Subgroups — C₃₁×#32830 #21489589

Order 7936.

612 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2647	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#2640	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2096	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2094	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#2074	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2073	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#2066	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2065	C₂	1	2	yes	maximal
9	C₃₁×#2058	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2042	C₂	1	2	yes	maximal
11	C₃₁×#1832	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
14	C₂×C₃₁×#106	C₂²	1	2	yes	—
15	C₂×C₃₁×#106	C₂²	1	2	yes	—
16	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₃₁×#103	C₂²	1	2	yes	—
18	C₂×C₃₁×#103	C₂²	1	2	yes	—
19	C₂×C₃₁×#102	C₂²	1	2	yes	—
20	C₂×C₃₁×#102	C₂²	1	2	yes	—
21	C₃₁×#400	—	2	2	no	—
22	C₃₁×#398	—	2	2	no	—
23	C₃₁×#397	—	2	2	no	—
24	C₃₁×#393	—	2	2	no	—
25	C₃₁×#391	C₂²	1	1	yes	characteristic
26	C₃₁×#391	C₂²	1	1	yes	characteristic
27	C₃₁×#390	C₂²	1	1	yes	characteristic
28	C₃₁×#390	C₂²	1	1	yes	characteristic
29	C₃₁×#389	C₂²	1	2	yes	—
30	C₃₁×#389	C₂²	1	2	yes	—
31	C₃₁×#384	C₂²	1	1	yes	characteristic
32	C₃₁×#382	C₂²	1	1	yes	characteristic
33	C₃₁×#376	C₂²	1	1	yes	characteristic
34	C₃₁×#340	C₂²	1	2	yes	—
35	C₃₁×#340	C₂²	1	2	yes	—
36	C₃₁×#336	C₂²	1	2	yes	—
37	C₃₁×#336	C₂²	1	1	yes	characteristic
38	C₃₁×#336	C₂²	1	1	yes	characteristic
39	C₂²×Q₈×C₃₁	—	2	1	no	—
40	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
41	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
44	C₃₁×C₄⋊Q₈	—	4	2	no	—
45	C₃₁×#124	—	4	2	no	—
46	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
47	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
48	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
49	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
50	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
51	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
52	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
54	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
55	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
56	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
58	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
61	C₃₁×#106	—	4	2	no	—
62	C₃₁×#106	—	4	2	no	—
63	C₃₁×C₄⋊C₈	—	4	2	no	—
64	C₃₁×#103	—	4	2	no	—
65	C₃₁×#103	—	4	2	no	—
66	C₃₁×#102	—	4	2	no	—
67	C₃₁×#102	—	4	2	no	—
68	C₃₁×#95	—	2	2	no	—
69	C₃₁×#95	—	2	2	no	—
70	C₃₁×#95	—	2	2	no	—
71	C₃₁×#95	—	2	2	no	—
72	C₃₁×#95	—	2	2	no	—
73	C₃₁×#95	D₄	1	2	yes	—
74	C₃₁×#95	D₄	1	2	yes	—
75	C₂⁴×C₃₁	—	2	1	no	—
76	C₂×Q₈×C₃₁	—	2	1	no	—
77	C₂×Q₈×C₃₁	—	2	2	no	—
78	C₂×Q₈×C₃₁	—	2	2	no	—
79	C₂×Q₈×C₃₁	—	2	1	no	—
