₁	1	1	yes	characteristic
141	#2283	C₂×C₃₁	1	1	yes	characteristic
142	#1770	C₂×C₃₁	1	2	yes	complemented
143	C₈×C₄⋊C₄	C₂×C₃₁	1	2	yes	complemented
144	#1752	C₂×C₃₁	1	2	yes	—
145	C₈×C₂²⋊C₄	C₂×C₃₁	1	2	yes	—
146	#1746	C₂×C₃₁	1	2	yes	complemented
147	#1726	C₂×C₃₁	1	2	yes	complemented
148	C₂²×C₃₁	—	2	2	no	—
149	C₂²×C₃₁	—	2	8	no	—
150	C₂²×C₃₁	—	2	2	no	—
151	C₂²×C₃₁	#405	1	4	yes	—
152	C₂²×C₃₁	C₂²×C₄²	1	1	yes	characteristic
153	C₂²×C₃₁	C₄×#41	1	2	yes	—
154	C₂²×C₃₁	C₂×#131	1	2	yes	—
155	C₂²×C₃₁	C₂×#131	1	2	yes	—
156	C₄×C₃₁	—	2	2	no	—
157	C₄×C₃₁	—	2	2	no	—
158	C₄×C₃₁	—	2	2	no	—
159	C₄×C₃₁	—	2	2	no	—
160	C₄×C₃₁	—	4	8	no	—
161	C₄×C₃₁	#405	1	4	yes	—
162	C₄×C₃₁	C₂×#117	1	1	yes	characteristic
163	C₄×C₃₁	C₂×#117	1	1	yes	characteristic
164	C₄×C₃₁	C₄×#41	1	2	yes	—
165	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
166	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
167	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
168	#432	C₄×C₃₁	1	8	yes	complemented
169	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
170	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
171	C₂×#97	C₂²×C₃₁	1	4	yes	—
172	C₂×#97	C₂²×C₃₁	1	2	yes	—
173	C₂×C₄×C₈	C₄×C₃₁	1	8	yes	complemented
174	C₂×C₄×C₈	C₂²×C₃₁	1	4	yes	—
175	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
176	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
177	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
178	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
179	#383	C₄×C₃₁	1	2	yes	—
180	#382	C₄×C₃₁	1	2	yes	—
181	#381	C₄×C₃₁	1	2	yes	—
182	#380	C₄×C₃₁	1	2	yes	—
183	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
184	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
185	#376	C₂²×C₃₁	1	2	yes	—
186	#336	C₂²×C₃₁	1	4	yes	—
187	#336	C₂²×C₃₁	1	4	yes	—
188	C₂×C₃₁	—	2	4	no	—
189	C₂×C₃₁	C₄×#117	1	1	yes	characteristic
190	C₂×C₃₁	C₂×#405	1	1	yes	characteristic
191	C₂×C₃₁	C₂×#405	1	1	yes	characteristic
192	C₂×C₃₁	#2966	1	4	yes	—
193	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
194	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
195	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
196	C₂²×C₈	—	2	4	no	—
197	C₂²×C₈	—	2	4	no	—
198	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
199	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
200	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
201	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
202	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
203	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
204	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
205	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
206	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
207	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
208	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
209	C₂×C₄²	C₂×C₄×C₃₁	1	4	yes	—
210	C₂×C₄²	C₂×C₄×C₃₁	1	4	yes	—
211	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
212	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
213	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
214	C₄⋊C₈	C₂×C₄×C₃₁	1	8	yes	—
215	C₂²⋊C₈	C₂×C₄×C₃₁	1	8	yes	—
216	#97	—	2	8	no	—
217	#97	C₂×C₄×C₃₁	1	8	yes	—
218	C₄×C₈	—	2	8	no	—
219	C₄×C₈	C₂×C₄×C₃₁	1	4	yes	—
220	C₄×C₈	C₂×C₄×C₃₁	1	4	yes	—
221	C₄×C₈	C₂×C₄×C₃₁	1	4	yes	—
222	C₄×C₈	C₂×C₄×C₃₁	1	4	yes	—
223	#95	C₂×C₄×C₃₁	1	4	yes	—
224	#95	C₂×C₄×C₃₁	1	4	yes	—
225	#95	C₂×C₄×C₃₁	1	4	yes	—
226	#95	C₂×C₄×C₃₁	1	4	yes	—
227	C₃₁	#20476	1	1	yes	characteristic, direct product factor, Sylow
228	C₂⁴	C₂²×C₄×C₃₁	1	1	yes	characteristic
229	C₂²×C₄	—	2	4	no	—
230	C₂²×C₄	—	2	4	no	—
231	C₂²×C₄	—	2	2	no	—
232	C₂²×C₄	—	2	2	no	—
233	C₂²×C₄	C₄²×C₃₁	1	4	yes	—
234	C₂²×C₄	C₄²×C₃₁	1	4	yes	—
235	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
236	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
237	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
238	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
239	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
240	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
241	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
242	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
243	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
244	C₂×C₈	—	2	4	no	—
245	C₂×C₈	—	2	4	no	—
246	C₂×C₈	—	2	2	no	—
247	C₂×C₈	—	2	2	no	—
248	C₂×C₈	—	2	8	no	—
249	C₂×C₈	—	2	8	no	—
250	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
251	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
252	C₂×C₈	C₂²×C₄×C₃₁	1	8	yes	—
253	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
254	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
255	C₂×C₈	#41×C₃₁	1	4	yes	—
256	C₂×C₈	#41×C₃₁	1	4	yes	—
257	C₄⋊C₄	—	2	8	no	—
258	C₂²⋊C₄	—	2	8	no	—
259	C₄²	—	2	4	no	—
260	C₄²	—	2	4	no	—
261	C₄²	C₄²×C₃₁	1	4	yes	—
262	C₄²	C₄²×C₃₁	1	4	yes	—
263	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
264	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
265	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
266	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
267	C₂³	—	2	2	no	—
268	C₂³	—	2	2	no	—
269	C₂³	C₂×C₄²×C₃₁	1	2	yes	—
270	C₂³	C₃₁×#131	1	4	yes	—
271	C₂³	C₂³×C₄×C₃₁	1	1	yes	characteristic
272	C₂×C₄	—	2	8	no	—
273	C₂×C₄	—	2	2	no	—
274	C₂×C₄	—	2	2	no	—
275	C₂×C₄	—	2	2	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	2	8	no	—
278	C₂×C₄	—	2	2	no	—
279	C₂×C₄	—	2	2	no	—
280	C₂×C₄	—	2	4	no	—
281	C₂×C₄	—	2	8	no	—
282	C₂×C₄	—	2	8	no	—
283	C₂×C₄	—	2	8	no	—
284	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
285	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
286	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
287	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
288	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
289	C₂×C₄	C₃₁×#131	1	4	yes	—
290	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
291	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
292	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
293	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
294	C₈	—	2	2	no	—
295	C₈	—	2	2	no	—
296	C₈	—	2	8	no	—
297	C₈	C₃₁×#117	1	4	yes	—
298	C₈	C₃₁×#117	1	4	yes	—
299	C₂²	—	2	2	no	—
300	C₂²	—	2	8	no	—
301	C₂²	—	2	2	no	—
302	C₂²	C₃₁×#405	1	4	yes	—
303	C₂²	C₂²×C₄²×C₃₁	1	1	yes	characteristic
304	C₂²	C₄×#41×C₃₁	1	2	yes	—
305	C₂²	C₂×C₃₁×#131	1	2	yes	—
306	C₂²	C₂×C₃₁×#131	1	2	yes	—
307	C₄	—	2	2	no	—
308	C₄	—	2	2	no	—
309	C₄	—	2	2	no	—
310	C₄	—	2	2	no	—
311	C₄	—	4	8	no	—
312	C₄	C₃₁×#405	1	4	yes	—
313	C₄	C₂×C₃₁×#117	1	1	yes	characteristic
314	C₄	C₂×C₃₁×#117	1	1	yes	characteristic
315	C₄	C₄×#41×C₃₁	1	2	yes	—
316	C₂	—	2	4	no	—
317	C₂	C₄×C₃₁×#117	1	1	yes	characteristic
318	C₂	C₂×C₃₁×#405	1	1	yes	characteristic
319	C₂	C₂×C₃₁×#405	1	1	yes	characteristic
320	C₂	C₃₁×#2966	1	4	yes	—

