Subgroups — C₃₁×#61251 #21518010

Order 7936.

1842 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3475	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3357	C₂	1	2	yes	maximal, complemented
3	C₃₁×#3356	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3355	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3354	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3353	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3352	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3351	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3160	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3091	C₂	1	4	yes	maximal, complemented
11	C₃₁×#3076	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3054	C₂	1	2	yes	maximal, complemented
13	C₄×C₃₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃₁×#436	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2911	C₂	1	2	yes	maximal, complemented
16	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
18	C₃₁×#556	C₂²	1	2	yes	—
19	C₃₁×#555	C₂²	1	2	yes	—
20	C₃₁×#554	C₂²	1	2	yes	—
21	C₃₁×#553	C₂²	1	4	yes	—
22	C₃₁×#552	—	2	2	no	—
23	C₃₁×#552	C₂²	1	4	yes	—
24	C₃₁×#551	—	2	4	no	—
25	C₃₁×#547	C₂²	1	2	yes	—
26	C₃₁×#546	—	2	2	no	—
27	C₃₁×#533	C₂²	1	2	yes	—
28	C₃₁×#529	—	2	4	no	—
29	C₃₁×#529	—	2	2	no	—
30	C₃₁×#525	C₂²	1	4	yes	—
31	C₄×#41×C₃₁	—	2	2	no	—
32	C₄×#41×C₃₁	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
34	C₂×C₃₁×#117	C₂²	1	4	yes	—
35	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
37	C₃₁×#499	C₂²	1	2	yes	complemented
38	C₃₁×#499	C₂²	1	2	yes	complemented
39	C₃₁×#498	C₂²	1	2	yes	complemented
40	C₃₁×#485	C₂²	1	4	yes	complemented
41	C₃₁×#485	C₂²	1	4	yes	complemented
42	C₃₁×#484	C₂²	1	4	yes	complemented
43	C₃₁×#483	C₂²	1	4	yes	complemented
44	C₃₁×#482	C₂²	1	4	yes	complemented
45	C₃₁×#482	C₂²	1	4	yes	complemented
46	C₃₁×#481	C₂²	1	4	yes	complemented
47	C₃₁×#480	C₂²	1	4	yes	complemented
48	C₃₁×#479	C₂²	1	4	yes	complemented
49	C₃₁×#478	C₂²	1	4	yes	complemented
50	C₃₁×#477	C₂²	1	2	yes	complemented
51	C₃₁×#476	C₂²	1	2	yes	complemented
52	C₃₁×#475	C₂²	1	2	yes	complemented
53	C₃₁×#474	C₂²	1	2	yes	complemented
54	C₃₁×#470	C₂²	1	4	yes	complemented
55	C₃₁×#469	C₂²	1	4	yes	complemented
56	C₃₁×#468	C₂²	1	4	yes	complemented
57	C₃₁×#468	C₂²	1	4	yes	complemented
58	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
59	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
60	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
61	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
62	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
63	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#436	C₂²	1	2	yes	—
65	C₃₁×#436	C₂²	1	2	yes	—
66	C₃₁×#436	C₂²	1	2	yes	—
67	C₃₁×#436	C₂²	1	2	yes	—
68	C₃₁×#428	C₂²	1	4	yes	complemented
69	C₃₁×#428	C₂²	1	4	yes	complemented
70	C₃₁×#428	C₂²	1	4	yes	complemented