80	C₂×Q₈×C₃₁	—	4	2	no	—
81	C₂×Q₈×C₃₁	—	8	2	no	—
82	C₂×D₄×C₃₁	—	2	1	no	—
83	C₂×D₄×C₃₁	—	2	2	no	—
84	C₂×D₄×C₃₁	—	2	2	no	—
85	C₂×D₄×C₃₁	—	2	1	no	—
86	C₂²×C₄×C₃₁	—	2	1	no	—
87	C₂²×C₄×C₃₁	—	2	2	no	—
88	C₂²×C₄×C₃₁	—	2	1	no	—
89	C₂²×C₄×C₃₁	—	2	1	no	—
90	C₂²×C₄×C₃₁	—	2	2	no	—
91	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
96	C₂×C₈×C₃₁	—	2	2	no	—
97	C₂×C₈×C₃₁	—	2	2	no	—
98	C₂×C₈×C₃₁	—	2	2	no	—
99	C₂×C₈×C₃₁	—	2	2	no	—
100	C₂×C₈×C₃₁	—	2	2	no	—
101	C₂×C₈×C₃₁	—	2	2	no	—
102	C₄⋊C₄×C₃₁	—	2	2	no	—
103	C₄⋊C₄×C₃₁	—	2	2	no	—
104	C₄⋊C₄×C₃₁	—	2	2	no	—
105	C₄⋊C₄×C₃₁	—	2	2	no	—
106	C₄⋊C₄×C₃₁	—	2	2	no	—
107	C₄⋊C₄×C₃₁	—	2	2	no	—
108	C₄⋊C₄×C₃₁	—	4	2	no	—
109	C₄⋊C₄×C₃₁	—	8	2	no	—
110	C₄⋊C₄×C₃₁	—	8	2	no	—
111	C₄⋊C₄×C₃₁	—	8	2	no	—
112	C₂²⋊C₄×C₃₁	—	4	2	no	—
113	C₂²⋊C₄×C₃₁	—	4	2	no	—
114	C₂²⋊C₄×C₃₁	—	8	2	no	—
115	C₂²⋊C₄×C₃₁	—	8	2	no	—
116	C₄²×C₃₁	—	2	1	no	—
117	C₄²×C₃₁	—	2	2	no	—
118	C₄²×C₃₁	—	2	2	no	—
119	C₄²×C₃₁	—	2	1	no	—
120	#32830	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂³×C₃₁	—	4	1	no	—
122	C₂³×C₃₁	—	4	1	no	—
123	C₂³×C₃₁	—	4	1	no	—
124	C₂³×C₃₁	—	4	2	no	—
125	C₂³×C₃₁	—	4	2	no	—
126	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
127	Q₈×C₃₁	—	4	2	no	—
128	Q₈×C₃₁	—	4	2	no	—
129	Q₈×C₃₁	—	8	4	no	—
130	D₄×C₃₁	—	4	2	no	—
131	D₄×C₃₁	—	4	2	no	—
132	C₂×C₄×C₃₁	—	2	1	no	—
133	C₂×C₄×C₃₁	—	2	1	no	—
134	C₂×C₄×C₃₁	—	2	2	no	—
135	C₂×C₄×C₃₁	—	2	2	no	—
136	C₂×C₄×C₃₁	—	2	2	no	—
137	C₂×C₄×C₃₁	—	2	2	no	—
138	C₂×C₄×C₃₁	—	2	2	no	—
139	C₂×C₄×C₃₁	—	2	2	no	—
140	C₂×C₄×C₃₁	—	2	2	no	—
141	C₂×C₄×C₃₁	—	2	2	no	—
142	C₂×C₄×C₃₁	—	4	1	no	—
143	C₂×C₄×C₃₁	—	4	1	no	—
144	C₂×C₄×C₃₁	—	4	1	no	—
145	C₂×C₄×C₃₁	—	4	2	no	—
146	C₂×C₄×C₃₁	—	4	1	no	—
147	C₂×C₄×C₃₁	—	4	2	no	—
148	C₂×C₄×C₃₁	—	4	1	no	—
149	C₂×C₄×C₃₁	—	4	2	no	—
150	C₂×C₄×C₃₁	—	4	2	no	—
151	C₂×C₄×C₃₁	—	4	2	no	—
152	C₂×C₄×C₃₁	—	4	2	no	—
153	C₂×C₄×C₃₁	—	4	2	no	—
154	C₂×C₄×C₃₁	—	4	2	no	—
155	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
156	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
157	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
158	C₂×C₄×C₃₁	2₋¹⁺⁴	1	1	yes	characteristic
159	C₈×C₃₁	—	4	2	no	—
160	C₈×C₃₁	—	4	2	no	—
161	#2647	C₂×C₃₁	1	1	yes	characteristic, complemented
162	#2640	C₂×C₃₁	1	1	yes	characteristic
163	#2096	C₂×C₃₁	1	1	yes	characteristic, complemented
164	#2094	C₂×C₃₁	1	1	yes	characteristic
165	#2074	C₂×C₃₁	1	1	yes	characteristic, complemented
166	#2073	C₂×C₃₁	1	1	yes	characteristic
167	#2066	C₂×C₃₁	1	2	yes	complemented
168	#2065	C₂×C₃₁	1	2	yes	—
169	#2058	C₂×C₃₁	1	2	yes	complemented
170	#2042	C₂×C₃₁	1	2	yes	—
171	#1832	C₂×C₃₁	1	1	yes	characteristic, complemented
172	C₂²×C₃₁	—	8	1	no	—
173	C₂²×C₃₁	—	8	1	no	—
174	C₂²×C₃₁	—	8	1	no	—
175	C₂²×C₃₁	—	8	2	no	—
176	C₂²×C₃₁	—	8	2	no	—
177	C₂²×C₃₁	#535	1	1	yes	characteristic
