Subgroups — C₃₁×#62537 #21519296

Order 7936.

1818 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3508	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3375	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3333	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3314	C₂	1	8	yes	maximal, complemented
6	C₃₁×#3230	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3226	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3210	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3208	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3182	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3170	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3141	C₂	1	2	yes	maximal, complemented
13	C₂×C₃₁×#486	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2965	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#559	—	2	1	no	—
16	C₃₁×#559	C₂²	1	2	yes	—
17	Q₈²×C₃₁	C₂²	1	2	yes	complemented
18	C₃₁×#557	—	2	1	no	—
19	C₃₁×#554	C₂²	1	4	yes	—
20	C₃₁×#554	C₂²	1	2	yes	complemented
21	C₃₁×#550	—	2	1	no	—
22	C₃₁×#550	C₂²	1	2	yes	—
23	D₄×Q₈×C₃₁	—	2	2	no	—
24	D₄×Q₈×C₃₁	—	2	1	no	—
25	C₃₁×#546	—	2	2	no	—
26	C₃₁×#546	C₂²	1	4	yes	—
27	C₃₁×#544	—	2	1	no	—
28	C₃₁×#544	—	2	2	no	—
29	C₃₁×#540	—	2	2	no	—
30	C₃₁×#535	—	2	1	no	—
31	C₃₁×#533	C₂²	1	1	yes	characteristic
32	C₃₁×#533	C₂²	1	1	yes	characteristic
33	C₃₁×#533	C₂²	1	2	yes	complemented
34	C₃₁×#532	C₂²	1	2	yes	—
35	C₃₁×#532	C₂²	1	2	yes	—
36	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	complemented
38	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
39	C₃₁×#520	—	2	1	no	—
40	C₃₁×#518	—	2	1	no	—
41	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
42	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
43	C₃₁×#500	C₂²	1	2	yes	complemented
44	C₃₁×#494	C₂²	1	1	yes	characteristic, complemented
45	C₃₁×#492	C₂²	1	2	yes	—
46	C₃₁×#489	C₂²	1	8	yes	complemented
47	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#487	C₂²	1	2	yes	complemented
49	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#486	C₂²	1	4	yes	—
51	C₃₁×#486	C₂²	1	2	yes	—
52	C₃₁×#486	C₂²	1	2	yes	—
53	C₃₁×#486	C₂²	1	2	yes	—
54	C₃₁×#484	C₂²	1	4	yes	—
55	C₃₁×#480	C₂²	1	8	yes	complemented
56	C₃₁×#477	C₂²	1	4	yes	complemented
57	C₃₁×#474	C₂²	1	8	yes	complemented
58	C₃₁×#468	C₂²	1	8	yes	complemented
59	C₃₁×#467	C₂²	1	4	yes	—
60	C₃₁×#464	C₂²	1	8	yes	complemented
61	C₃₁×#460	C₂²	1	4	yes	—
62	C₃₁×#452	C₂²	1	8	yes	complemented
63	C₃₁×#450	C₂²	1	4	yes	—
64	C₃₁×#446	C₂²	1	2	yes	complemented
65	C₃₁×#440	C₂²	1	8	yes	complemented
66	C₄×Q₁₆×C₃₁	C₂²	1	4	yes	complemented
67	C₃₁×#436	C₂²	1	2	yes	complemented
68	C₃₁×#435	C₂²	1	4	yes	—
69	C₃₁×#431	C₂²	1	1	yes	characteristic
70	C₃₁×#431	C₂²	1	2	yes	complemented
71	C₃₁×#417	C₂²	1	8	yes	complemented
72	C₂×C₃₁×#102	C₂²	1	4	yes	—
73	C₄×M₁₆×C₃₁	C₂²	1	2	yes	complemented
74	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
75	C₂×#41×C₃₁	—	2	2	no	—
76	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
77	C₂×#41×C₃₁	C₂³	1	4	yes	—
78	C₂²×Q₈×C₃₁	—	2	1	no	—
79	C₂²×Q₈×C₃₁	—	2	2	no	—
80	C₂²×D₄×C₃₁	—	2	1	no	—
81	C₂²×D₄×C₃₁	—	2	1	no	—
82	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
83	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
84	C₂×SD₁₆×C₃₁	C₂³	1	8	yes	—
