Subgroups — C₃₁×#10310 #21467069

Order 7936.

670 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#492	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁×#486	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1990	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1990	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1957	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#1273	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×SD₁₆×C₃₁	—	2	2	no	—
9	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
12	C₃₁×#492	—	2	2	no	—
13	C₃₁×#492	—	2	2	no	—
14	C₃₁×#487	—	2	2	no	—
15	C₃₁×#487	—	2	2	no	—
16	C₃₁×#486	—	2	2	no	—
17	C₃₁×#486	—	2	2	no	—
18	C₂×C₃₁×#103	—	2	2	no	—
19	C₂×C₃₁×#102	—	2	2	no	—
20	C₂×C₃₁×#102	—	2	2	no	—
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×#384	C₂²	1	1	yes	characteristic
25	C₃₁×#340	—	2	2	no	—
26	C₃₁×#340	—	2	2	no	—
27	C₂²×Q₈×C₃₁	—	2	1	no	—
28	C₂²×Q₈×C₃₁	—	2	1	no	—
29	C₂²×D₄×C₃₁	—	2	1	no	—
30	C₂²×D₄×C₃₁	—	2	1	no	—
31	C₂²×D₄×C₃₁	—	2	1	no	—
32	C₂×SD₁₆×C₃₁	—	2	8	no	—
33	C₂×SD₁₆×C₃₁	—	4	4	no	—
34	C₂×SD₁₆×C₃₁	—	4	4	no	—
35	C₂²×C₈×C₃₁	D₄	1	2	yes	—
36	C₂²×C₈×C₃₁	D₄	1	2	yes	—
37	C₂²×C₈×C₃₁	D₄	1	2	yes	—
38	C₃₁×C₄⋊Q₈	—	2	1	no	—
39	C₃₁×C₄⋊Q₈	—	2	1	no	—
40	C₃₁×C₄⋊Q₈	—	2	1	no	—
41	C₃₁×C₄⋊Q₈	—	2	1	no	—
42	C₃₁×C₄⋊Q₈	—	2	1	no	—
43	C₃₁×C₄⋊Q₈	—	2	1	no	—
44	C₃₁×C₄⋊Q₈	D₄	1	2	yes	—
45	C₃₁×C₄⋊Q₈	D₄	1	2	yes	—
46	C₃₁×#127	—	2	1	no	—
47	C₃₁×#127	—	2	1	no	—
48	C₃₁×#127	—	2	1	no	—
49	C₃₁×#127	D₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
51	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
52	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
53	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
54	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
55	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
56	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
57	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
58	C₃₁×#103	—	2	8	no	—
59	C₃₁×#102	—	2	8	no	—
60	C₃₁×#102	—	4	4	no	—
61	C₄×C₈×C₃₁	—	2	1	no	—
62	C₄×C₈×C₃₁	—	2	1	no	—
63	C₄×C₈×C₃₁	—	2	1	no	—
64	C₄×C₈×C₃₁	—	2	1	no	—
65	C₄×C₈×C₃₁	—	2	1	no	—
66	C₄×C₈×C₃₁	—	2	1	no	—
67	C₂⁴×C₃₁	—	4	1	no	—
68	C₂×Q₈×C₃₁	—	2	2	no	—
69	C₂×Q₈×C₃₁	—	2	2	no	—
70	C₂×Q₈×C₃₁	—	4	1	no	—
71	C₂×Q₈×C₃₁	—	4	1	no	—
72	C₂×Q₈×C₃₁	—	4	2	no	—
73	C₂×Q₈×C₃₁	—	4	2	no	—
74	C₂×Q₈×C₃₁	—	4	2	no	—
75	C₂×Q₈×C₃₁	—	4	2	no	—
76	C₂×D₄×C₃₁	—	2	2	no	—
77	C₂×D₄×C₃₁	—	2	2	no	—
78	C₂×D₄×C₃₁	—	2	2	no	—
79	C₂×D₄×C₃₁	—	4	1	no	—
80	C₂×D₄×C₃₁	—	4	1	no	—
81	C₂×D₄×C₃₁	—	4	1	no	—
82	C₂×D₄×C₃₁	—	4	2	no	—
83	C₂×D₄×C₃₁	—	4	2	no	—
84	C₂×D₄×C₃₁	—	4	2	no	—
85	C₂×D₄×C₃₁	—	4	2	no	—
86	C₂×D₄×C₃₁	—	4	2	no	—
87	C₂×D₄×C₃₁	—	4	2	no	—
88	C₂²×C₄×C₃₁	—	4	1	no	—
89	C₂²×C₄×C₃₁	—	4	1	no	—
90	C₂²×C₄×C₃₁	—	4	1	no	—
91	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
94	SD₁₆×C₃₁	—	4	16	no	—