71	C₃₁×#428	C₂²	1	4	yes	complemented
72	C₃₁×#427	C₂²	1	4	yes	—
73	C₃₁×#427	C₂²	1	2	yes	—
74	C₃₁×#427	C₂²	1	2	yes	—
75	C₃₁×#427	C₂²	1	1	yes	characteristic
76	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
77	C₃₁×#416	C₂²	1	4	yes	—
78	C₃₁×#416	C₂²	1	2	yes	—
79	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
80	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
81	C₂×#41×C₃₁	—	2	2	no	—
82	C₂×#41×C₃₁	C₂³	1	2	yes	—
83	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
84	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
85	C₃₁×#135	—	2	4	no	—
86	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
87	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
88	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
89	C₂×M₁₆×C₃₁	—	2	8	no	—
90	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
91	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
92	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
94	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
95	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
96	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
97	C₃₁×#126	—	2	4	no	—
98	C₃₁×#126	—	2	4	no	—
99	C₃₁×#126	—	2	4	no	—
100	C₃₁×#125	—	2	4	no	—
101	C₃₁×#125	—	2	2	no	—
102	C₃₁×#125	C₂³	1	4	yes	—
103	C₃₁×#124	—	2	2	no	—
104	C₃₁×#124	—	2	4	no	—
105	C₃₁×#123	—	2	4	no	—
106	C₃₁×#123	—	2	4	no	—
107	C₃₁×#123	—	2	4	no	—
108	C₃₁×#123	—	2	4	no	—
109	C₃₁×C₂²⋊Q₈	—	2	2	no	—
110	C₃₁×C₂²⋊Q₈	—	2	2	no	—
111	C₃₁×C₂²⋊Q₈	—	2	2	no	—
112	C₃₁×C₂²⋊Q₈	—	2	4	no	—
113	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
114	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
115	C₃₁×#121	—	2	4	no	—
116	C₃₁×#121	—	2	2	no	—
117	C₃₁×#121	C₂³	1	4	yes	—
118	C₃₁×#121	C₂³	1	4	yes	—
119	C₃₁×#120	—	2	4	no	—
120	C₄×Q₈×C₃₁	—	2	2	no	—
121	C₄×Q₈×C₃₁	—	2	2	no	—
122	C₄×Q₈×C₃₁	—	2	2	no	—
123	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
124	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
125	C₄×D₄×C₃₁	—	2	2	no	—
126	C₄×D₄×C₃₁	—	2	4	no	—
127	C₄×D₄×C₃₁	—	2	2	no	—
128	C₄×D₄×C₃₁	—	2	2	no	—
129	C₄×D₄×C₃₁	—	2	4	no	—
130	C₄×D₄×C₃₁	—	2	4	no	—
131	C₄×D₄×C₃₁	D₄	1	2	yes	—
132	C₄×D₄×C₃₁	D₄	1	2	yes	—
133	C₄×D₄×C₃₁	C₂³	1	2	yes	—
134	C₄×D₄×C₃₁	C₂³	1	2	yes	—
135	C₄×D₄×C₃₁	C₂³	1	2	yes	—
136	C₄×D₄×C₃₁	C₂³	1	2	yes	—
137	C₃₁×#117	—	2	4	no	—
138	C₃₁×#117	—	2	4	no	—
139	C₃₁×#117	—	2	2	no	—
140	C₃₁×#117	—	2	4	no	—
141	C₃₁×#117	—	2	2	no	—
142	C₃₁×#117	C₂³	1	2	yes	—
143	C₃₁×#117	C₂³	1	4	yes	—
144	C₃₁×#117	C₂³	1	4	yes	—
145	C₃₁×#117	C₂³	1	4	yes	—
146	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
148	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
150	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
151	C₂×C₄²×C₃₁	—	2	4	no	—
152	C₂×C₄²×C₃₁	—	2	2	no	—
153	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
154	C₃₁×#107	C₂³	1	1	yes	characteristic
155	C₃₁×#107	C₂³	1	1	yes	characteristic