178	C₂²×C₃₁	#536	1	1	yes	characteristic
179	C₂²×C₃₁	#537	1	1	yes	characteristic
180	C₂²×C₃₁	#577	1	2	yes	—
181	C₂²×C₃₁	#577	1	2	yes	—
182	C₄×C₃₁	—	4	1	no	—
183	C₄×C₃₁	—	4	1	no	—
184	C₄×C₃₁	—	4	2	no	—
185	C₄×C₃₁	—	4	2	no	—
186	C₄×C₃₁	—	8	1	no	—
187	C₄×C₃₁	—	8	2	no	—
188	C₄×C₃₁	—	8	1	no	—
189	C₄×C₃₁	—	8	1	no	—
190	C₄×C₃₁	—	8	2	no	—
191	C₄×C₃₁	#562	1	2	yes	—
192	C₄×C₃₁	#563	1	2	yes	—
193	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
194	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
195	C₂×#106	C₂²×C₃₁	1	2	yes	—
196	C₂×#106	C₂²×C₃₁	1	2	yes	—
197	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
198	C₂×#103	C₂²×C₃₁	1	2	yes	—
199	C₂×#103	C₂²×C₃₁	1	2	yes	—
200	C₂×#102	C₂²×C₃₁	1	2	yes	—
201	C₂×#102	C₂²×C₃₁	1	2	yes	—
202	#400	—	2	2	no	—
203	#398	—	2	2	no	—
204	#397	—	2	2	no	—
205	#393	—	2	2	no	—
206	#391	C₂²×C₃₁	1	1	yes	characteristic
207	#391	C₂²×C₃₁	1	1	yes	characteristic
208	#390	C₂²×C₃₁	1	1	yes	characteristic
209	#390	C₂²×C₃₁	1	1	yes	characteristic
210	#389	C₂²×C₃₁	1	2	yes	—
211	#389	C₂²×C₃₁	1	2	yes	—
212	#384	C₂²×C₃₁	1	1	yes	characteristic
213	#382	C₂²×C₃₁	1	1	yes	characteristic
214	#376	C₂²×C₃₁	1	1	yes	characteristic
215	#340	C₂²×C₃₁	1	2	yes	—
216	#340	C₂²×C₃₁	1	2	yes	—
217	#336	C₂²×C₃₁	1	2	yes	—
218	#336	C₂²×C₃₁	1	1	yes	characteristic
219	#336	C₂²×C₃₁	1	1	yes	characteristic
220	C₂×C₃₁	—	16	1	no	—
221	C₂×C₃₁	#2820	1	1	yes	characteristic
222	C₂×C₃₁	#3221	1	1	yes	characteristic
223	C₂×C₃₁	#3222	1	1	yes	characteristic
224	C₂×C₃₁	#3244	1	2	yes	—
225	C₂×C₃₁	#3263	1	2	yes	—
226	C₂²×Q₈	—	2	1	no	—
227	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
228	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
229	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
230	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
231	C₄⋊Q₈	—	4	2	no	—
232	#124	—	4	2	no	—
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₄⋊C₄	—	2	2	no	—
235	C₂×C₄⋊C₄	—	2	2	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
239	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
240	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
241	C₂×C₂²⋊C₄	—	2	1	no	—
242	C₂×C₂²⋊C₄	—	2	1	no	—
243	C₂×C₂²⋊C₄	—	2	2	no	—
244	C₂×C₂²⋊C₄	—	2	2	no	—
245	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
246	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
247	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
248	#106	—	4	2	no	—
249	#106	—	4	2	no	—
250	C₄⋊C₈	—	4	2	no	—
251	#103	—	4	2	no	—
252	#103	—	4	2	no	—
253	#102	—	4	2	no	—
254	#102	—	4	2	no	—
255	#95	—	2	2	no	—
256	#95	—	2	2	no	—
257	#95	—	2	2	no	—
258	#95	—	2	2	no	—
259	#95	—	2	2	no	—
260	#95	D₄×C₃₁	1	2	yes	—
261	#95	D₄×C₃₁	1	2	yes	—
262	C₃₁	#32830	1	1	yes	characteristic, direct product factor, Sylow
263	C₂⁴	—	2	1	no	—
264	C₂×Q₈	—	2	1	no	—
265	C₂×Q₈	—	2	2	no	—