95	C₂×C₈×C₃₁	—	2	2	no	—
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	C₂×C₈×C₃₁	—	2	2	no	—
103	C₂×C₈×C₃₁	SD₁₆	1	4	yes	—
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	1	no	—
109	C₄⋊C₄×C₃₁	—	4	1	no	—
110	C₄⋊C₄×C₃₁	—	4	1	no	—
111	C₄⋊C₄×C₃₁	—	4	1	no	—
112	C₄⋊C₄×C₃₁	—	4	2	no	—
113	C₄⋊C₄×C₃₁	—	4	2	no	—
114	C₄⋊C₄×C₃₁	—	4	2	no	—
115	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₃₁	#41	1	1	yes	characteristic
119	#10310	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂³×C₃₁	—	4	2	no	—
121	C₂³×C₃₁	—	8	1	no	—
122	C₂³×C₃₁	—	8	1	no	—
123	C₂³×C₃₁	—	8	1	no	—
124	C₂³×C₃₁	—	8	1	no	—
125	C₂³×C₃₁	—	8	1	no	—
126	C₂³×C₃₁	—	8	1	no	—
127	C₂³×C₃₁	#127	1	1	yes	characteristic
128	Q₈×C₃₁	—	4	4	no	—
129	Q₈×C₃₁	—	4	4	no	—
130	Q₈×C₃₁	—	8	2	no	—
131	Q₈×C₃₁	—	8	2	no	—
132	D₄×C₃₁	—	4	4	no	—
133	D₄×C₃₁	—	4	4	no	—
134	D₄×C₃₁	—	4	4	no	—
135	D₄×C₃₁	—	8	2	no	—
136	D₄×C₃₁	—	8	2	no	—
137	D₄×C₃₁	—	8	2	no	—
138	C₂×C₄×C₃₁	—	4	2	no	—
139	C₂×C₄×C₃₁	—	4	2	no	—
140	C₂×C₄×C₃₁	—	8	1	no	—
141	C₂×C₄×C₃₁	—	8	1	no	—
142	C₂×C₄×C₃₁	—	8	1	no	—
143	C₂×C₄×C₃₁	—	8	1	no	—
144	C₂×C₄×C₃₁	—	8	1	no	—
145	C₂×C₄×C₃₁	—	8	1	no	—
146	C₂×C₄×C₃₁	—	8	1	no	—
147	C₂×C₄×C₃₁	#120	1	1	yes	characteristic
148	C₂×C₄×C₃₁	#120	1	1	yes	characteristic
149	C₂×C₄×C₃₁	#120	1	1	yes	characteristic
150	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
151	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
152	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
153	C₂×C₄×C₃₁	C₂×SD₁₆	1	2	yes	—
154	C₂×C₄×C₃₁	#135	1	2	yes	—
155	C₂×C₄×C₃₁	#135	1	2	yes	—
156	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
157	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
158	C₂×C₄×C₃₁	#137	1	2	yes	—
159	C₈×C₃₁	—	2	4	no	—
160	C₈×C₃₁	—	4	2	no	—
161	C₈×C₃₁	—	4	2	no	—
162	C₂×#492	C₂×C₃₁	1	1	yes	characteristic
163	C₂×#487	C₂×C₃₁	1	1	yes	characteristic, complemented
164	C₂×#486	C₂×C₃₁	1	1	yes	characteristic
165	#1990	C₂×C₃₁	1	1	yes	characteristic, complemented
166	#1990	C₂×C₃₁	1	1	yes	characteristic, complemented
167	#1957	C₂×C₃₁	1	1	yes	characteristic
168	#1273	C₂×C₃₁	1	1	yes	characteristic, complemented
169	C₂²×C₃₁	—	8	2	no	—
170	C₂²×C₃₁	—	8	2	no	—
171	C₂²×C₃₁	—	8	2	no	—
172	C₂²×C₃₁	—	16	1	no	—
173	C₂²×C₃₁	—	16	1	no	—
174	C₂²×C₃₁	—	16	1	no	—
175	C₂²×C₃₁	—	16	1	no	—
176	C₂²×C₃₁	#392	1	1	yes	characteristic
177	C₂²×C₃₁	#492	1	1	yes	characteristic
178	C₂²×C₃₁	#495	1	1	yes	characteristic
179	C₂²×C₃₁	#495	1	1	yes	characteristic
180	C₂²×C₃₁	#496	1	1	yes	characteristic
181	C₂²×C₃₁	#496	1	1	yes	characteristic
182	C₂²×C₃₁	#497	1	1	yes	characteristic
183	C₄×C₃₁	—	8	2	no	—
184	C₄×C₃₁	—	8	2	no	—
185	C₄×C₃₁	—	16	1	no	—
186	C₄×C₃₁	#449	1	2	yes	—
187	C₄×C₃₁	#450	1	2	yes	—
188	C₄×C₃₁	#452	1	2	yes	—
189	C₄×C₃₁	#460	1	2	yes	—
190	C₄×C₃₁	#463	1	2	yes	—
191	C₄×C₃₁	#464	1	2	yes	—