85	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
86	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
87	C₃₁×C₄⋊Q₈	—	2	2	no	—
88	C₃₁×C₄⋊Q₈	—	2	4	no	—
89	C₃₁×C₄⋊Q₈	—	2	1	no	—
90	C₃₁×C₄⋊Q₈	—	2	1	no	—
91	C₃₁×C₄⋊Q₈	—	2	2	no	—
92	C₃₁×C₄⋊Q₈	—	2	2	no	—
93	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
94	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
95	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
96	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
97	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
98	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
99	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
100	C₃₁×#127	—	2	2	no	—
101	C₃₁×#127	—	2	1	no	—
102	C₃₁×#127	—	2	1	no	—
103	C₃₁×#127	C₂³	1	2	yes	—
104	C₃₁×#127	C₂³	1	2	yes	—
105	C₃₁×#125	—	2	4	no	—
106	C₃₁×#125	—	2	2	no	—
107	C₃₁×#125	—	2	1	no	—
108	C₃₁×#125	—	2	1	no	—
109	C₃₁×#125	—	2	2	no	—
110	C₃₁×#124	—	2	2	no	—
111	C₃₁×#124	—	2	2	no	—
112	C₃₁×#124	C₂³	1	4	yes	—
113	C₃₁×#123	—	2	4	no	—
114	C₃₁×#123	—	2	4	no	—
115	C₃₁×C₂²⋊Q₈	—	2	1	no	—
116	C₃₁×C₂²⋊Q₈	—	2	1	no	—
117	C₃₁×C₂²⋊Q₈	—	2	2	no	—
118	C₃₁×C₂²⋊Q₈	—	2	4	no	—
119	C₃₁×C₂²⋊Q₈	—	2	4	no	—
120	C₃₁×C₂²⋊Q₈	—	2	4	no	—
121	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
122	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
123	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
124	C₃₁×#121	—	2	2	no	—
125	C₃₁×#121	—	2	2	no	—
126	C₃₁×#121	—	2	2	no	—
127	C₃₁×#121	—	2	4	no	—
128	C₃₁×#121	—	2	4	no	—
129	C₃₁×#121	C₂³	1	4	yes	—
130	C₃₁×#120	—	2	4	no	—
131	C₄×Q₈×C₃₁	—	2	2	no	—
132	C₄×Q₈×C₃₁	—	2	1	no	—
133	C₄×Q₈×C₃₁	—	2	1	no	—
134	C₄×Q₈×C₃₁	—	2	2	no	—
135	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
136	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
137	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
138	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
139	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
140	C₄×D₄×C₃₁	—	2	4	no	—
141	C₄×D₄×C₃₁	—	2	2	no	—
142	C₄×D₄×C₃₁	—	2	2	no	—
143	C₄×D₄×C₃₁	—	2	2	no	—
144	C₄×D₄×C₃₁	—	2	2	no	—
145	C₄×D₄×C₃₁	—	2	2	no	—
146	C₄×D₄×C₃₁	—	2	2	no	—
147	C₄×D₄×C₃₁	D₄	1	2	yes	—
148	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
149	C₄×D₄×C₃₁	C₂³	1	4	yes	—
150	C₄×D₄×C₃₁	C₂³	1	2	yes	—
151	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
152	C₃₁×#117	—	2	1	no	—
153	C₃₁×#117	—	2	1	no	—
154	C₃₁×#117	—	2	2	no	—
155	C₃₁×#117	D₄	1	1	yes	characteristic
156	C₃₁×#117	D₄	1	2	yes	—
157	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
158	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
159	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
161	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
162	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
164	C₃₁×#107	C₂³	1	4	yes	—
165	C₃₁×#107	C₂³	1	8	yes	—
166	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
167	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
168	C₃₁×#103	C₂³	1	4	yes	—
169	C₃₁×#103	C₂³	1	8	yes	—
170	C₃₁×#103	C₂³	1	4	yes	—
171	C₃₁×#102	C₂³	1	8	yes	—
172	C₃₁×#102	C₂³	1	8	yes	—
173	C₃₁×#102	C₂³	1	8	yes	—
174	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
175	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
176	C₃₁×#97	C₂³	1	4	yes	—
177	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