156	C₃₁×#107	C₂³	1	2	yes	—
157	C₃₁×#107	C₂³	1	2	yes	—
158	C₃₁×#107	C₂³	1	4	yes	—
159	C₃₁×#107	C₂³	1	4	yes	—
160	C₃₁×#107	C₂³	1	2	yes	—
161	C₃₁×#107	C₂³	1	2	yes	—
162	C₃₁×#106	C₂³	1	2	yes	—
163	C₃₁×#106	C₂³	1	4	yes	—
164	C₃₁×#106	C₂³	1	4	yes	—
165	C₃₁×#106	C₂³	1	4	yes	—
166	C₃₁×#106	C₂³	1	4	yes	—
167	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
168	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
169	C₃₁×#103	C₂³	1	2	yes	—
170	C₃₁×#103	C₂³	1	2	yes	—
171	C₃₁×#103	C₂³	1	4	yes	—
172	C₃₁×#103	C₂³	1	4	yes	—
173	C₃₁×#102	C₂³	1	2	yes	—
174	C₃₁×#102	C₂³	1	2	yes	—
175	C₃₁×#102	C₂³	1	4	yes	—
176	C₃₁×#102	C₂³	1	4	yes	—
177	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
178	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
179	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
180	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
181	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
182	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
183	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
184	#41×C₃₁	—	2	4	no	—
185	#41×C₃₁	—	2	4	no	—
186	#41×C₃₁	—	4	8	no	—
187	C₂×Q₈×C₃₁	—	2	2	no	—
188	C₂×Q₈×C₃₁	—	2	2	no	—
189	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
190	C₂×D₄×C₃₁	—	2	2	no	—
191	C₂×D₄×C₃₁	—	2	4	no	—
192	C₂×D₄×C₃₁	—	2	4	no	—
193	C₂×D₄×C₃₁	—	4	2	no	—
194	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
195	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
196	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₃₁	—	2	4	no	—
198	C₂²×C₄×C₃₁	—	2	4	no	—
199	C₂²×C₄×C₃₁	—	2	4	no	—
200	C₂²×C₄×C₃₁	—	2	4	no	—
201	C₂²×C₄×C₃₁	—	2	2	no	—
202	C₂²×C₄×C₃₁	—	2	2	no	—
203	C₂²×C₄×C₃₁	—	2	2	no	—
204	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
206	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
207	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
209	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
210	Q₁₆×C₃₁	—	2	2	no	—
211	SD₁₆×C₃₁	—	2	4	no	—
212	D₈×C₃₁	—	2	2	no	—
213	M₁₆×C₃₁	—	2	8	no	—
214	M₁₆×C₃₁	—	2	8	no	—
215	C₂×C₈×C₃₁	—	2	4	no	—
216	C₂×C₈×C₃₁	—	2	2	no	—
217	C₂×C₈×C₃₁	#41	1	4	yes	complemented
218	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
219	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
220	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
221	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
222	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
223	C₄⋊C₄×C₃₁	—	2	4	no	—
224	C₄⋊C₄×C₃₁	—	2	4	no	—
225	C₄⋊C₄×C₃₁	—	2	2	no	—
226	C₄⋊C₄×C₃₁	—	2	4	no	—
227	C₄⋊C₄×C₃₁	—	2	4	no	—
228	C₄⋊C₄×C₃₁	—	2	2	no	—
229	C₄⋊C₄×C₃₁	—	2	2	no	—
230	C₄⋊C₄×C₃₁	—	2	4	no	—
231	C₄⋊C₄×C₃₁	—	2	4	no	—
232	C₄⋊C₄×C₃₁	—	2	2	no	—
233	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
234	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
235	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