192	C₂²×SD₁₆	—	2	2	no	—
193	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
194	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
195	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
196	#492	—	2	2	no	—
197	#492	—	2	2	no	—
198	#487	—	2	2	no	—
199	#487	—	2	2	no	—
200	#486	—	2	2	no	—
201	#486	—	2	2	no	—
202	C₂×#103	—	2	2	no	—
203	C₂×#102	—	2	2	no	—
204	C₂×#102	—	2	2	no	—
205	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
206	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
207	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
208	#384	C₂²×C₃₁	1	1	yes	characteristic
209	#340	—	2	2	no	—
210	#340	—	2	2	no	—
211	C₂×C₃₁	—	16	2	no	—
212	C₂×C₃₁	#1708	1	1	yes	characteristic
213	C₂×C₃₁	#1714	1	1	yes	characteristic
214	C₂×C₃₁	#1717	1	1	yes	characteristic
215	C₂×C₃₁	#1719	1	1	yes	characteristic
216	C₂×C₃₁	#2012	1	1	yes	characteristic
217	C₂×C₃₁	#2014	1	1	yes	characteristic
218	C₂×C₃₁	#2015	1	1	yes	characteristic
219	C₂²×Q₈	—	2	1	no	—
220	C₂²×Q₈	—	2	1	no	—
221	C₂²×D₄	—	2	1	no	—
222	C₂²×D₄	—	2	1	no	—
223	C₂²×D₄	—	2	1	no	—
224	C₂×SD₁₆	—	2	8	no	—
225	C₂×SD₁₆	—	4	4	no	—
226	C₂×SD₁₆	—	4	4	no	—
227	C₂²×C₈	D₄×C₃₁	1	2	yes	—
228	C₂²×C₈	D₄×C₃₁	1	2	yes	—
229	C₂²×C₈	D₄×C₃₁	1	2	yes	—
230	C₄⋊Q₈	—	2	1	no	—
231	C₄⋊Q₈	—	2	1	no	—
232	C₄⋊Q₈	—	2	1	no	—
233	C₄⋊Q₈	—	2	1	no	—
234	C₄⋊Q₈	—	2	1	no	—
235	C₄⋊Q₈	—	2	1	no	—
236	C₄⋊Q₈	D₄×C₃₁	1	2	yes	—
237	C₄⋊Q₈	D₄×C₃₁	1	2	yes	—
238	#127	—	2	1	no	—
239	#127	—	2	1	no	—
240	#127	—	2	1	no	—
241	#127	D₄×C₃₁	1	2	yes	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
250	#103	—	2	8	no	—
251	#102	—	2	8	no	—
252	#102	—	4	4	no	—
253	C₄×C₈	—	2	1	no	—
254	C₄×C₈	—	2	1	no	—
255	C₄×C₈	—	2	1	no	—
256	C₄×C₈	—	2	1	no	—
257	C₄×C₈	—	2	1	no	—
258	C₄×C₈	—	2	1	no	—
259	C₃₁	#10310	1	1	yes	characteristic, direct product factor, Sylow
260	C₂⁴	—	4	1	no	—
261	C₂×Q₈	—	2	2	no	—
262	C₂×Q₈	—	2	2	no	—
263	C₂×Q₈	—	4	1	no	—
264	C₂×Q₈	—	4	1	no	—
265	C₂×Q₈	—	4	2	no	—
266	C₂×Q₈	—	4	2	no	—
267	C₂×Q₈	—	4	2	no	—
268	C₂×Q₈	—	4	2	no	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	—	2	2	no	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	4	1	no	—
273	C₂×D₄	—	4	1	no	—
274	C₂×D₄	—	4	1	no	—
275	C₂×D₄	—	4	2	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	2	no	—
280	C₂×D₄	—	4	2	no	—
281	C₂²×C₄	—	4	1	no	—
282	C₂²×C₄	—	4	1	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
285	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
287	SD₁₆	—	4	16	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	SD₁₆×C₃₁	1	4	yes	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	4	1	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	4	2	no	—
306	C₄⋊C₄	—	4	2	no	—
307	C₄⋊C₄	—	4	2	no	—
308	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
309	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