178	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
179	C₄×C₈×C₃₁	C₂³	1	2	yes	—
180	C₄×C₈×C₃₁	C₂³	1	2	yes	—
181	C₂⁴×C₃₁	—	2	2	no	—
182	#41×C₃₁	—	2	4	no	—
183	#41×C₃₁	—	4	8	no	—
184	#41×C₃₁	—	8	4	no	—
185	C₂×Q₈×C₃₁	—	2	1	no	—
186	C₂×Q₈×C₃₁	—	2	1	no	—
187	C₂×Q₈×C₃₁	—	2	2	no	—
188	C₂×Q₈×C₃₁	—	2	4	no	—
189	C₂×Q₈×C₃₁	—	2	2	no	—
190	C₂×Q₈×C₃₁	—	8	2	no	—
191	C₂×Q₈×C₃₁	—	8	4	no	—
192	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
193	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
194	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
195	C₂×D₄×C₃₁	—	2	4	no	—
196	C₂×D₄×C₃₁	—	2	4	no	—
197	C₂×D₄×C₃₁	—	2	2	no	—
198	C₂×D₄×C₃₁	—	2	2	no	—
199	C₂×D₄×C₃₁	—	2	2	no	—
200	C₂×D₄×C₃₁	—	2	2	no	—
201	C₂×D₄×C₃₁	—	2	2	no	—
202	C₂×D₄×C₃₁	—	4	4	no	—
203	C₂×D₄×C₃₁	—	4	4	no	—
204	C₂×D₄×C₃₁	—	8	2	no	—
205	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
206	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
207	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
208	C₂²×C₄×C₃₁	—	2	4	no	—
209	C₂²×C₄×C₃₁	—	2	2	no	—
210	C₂²×C₄×C₃₁	—	2	4	no	—
211	C₂²×C₄×C₃₁	—	2	4	no	—
212	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
213	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
214	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
218	Q₁₆×C₃₁	—	4	4	no	—
219	SD₁₆×C₃₁	—	4	8	no	—
220	M₁₆×C₃₁	—	4	4	no	—
221	C₂×C₈×C₃₁	—	4	2	no	—
222	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
223	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
224	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
225	C₄⋊C₄×C₃₁	—	2	2	no	—
226	C₄⋊C₄×C₃₁	—	2	1	no	—
227	C₄⋊C₄×C₃₁	—	2	4	no	—
228	C₄⋊C₄×C₃₁	—	2	2	no	—
229	C₄⋊C₄×C₃₁	—	2	4	no	—
230	C₄⋊C₄×C₃₁	—	2	2	no	—
231	C₄⋊C₄×C₃₁	—	2	1	no	—
232	C₄⋊C₄×C₃₁	—	2	1	no	—
233	C₄⋊C₄×C₃₁	—	2	1	no	—
234	C₄⋊C₄×C₃₁	—	2	1	no	—
235	C₄⋊C₄×C₃₁	—	2	1	no	—
236	C₄⋊C₄×C₃₁	—	2	2	no	—
237	C₄⋊C₄×C₃₁	—	2	4	no	—
238	C₄⋊C₄×C₃₁	—	2	2	no	—
239	C₄⋊C₄×C₃₁	—	2	2	no	—
240	C₄⋊C₄×C₃₁	—	2	4	no	—
241	C₄⋊C₄×C₃₁	—	2	2	no	—
242	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
243	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
244	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
245	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
246	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
247	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
248	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
249	C₂²⋊C₄×C₃₁	—	2	2	no	—
250	C₂²⋊C₄×C₃₁	—	2	4	no	—
251	C₂²⋊C₄×C₃₁	—	2	2	no	—
252	C₂²⋊C₄×C₃₁	—	2	4	no	—
253	C₂²⋊C₄×C₃₁	—	2	4	no	—
254	C₂²⋊C₄×C₃₁	—	2	4	no	—
255	C₂²⋊C₄×C₃₁	—	2	4	no	—
256	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
257	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
258	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
259	C₄²×C₃₁	—	2	2	no	—
260	C₄²×C₃₁	—	2	4	no	—
261	C₄²×C₃₁	—	2	2	no	—
262	C₄²×C₃₁	C₂×D₄	1	2	yes	—
263	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
264	C₄²×C₃₁	C₂×D₄	1	2	yes	—
265	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
266	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
267	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
268	C₄²×C₃₁	C₂⁴	1	2	yes	—
269	#62537	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
270	C₂³×C₃₁	—	2	4	no	—