236	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
237	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
238	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
239	C₂²⋊C₄×C₃₁	—	2	2	no	—
240	C₂²⋊C₄×C₃₁	—	2	4	no	—
241	C₂²⋊C₄×C₃₁	—	2	4	no	—
242	C₂²⋊C₄×C₃₁	—	2	4	no	—
243	C₂²⋊C₄×C₃₁	—	2	4	no	—
244	C₂²⋊C₄×C₃₁	—	2	4	no	—
245	C₂²⋊C₄×C₃₁	—	2	4	no	—
246	C₂²⋊C₄×C₃₁	—	2	2	no	—
247	C₂²⋊C₄×C₃₁	—	2	2	no	—
248	C₂²⋊C₄×C₃₁	—	2	4	no	—
249	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
250	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
251	C₄²×C₃₁	—	2	4	no	—
252	C₄²×C₃₁	—	2	2	no	—
253	C₄²×C₃₁	—	2	4	no	—
254	C₄²×C₃₁	—	2	2	no	—
255	C₄²×C₃₁	—	2	2	no	—
256	C₄²×C₃₁	—	2	4	no	—
257	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
258	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
259	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
260	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
261	#61251	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
262	C₂³×C₃₁	—	2	4	no	—
263	C₂³×C₃₁	—	2	2	no	—
264	C₂³×C₃₁	—	4	2	no	—
265	C₂³×C₃₁	—	4	2	no	—
266	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
267	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
268	Q₈×C₃₁	—	2	2	no	—
269	Q₈×C₃₁	—	2	2	no	—
270	Q₈×C₃₁	—	4	4	no	—
271	Q₈×C₃₁	—	8	2	no	—
272	D₄×C₃₁	—	2	4	no	—
273	D₄×C₃₁	—	2	2	no	—
274	D₄×C₃₁	—	2	2	no	—
275	D₄×C₃₁	—	4	2	no	—
276	D₄×C₃₁	—	4	8	no	—
277	D₄×C₃₁	—	4	4	no	—
278	D₄×C₃₁	—	8	4	no	—
279	C₂×C₄×C₃₁	—	2	4	no	—
280	C₂×C₄×C₃₁	—	2	8	no	—
281	C₂×C₄×C₃₁	—	2	2	no	—
282	C₂×C₄×C₃₁	—	2	4	no	—
283	C₂×C₄×C₃₁	—	2	4	no	—
284	C₂×C₄×C₃₁	—	2	2	no	—
285	C₂×C₄×C₃₁	—	2	2	no	—
286	C₂×C₄×C₃₁	—	2	2	no	—
287	C₂×C₄×C₃₁	—	2	4	no	—
288	C₂×C₄×C₃₁	—	2	4	no	—
289	C₂×C₄×C₃₁	—	4	1	no	—
290	C₂×C₄×C₃₁	—	4	8	no	—
291	C₂×C₄×C₃₁	—	4	4	no	—
292	C₂×C₄×C₃₁	—	4	4	no	—
293	C₂×C₄×C₃₁	—	8	2	no	—
294	C₂×C₄×C₃₁	—	8	4	no	—
295	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
297	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
298	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
299	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
300	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
301	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
302	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
303	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
304	C₈×C₃₁	—	2	4	no	—
305	C₈×C₃₁	—	2	1	no	—
306	C₈×C₃₁	—	2	1	no	—
307	C₈×C₃₁	C₂×#41	1	2	yes	—
308	C₈×C₃₁	C₂×#41	1	2	yes	—
309	#3475	C₂×C₃₁	1	2	yes	complemented
310	#3357	C₂×C₃₁	1	2	yes	complemented
311	#3356	C₂×C₃₁	1	2	yes	complemented
312	#3355	C₂×C₃₁	1	2	yes	complemented
313	#3354	C₂×C₃₁	1	2	yes	complemented
314	#3353	C₂×C₃₁	1	2	yes	complemented
315	#3352	C₂×C₃₁	1	2	yes	complemented
316	#3351	C₂×C₃₁	1	4	yes	complemented
317	#3160	C₂×C₃₁	1	1	yes	characteristic, complemented
318	#3091	C₂×C₃₁	1	4	yes	complemented