310	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
311	C₄²	#41×C₃₁	1	1	yes	characteristic
312	C₂³	—	4	2	no	—
313	C₂³	—	8	1	no	—
314	C₂³	—	8	1	no	—
315	C₂³	—	8	1	no	—
316	C₂³	—	8	1	no	—
317	C₂³	—	8	1	no	—
318	C₂³	—	8	1	no	—
319	C₂³	C₃₁×#127	1	1	yes	characteristic
320	Q₈	—	4	4	no	—
321	Q₈	—	4	4	no	—
322	Q₈	—	8	2	no	—
323	Q₈	—	8	2	no	—
324	D₄	—	4	4	no	—
325	D₄	—	4	4	no	—
326	D₄	—	4	4	no	—
327	D₄	—	8	2	no	—
328	D₄	—	8	2	no	—
329	D₄	—	8	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	8	1	no	—
333	C₂×C₄	—	8	1	no	—
334	C₂×C₄	—	8	1	no	—
335	C₂×C₄	—	8	1	no	—
336	C₂×C₄	—	8	1	no	—
337	C₂×C₄	—	8	1	no	—
338	C₂×C₄	—	8	1	no	—
339	C₂×C₄	C₃₁×#120	1	1	yes	characteristic
340	C₂×C₄	C₃₁×#120	1	1	yes	characteristic
341	C₂×C₄	C₃₁×#120	1	1	yes	characteristic
342	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
343	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
344	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
345	C₂×C₄	C₂×SD₁₆×C₃₁	1	2	yes	—
346	C₂×C₄	C₃₁×#135	1	2	yes	—
347	C₂×C₄	C₃₁×#135	1	2	yes	—
348	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
349	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
350	C₂×C₄	C₃₁×#137	1	2	yes	—
351	C₈	—	2	4	no	—
352	C₈	—	4	2	no	—
353	C₈	—	4	2	no	—
354	C₂²	—	8	2	no	—
355	C₂²	—	8	2	no	—
356	C₂²	—	8	2	no	—
357	C₂²	—	16	1	no	—
358	C₂²	—	16	1	no	—
359	C₂²	—	16	1	no	—
360	C₂²	—	16	1	no	—
361	C₂²	C₃₁×#392	1	1	yes	characteristic
362	C₂²	C₃₁×#492	1	1	yes	characteristic
363	C₂²	C₃₁×#495	1	1	yes	characteristic
364	C₂²	C₃₁×#495	1	1	yes	characteristic
365	C₂²	C₃₁×#496	1	1	yes	characteristic
366	C₂²	C₃₁×#496	1	1	yes	characteristic
367	C₂²	C₃₁×#497	1	1	yes	characteristic
368	C₄	—	8	2	no	—
369	C₄	—	8	2	no	—
370	C₄	—	16	1	no	—
371	C₄	C₃₁×#449	1	2	yes	—
372	C₄	C₃₁×#450	1	2	yes	—
373	C₄	C₃₁×#452	1	2	yes	—
374	C₄	C₃₁×#460	1	2	yes	—
375	C₄	C₃₁×#463	1	2	yes	—
376	C₄	C₃₁×#464	1	2	yes	—
377	C₂	—	16	2	no	—
378	C₂	C₃₁×#1708	1	1	yes	characteristic
379	C₂	C₃₁×#1714	1	1	yes	characteristic
380	C₂	C₃₁×#1717	1	1	yes	characteristic
381	C₂	C₃₁×#1719	1	1	yes	characteristic
382	C₂	C₃₁×#2012	1	1	yes	characteristic
383	C₂	C₃₁×#2014	1	1	yes	characteristic
384	C₂	C₃₁×#2015	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₃₁
prime radical	C₂×C₃₁×#127	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₁×#487	C₂	semidirect
4. C₃₁×#1990	C₂	semidirect
5. C₃₁×#1990	C₂	semidirect
7. C₃₁×#1273	C₂	semidirect
119. #10310	C₃₁	direct (N × H)
163. C₂×#487	C₂×C₃₁	semidirect
165. #1990	C₂×C₃₁	semidirect
166. #1990	C₂×C₃₁	semidirect
168. #1273	C₂×C₃₁	semidirect
259. C₃₁	#10310	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×#492	2
C₂×C₃₁×#487	2
C₂×C₃₁×#486	2
C₃₁×#1990	2
C₃₁×#1957	2
C₃₁×#1273	2
#10310	31

Subgroups — C31×#10310 #21467069

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#10310 #21467069