271	C₂³×C₃₁	—	4	4	no	—
272	C₂³×C₃₁	—	8	2	no	—
273	C₂³×C₃₁	—	8	2	no	—
274	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
275	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
276	Q₈×C₃₁	—	2	2	no	—
277	Q₈×C₃₁	—	2	4	no	—
278	Q₈×C₃₁	—	2	4	no	—
279	Q₈×C₃₁	—	4	2	no	—
280	Q₈×C₃₁	—	4	4	no	—
281	Q₈×C₃₁	—	4	2	no	—
282	Q₈×C₃₁	—	8	4	no	—
283	Q₈×C₃₁	—	8	2	no	—
284	D₄×C₃₁	—	2	4	no	—
285	D₄×C₃₁	—	2	2	no	—
286	D₄×C₃₁	—	2	8	no	—
287	D₄×C₃₁	—	4	4	no	—
288	D₄×C₃₁	—	4	4	no	—
289	D₄×C₃₁	—	4	4	no	—
290	D₄×C₃₁	—	8	2	no	—
291	D₄×C₃₁	—	8	2	no	—
292	D₄×C₃₁	—	8	4	no	—
293	D₄×C₃₁	—	8	4	no	—
294	C₂×C₄×C₃₁	—	2	4	no	—
295	C₂×C₄×C₃₁	—	2	2	no	—
296	C₂×C₄×C₃₁	—	2	4	no	—
297	C₂×C₄×C₃₁	—	2	2	no	—
298	C₂×C₄×C₃₁	—	2	4	no	—
299	C₂×C₄×C₃₁	—	2	2	no	—
300	C₂×C₄×C₃₁	—	2	2	no	—
301	C₂×C₄×C₃₁	—	2	2	no	—
302	C₂×C₄×C₃₁	—	2	4	no	—
303	C₂×C₄×C₃₁	—	2	2	no	—
304	C₂×C₄×C₃₁	—	8	4	no	—
305	C₂×C₄×C₃₁	—	8	4	no	—
306	C₂×C₄×C₃₁	—	8	2	no	—
307	C₂×C₄×C₃₁	—	8	4	no	—
308	C₂×C₄×C₃₁	#137	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	1	yes	characteristic
312	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
313	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
314	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
315	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
316	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
317	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
318	C₈×C₃₁	—	2	2	no	—
319	C₈×C₃₁	—	2	2	no	—
320	C₈×C₃₁	—	2	4	no	—
321	#3508	C₂×C₃₁	1	1	yes	characteristic
322	#3503	C₂×C₃₁	1	1	yes	characteristic, complemented
323	#3375	C₂×C₃₁	1	4	yes	complemented
324	#3333	C₂×C₃₁	1	4	yes	complemented
325	#3314	C₂×C₃₁	1	8	yes	complemented
326	#3230	C₂×C₃₁	1	1	yes	characteristic, complemented
327	#3226	C₂×C₃₁	1	2	yes	complemented
328	#3210	C₂×C₃₁	1	2	yes	complemented
329	#3208	C₂×C₃₁	1	1	yes	characteristic, complemented
330	#3182	C₂×C₃₁	1	2	yes	complemented
331	#3170	C₂×C₃₁	1	1	yes	characteristic, complemented
332	#3141	C₂×C₃₁	1	2	yes	complemented
333	C₂×#486	C₂×C₃₁	1	1	yes	characteristic, complemented
334	#2965	C₂×C₃₁	1	1	yes	characteristic, complemented
335	C₂²×C₃₁	—	2	1	no	—
336	C₂²×C₃₁	—	2	1	no	—
337	C₂²×C₃₁	—	2	2	no	—
338	C₂²×C₃₁	—	2	2	no	—
339	C₂²×C₃₁	—	2	2	no	—
340	C₂²×C₃₁	—	4	4	no	—
341	C₂²×C₃₁	—	4	4	no	—
342	C₂²×C₃₁	—	4	4	no	—
343	C₂²×C₃₁	—	16	4	no	—
344	C₂²×C₃₁	C₂×#137	1	2	yes	—
345	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
346	C₄×C₃₁	—	2	2	no	—
347	C₄×C₃₁	—	2	1	no	—
348	C₄×C₃₁	—	2	2	no	—
349	C₄×C₃₁	—	2	2	no	—
350	C₄×C₃₁	—	2	1	no	—
351	C₄×C₃₁	—	4	2	no	—
352	C₄×C₃₁	—	4	2	no	—
353	C₄×C₃₁	—	4	2	no	—
354	C₄×C₃₁	—	4	4	no	—
355	C₄×C₃₁	—	4	2	no	—
356	C₄×C₃₁	C₂×#137	1	2	yes	—
357	C₄×C₃₁	C₂×#137	1	2	yes	—
358	C₄×C₃₁	#576	1	2	yes	—
359	C₄×C₃₁	#585	1	2	yes	—
360	#559	—	2	1	no	—
361	#559	C₂²×C₃₁	1	2	yes	—
362	Q₈²	C₂²×C₃₁	1	2	yes	complemented
363	#557	—	2	1	no	—
364	#554	C₂²×C₃₁	1	4	yes	—
365	#554	C₂²×C₃₁	1	2	yes	complemented
366	#550	—	2	1	no	—
367	#550	C₂²×C₃₁	1	2	yes	—
368	D₄×Q₈	—	2	2	no	—
369	D₄×Q₈	—	2	1	no	—
370	#546	—	2	2	no	—
371	#546	C₂²×C₃₁	1	4	yes	—
372	#544	—	2	1	no	—
373	#544	—	2	2	no	—
374	#540	—	2	2	no	—
375	#535	—	2	1	no	—
376	#533	C₂²×C₃₁	1	1	yes	characteristic
377	#533	C₂²×C₃₁	1	1	yes	characteristic
378	#533	C₂²×C₃₁	1	2	yes	complemented