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	2	1	no	—
268	C₂×Q₈	—	4	2	no	—
269	C₂×Q₈	—	8	2	no	—
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	2	1	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
280	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
281	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
283	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	4	2	no	—
297	C₄⋊C₄	—	8	2	no	—
298	C₄⋊C₄	—	8	2	no	—
299	C₄⋊C₄	—	8	2	no	—
300	C₂²⋊C₄	—	4	2	no	—
301	C₂²⋊C₄	—	4	2	no	—
302	C₂²⋊C₄	—	8	2	no	—
303	C₂²⋊C₄	—	8	2	no	—
304	C₄²	—	2	1	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	2	1	no	—
308	C₂³	—	4	1	no	—
309	C₂³	—	4	1	no	—
310	C₂³	—	4	1	no	—
311	C₂³	—	4	2	no	—
312	C₂³	—	4	2	no	—
313	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
314	Q₈	—	4	2	no	—
315	Q₈	—	4	2	no	—
316	Q₈	—	8	4	no	—
317	D₄	—	4	2	no	—
318	D₄	—	4	2	no	—
319	C₂×C₄	—	2	1	no	—
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	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
343	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
344	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
345	C₂×C₄	C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
346	C₈	—	4	2	no	—
347	C₈	—	4	2	no	—
348	C₂²	—	8	1	no	—
349	C₂²	—	8	1	no	—
350	C₂²	—	8	1	no	—
351	C₂²	—	8	2	no	—
352	C₂²	—	8	2	no	—
353	C₂²	C₃₁×#535	1	1	yes	characteristic
354	C₂²	C₃₁×#536	1	1	yes	characteristic
355	C₂²	C₃₁×#537	1	1	yes	characteristic
356	C₂²	C₃₁×#577	1	2	yes	—
357	C₂²	C₃₁×#577	1	2	yes	—
358	C₄	—	4	1	no	—
359	C₄	—	4	1	no	—
360	C₄	—	4	2	no	—
361	C₄	—	4	2	no	—
362	C₄	—	8	1	no	—
363	C₄	—	8	2	no	—
364	C₄	—	8	1	no	—
365	C₄	—	8	1	no	—
366	C₄	—	8	2	no	—
367	C₄	C₃₁×#562	1	2	yes	—
368	C₄	C₃₁×#563	1	2	yes	—
369	C₂	—	16	1	no	—
370	C₂	C₃₁×#2820	1	1	yes	characteristic
371	C₂	C₃₁×#3221	1	1	yes	characteristic
372	C₂	C₃₁×#3222	1	1	yes	characteristic
373	C₂	C₃₁×#3244	1	2	yes	—
374	C₂	C₃₁×#3263	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂²×D₄×C₃₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₃₁×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#2647	C₂	semidirect
3. C₃₁×#2096	C₂	semidirect
5. C₃₁×#2074	C₂	semidirect
7. C₃₁×#2066	C₂	semidirect
9. C₃₁×#2058	C₂	semidirect
11. C₃₁×#1832	C₂	semidirect
120. #32830	C₃₁	direct (N × H)
161. #2647	C₂×C₃₁	semidirect
163. #2096	C₂×C₃₁	semidirect
165. #2074	C₂×C₃₁	semidirect
167. #2066	C₂×C₃₁	semidirect
169. #2058	C₂×C₃₁	semidirect
171. #1832	C₂×C₃₁	semidirect
262. C₃₁	#32830	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×#2647	2
C₃₁×#2640	2
C₃₁×#2096	2
C₃₁×#2094	2
C₃₁×#2074	2
C₃₁×#2073	2
C₃₁×#2066	2
C₃₁×#2065	2
C₃₁×#2058	2
C₃₁×#2042	2
C₃₁×#1832	2
#32830	31

Subgroups — C31×#32830 #21489589

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#32830 #21489589