	subgroup	G/H
center	C₂²×C₈×C₃₁	C₂³
commutator	C₂²	C₂²×C₄²×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
socle	C₂³×C₃₁	C₂³×C₄
prime radical	C₂⁴×C₃₁	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₃₁×#1770	C₂	semidirect
5. C₈×C₄⋊C₄×C₃₁	C₂	semidirect
8. C₃₁×#1746	C₂	semidirect
9. C₃₁×#1726	C₂	semidirect
13. C₃₁×#432	C₄	semidirect
18. C₂×C₄×C₈×C₃₁	C₄	semidirect
106. #20476	C₃₁	direct (N × H)
142. #1770	C₂×C₃₁	semidirect
143. C₈×C₄⋊C₄	C₂×C₃₁	semidirect
146. #1746	C₂×C₃₁	semidirect
147. #1726	C₂×C₃₁	semidirect
168. #432	C₄×C₃₁	semidirect
173. C₂×C₄×C₈	C₄×C₃₁	semidirect
227. C₃₁	#20476	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×#432	2
C₂²×C₄×C₈×C₃₁	2
C₃₁×#2283	2
C₃₁×#1770	2
C₈×C₄⋊C₄×C₃₁	2
C₃₁×#1752	2
C₈×C₂²⋊C₄×C₃₁	2
C₃₁×#1746	2
C₃₁×#1726	2
#20476	31

Subgroups — C31×#20476 #21477235

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#20476 #21477235