379	#532	C₂²×C₃₁	1	2	yes	—
380	#532	C₂²×C₃₁	1	2	yes	—
381	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
382	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
383	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
384	#520	—	2	1	no	—
385	#518	—	2	1	no	—
386	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
387	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
388	#500	C₂²×C₃₁	1	2	yes	complemented
389	#494	C₂²×C₃₁	1	1	yes	characteristic, complemented
390	#492	C₂²×C₃₁	1	2	yes	—
391	#489	C₂²×C₃₁	1	8	yes	complemented
392	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
393	#487	C₂²×C₃₁	1	2	yes	complemented
394	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
395	#486	C₂²×C₃₁	1	4	yes	—
396	#486	C₂²×C₃₁	1	2	yes	—
397	#486	C₂²×C₃₁	1	2	yes	—
398	#486	C₂²×C₃₁	1	2	yes	—
399	#484	C₂²×C₃₁	1	4	yes	—
400	#480	C₂²×C₃₁	1	8	yes	complemented
401	#477	C₂²×C₃₁	1	4	yes	complemented
402	#474	C₂²×C₃₁	1	8	yes	complemented
403	#468	C₂²×C₃₁	1	8	yes	complemented
404	#467	C₂²×C₃₁	1	4	yes	—
405	#464	C₂²×C₃₁	1	8	yes	complemented
406	#460	C₂²×C₃₁	1	4	yes	—
407	#452	C₂²×C₃₁	1	8	yes	complemented
408	#450	C₂²×C₃₁	1	4	yes	—
409	#446	C₂²×C₃₁	1	2	yes	complemented
410	#440	C₂²×C₃₁	1	8	yes	complemented
411	C₄×Q₁₆	C₂²×C₃₁	1	4	yes	complemented
412	#436	C₂²×C₃₁	1	2	yes	complemented
413	#435	C₂²×C₃₁	1	4	yes	—
414	#431	C₂²×C₃₁	1	1	yes	characteristic
415	#431	C₂²×C₃₁	1	2	yes	complemented
416	#417	C₂²×C₃₁	1	8	yes	complemented
417	C₂×#102	C₂²×C₃₁	1	4	yes	—
418	C₄×M₁₆	C₂²×C₃₁	1	2	yes	complemented
419	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
420	C₂×C₃₁	—	2	2	no	—
421	C₂×C₃₁	—	4	2	no	—
422	C₂×C₃₁	—	8	4	no	—
423	C₂×C₃₁	#3500	1	1	yes	characteristic
424	C₂×C₃₁	C₂²×#137	1	1	yes	characteristic
425	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
426	C₂×#41	—	2	2	no	—
427	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
428	C₂×#41	C₂³×C₃₁	1	4	yes	—
429	C₂²×Q₈	—	2	1	no	—
430	C₂²×Q₈	—	2	2	no	—
431	C₂²×D₄	—	2	1	no	—
432	C₂²×D₄	—	2	1	no	—
433	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
434	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
435	C₂×SD₁₆	C₂³×C₃₁	1	8	yes	—
436	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
437	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
438	C₄⋊Q₈	—	2	2	no	—
439	C₄⋊Q₈	—	2	4	no	—
440	C₄⋊Q₈	—	2	1	no	—
441	C₄⋊Q₈	—	2	1	no	—
442	C₄⋊Q₈	—	2	2	no	—
443	C₄⋊Q₈	—	2	2	no	—
444	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
445	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
446	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
447	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
448	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
449	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
450	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
451	#127	—	2	2	no	—
452	#127	—	2	1	no	—
453	#127	—	2	1	no	—
454	#127	C₂³×C₃₁	1	2	yes	—
455	#127	C₂³×C₃₁	1	2	yes	—
456	#125	—	2	4	no	—
457	#125	—	2	2	no	—
458	#125	—	2	1	no	—
459	#125	—	2	1	no	—
460	#125	—	2	2	no	—
461	#124	—	2	2	no	—
462	#124	—	2	2	no	—
463	#124	C₂³×C₃₁	1	4	yes	—
464	#123	—	2	4	no	—
465	#123	—	2	4	no	—
466	C₂²⋊Q₈	—	2	1	no	—
467	C₂²⋊Q₈	—	2	1	no	—
468	C₂²⋊Q₈	—	2	2	no	—
469	C₂²⋊Q₈	—	2	4	no	—
470	C₂²⋊Q₈	—	2	4	no	—
471	C₂²⋊Q₈	—	2	4	no	—
472	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
473	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
474	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
475	#121	—	2	2	no	—
476	#121	—	2	2	no	—
477	#121	—	2	2	no	—
478	#121	—	2	4	no	—
479	#121	—	2	4	no	—
480	#121	C₂³×C₃₁	1	4	yes	—
481	#120	—	2	4	no	—
482	C₄×Q₈	—	2	2	no	—
483	C₄×Q₈	—	2	1	no	—
484	C₄×Q₈	—	2	1	no	—
485	C₄×Q₈	—	2	2	no	—
486	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
487	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
488	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
489	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
490	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
491	C₄×D₄	—	2	4	no	—
492	C₄×D₄	—	2	2	no	—
493	C₄×D₄	—	2	2	no	—
494	C₄×D₄	—	2	2	no	—
495	C₄×D₄	—	2	2	no	—
496	C₄×D₄	—	2	2	no	—
497	C₄×D₄	—	2	2	no	—
498	C₄×D₄	D₄×C₃₁	1	2	yes	—
499	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
500	C₄×D₄	C₂³×C₃₁	1	4	yes	—
501	C₄×D₄	C₂³×C₃₁	1	2	yes	—
502	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
503	#117	—	2	1	no	—
504	#117	—	2	1	no	—
505	#117	—	2	2	no	—
506	#117	D₄×C₃₁	1	1	yes	characteristic
507	#117	D₄×C₃₁	1	2	yes	—
508	C₂×C₄⋊C₄	—	2	1	no	—
509	C₂×C₄⋊C₄	—	2	2	no	—
510	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
512	C₂×C₂²⋊C₄	—	2	4	no	—
513	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
514	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
515	#107	C₂³×C₃₁	1	4	yes	—
516	#107	C₂³×C₃₁	1	8	yes	—
517	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
518	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
519	#103	C₂³×C₃₁	1	4	yes	—
520	#103	C₂³×C₃₁	1	8	yes	—
521	#103	C₂³×C₃₁	1	4	yes	—
522	#102	C₂³×C₃₁	1	8	yes	—
523	#102	C₂³×C₃₁	1	8	yes	—
524	#102	C₂³×C₃₁	1	8	yes	—
525	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
526	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
527	#97	C₂³×C₃₁	1	4	yes	—
528	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
529	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
530	C₄×C₈	C₂³×C₃₁	1	2	yes	—
531	C₄×C₈	C₂³×C₃₁	1	2	yes	—
532	C₃₁	#62537	1	1	yes	characteristic, direct product factor, Sylow
533	C₂⁴	—	2	2	no	—
534	#41	—	2	4	no	—
535	#41	—	4	8	no	—
536	#41	—	8	4	no	—
537	C₂×Q₈	—	2	1	no	—
538	C₂×Q₈	—	2	1	no	—
539	C₂×Q₈	—	2	2	no	—
540	C₂×Q₈	—	2	4	no	—
541	C₂×Q₈	—	2	2	no	—
542	C₂×Q₈	—	8	2	no	—
543	C₂×Q₈	—	8	4	no	—
544	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
545	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
546	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
547	C₂×D₄	—	2	4	no	—
548	C₂×D₄	—	2	4	no	—
549	C₂×D₄	—	2	2	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	4	4	no	—
555	C₂×D₄	—	4	4	no	—
556	C₂×D₄	—	8	2	no	—
557	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
558	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
559	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
560	C₂²×C₄	—	2	4	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	4	no	—
563	C₂²×C₄	—	2	4	no	—
564	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
565	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
566	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
567	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
568	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
570	Q₁₆	—	4	4	no	—
571	SD₁₆	—	4	8	no	—
572	M₁₆	—	4	4	no	—
573	C₂×C₈	—	4	2	no	—
574	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
575	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
576	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
577	C₄⋊C₄	—	2	2	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	2	no	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	2	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	2	no	—
589	C₄⋊C₄	—	2	4	no	—
590	C₄⋊C₄	—	2	2	no	—
591	C₄⋊C₄	—	2	2	no	—
592	C₄⋊C₄	—	2	4	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
595	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
596	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
597	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
598	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
599	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
600	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
601	C₂²⋊C₄	—	2	2	no	—
602	C₂²⋊C₄	—	2	4	no	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	4	no	—
605	C₂²⋊C₄	—	2	4	no	—
606	C₂²⋊C₄	—	2	4	no	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
609	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
610	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
611	C₄²	—	2	2	no	—
612	C₄²	—	2	4	no	—
613	C₄²	—	2	2	no	—
614	C₄²	C₂×D₄×C₃₁	1	2	yes	—
615	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
616	C₄²	C₂×D₄×C₃₁	1	2	yes	—
617	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
618	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
619	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
620	C₄²	C₂⁴×C₃₁	1	2	yes	—
621	C₂³	—	2	4	no	—
622	C₂³	—	4	4	no	—
623	C₂³	—	8	2	no	—
624	C₂³	—	8	2	no	—
625	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
626	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
627	Q₈	—	2	2	no	—
628	Q₈	—	2	4	no	—
629	Q₈	—	2	4	no	—
630	Q₈	—	4	2	no	—
631	Q₈	—	4	4	no	—
632	Q₈	—	4	2	no	—
633	Q₈	—	8	4	no	—
634	Q₈	—	8	2	no	—
635	D₄	—	2	4	no	—
636	D₄	—	2	2	no	—
637	D₄	—	2	8	no	—
638	D₄	—	4	4	no	—
639	D₄	—	4	4	no	—
640	D₄	—	4	4	no	—
641	D₄	—	8	2	no	—
642	D₄	—	8	2	no	—
643	D₄	—	8	4	no	—
644	D₄	—	8	4	no	—
645	C₂×C₄	—	2	4	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	4	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	4	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	8	4	no	—
656	C₂×C₄	—	8	4	no	—
657	C₂×C₄	—	8	2	no	—
658	C₂×C₄	—	8	4	no	—
659	C₂×C₄	C₃₁×#137	1	4	yes	—
660	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
661	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
662	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
663	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
664	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
665	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
666	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
667	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
668	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
669	C₈	—	2	2	no	—
670	C₈	—	2	2	no	—
671	C₈	—	2	4	no	—
672	C₂²	—	2	1	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	4	4	no	—
678	C₂²	—	4	4	no	—
679	C₂²	—	4	4	no	—
680	C₂²	—	16	4	no	—
681	C₂²	C₂×C₃₁×#137	1	2	yes	—
682	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
683	C₄	—	2	2	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	2	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	1	no	—
688	C₄	—	4	2	no	—
689	C₄	—	4	2	no	—
690	C₄	—	4	2	no	—
691	C₄	—	4	4	no	—
692	C₄	—	4	2	no	—
693	C₄	C₂×C₃₁×#137	1	2	yes	—
694	C₄	C₂×C₃₁×#137	1	2	yes	—
695	C₄	C₃₁×#576	1	2	yes	—
696	C₄	C₃₁×#585	1	2	yes	—
697	C₂	—	2	2	no	—
698	C₂	—	4	2	no	—
699	C₂	—	8	4	no	—
700	C₂	C₃₁×#3500	1	1	yes	characteristic
701	C₂	C₂²×C₃₁×#137	1	1	yes	characteristic
702	C₂	C₂×C₃₁×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3508	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
2. C₃₁×#3503	C₂	semidirect
3. C₃₁×#3375	C₂	semidirect
4. C₃₁×#3333	C₂	semidirect
5. C₃₁×#3314	C₂	semidirect
6. C₃₁×#3230	C₂	semidirect
7. C₃₁×#3226	C₂	semidirect
8. C₃₁×#3210	C₂	semidirect
9. C₃₁×#3208	C₂	semidirect
10. C₃₁×#3182	C₂	semidirect
11. C₃₁×#3170	C₂	semidirect
12. C₃₁×#3141	C₂	semidirect
13. C₂×C₃₁×#486	C₂	semidirect
14. C₃₁×#2965	C₂	semidirect
17. Q₈²×C₃₁	C₂²	semidirect
20. C₃₁×#554	C₂²	semidirect
33. C₃₁×#533	C₂²	semidirect
37. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
42. C₃₁×#500	C₂²	semidirect
43. C₃₁×#500	C₂²	semidirect
44. C₃₁×#494	C₂²	semidirect
46. C₃₁×#489	C₂²	semidirect
47. C₃₁×#487	C₂²	semidirect
48. C₃₁×#487	C₂²	semidirect
49. C₃₁×#487	C₂²	semidirect
55. C₃₁×#480	C₂²	semidirect
56. C₃₁×#477	C₂²	semidirect
57. C₃₁×#474	C₂²	semidirect
58. C₃₁×#468	C₂²	semidirect
60. C₃₁×#464	C₂²	semidirect
62. C₃₁×#452	C₂²	semidirect
64. C₃₁×#446	C₂²	semidirect
65. C₃₁×#440	C₂²	semidirect
66. C₄×Q₁₆×C₃₁	C₂²	semidirect
67. C₃₁×#436	C₂²	semidirect
70. C₃₁×#431	C₂²	semidirect
71. C₃₁×#417	C₂²	semidirect
73. C₄×M₁₆×C₃₁	C₂²	semidirect
269. #62537	C₃₁	direct (N × H)
322. #3503	C₂×C₃₁	semidirect
323. #3375	C₂×C₃₁	semidirect
324. #3333	C₂×C₃₁	semidirect
325. #3314	C₂×C₃₁	semidirect
326. #3230	C₂×C₃₁	semidirect
327. #3226	C₂×C₃₁	semidirect
328. #3210	C₂×C₃₁	semidirect
329. #3208	C₂×C₃₁	semidirect
330. #3182	C₂×C₃₁	semidirect
331. #3170	C₂×C₃₁	semidirect
332. #3141	C₂×C₃₁	semidirect
333. C₂×#486	C₂×C₃₁	semidirect
334. #2965	C₂×C₃₁	semidirect
362. Q₈²	C₂²×C₃₁	semidirect
365. #554	C₂²×C₃₁	semidirect
378. #533	C₂²×C₃₁	semidirect
382. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
387. #500	C₂²×C₃₁	semidirect
388. #500	C₂²×C₃₁	semidirect
389. #494	C₂²×C₃₁	semidirect
391. #489	C₂²×C₃₁	semidirect
392. #487	C₂²×C₃₁	semidirect
393. #487	C₂²×C₃₁	semidirect
394. #487	C₂²×C₃₁	semidirect
400. #480	C₂²×C₃₁	semidirect
401. #477	C₂²×C₃₁	semidirect
402. #474	C₂²×C₃₁	semidirect
403. #468	C₂²×C₃₁	semidirect
405. #464	C₂²×C₃₁	semidirect
407. #452	C₂²×C₃₁	semidirect
409. #446	C₂²×C₃₁	semidirect
410. #440	C₂²×C₃₁	semidirect
411. C₄×Q₁₆	C₂²×C₃₁	semidirect
412. #436	C₂²×C₃₁	semidirect
415. #431	C₂²×C₃₁	semidirect
416. #417	C₂²×C₃₁	semidirect
418. C₄×M₁₆	C₂²×C₃₁	semidirect
532. C₃₁	#62537	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×#3508	2
C₃₁×#3503	2
C₃₁×#3375	2
C₃₁×#3333	2
C₃₁×#3314	2
C₃₁×#3230	2
C₃₁×#3226	2
C₃₁×#3210	2
C₃₁×#3208	2
C₃₁×#3182	2
C₃₁×#3170	2
C₃₁×#3141	2
C₂×C₃₁×#486	2
C₃₁×#2965	2
#62537	31

Subgroups — C31×#62537 #21519296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62537 #21519296