319	#3076	C₂×C₃₁	1	2	yes	complemented
320	#3054	C₂×C₃₁	1	2	yes	complemented
321	C₄×#135	C₂×C₃₁	1	1	yes	characteristic, complemented
322	C₂×#436	C₂×C₃₁	1	1	yes	characteristic, complemented
323	#2911	C₂×C₃₁	1	2	yes	complemented
324	C₂²×C₃₁	—	2	1	no	—
325	C₂²×C₃₁	—	2	1	no	—
326	C₂²×C₃₁	—	2	4	no	—
327	C₂²×C₃₁	—	2	4	no	—
328	C₂²×C₃₁	—	2	4	no	—
329	C₂²×C₃₁	—	4	2	no	—
330	C₂²×C₃₁	—	4	2	no	—
331	C₂²×C₃₁	—	4	2	no	—
332	C₂²×C₃₁	—	8	4	no	—
333	C₂²×C₃₁	#547	1	2	yes	—
334	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
335	C₄×C₃₁	—	2	1	no	—
336	C₄×C₃₁	—	2	1	no	—
337	C₄×C₃₁	—	2	4	no	—
338	C₄×C₃₁	—	2	1	no	—
339	C₄×C₃₁	—	4	2	no	—
340	C₄×C₃₁	—	4	4	no	—
341	C₄×C₃₁	—	4	2	no	—
342	C₄×C₃₁	—	4	2	no	—
343	C₄×C₃₁	—	4	4	no	—
344	C₄×C₃₁	#547	1	2	yes	—
345	C₄×C₃₁	#575	1	2	yes	—
346	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
347	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
348	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
349	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
350	#556	C₂²×C₃₁	1	2	yes	—
351	#555	C₂²×C₃₁	1	2	yes	—
352	#554	C₂²×C₃₁	1	2	yes	—
353	#553	C₂²×C₃₁	1	4	yes	—
354	#552	—	2	2	no	—
355	#552	C₂²×C₃₁	1	4	yes	—
356	#551	—	2	4	no	—
357	#547	C₂²×C₃₁	1	2	yes	—
358	#546	—	2	2	no	—
359	#533	C₂²×C₃₁	1	2	yes	—
360	#529	—	2	4	no	—
361	#529	—	2	2	no	—
362	#525	C₂²×C₃₁	1	4	yes	—
363	C₄×#41	—	2	2	no	—
364	C₄×#41	C₂²×C₃₁	1	2	yes	—
365	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
366	C₂×#117	C₂²×C₃₁	1	4	yes	—
367	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
368	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
369	#499	C₂²×C₃₁	1	2	yes	complemented
370	#499	C₂²×C₃₁	1	2	yes	complemented
371	#498	C₂²×C₃₁	1	2	yes	complemented
372	#485	C₂²×C₃₁	1	4	yes	complemented
373	#485	C₂²×C₃₁	1	4	yes	complemented
374	#484	C₂²×C₃₁	1	4	yes	complemented
375	#483	C₂²×C₃₁	1	4	yes	complemented
376	#482	C₂²×C₃₁	1	4	yes	complemented
377	#482	C₂²×C₃₁	1	4	yes	complemented
378	#481	C₂²×C₃₁	1	4	yes	complemented
379	#480	C₂²×C₃₁	1	4	yes	complemented
380	#479	C₂²×C₃₁	1	4	yes	complemented
381	#478	C₂²×C₃₁	1	4	yes	complemented
382	#477	C₂²×C₃₁	1	2	yes	complemented
383	#476	C₂²×C₃₁	1	2	yes	complemented
384	#475	C₂²×C₃₁	1	2	yes	complemented
385	#474	C₂²×C₃₁	1	2	yes	complemented
386	#470	C₂²×C₃₁	1	4	yes	complemented
387	#469	C₂²×C₃₁	1	4	yes	complemented
388	#468	C₂²×C₃₁	1	4	yes	complemented
389	#468	C₂²×C₃₁	1	4	yes	complemented
390	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
391	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
392	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
393	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
394	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
395	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
396	#436	C₂²×C₃₁	1	2	yes	—
397	#436	C₂²×C₃₁	1	2	yes	—
398	#436	C₂²×C₃₁	1	2	yes	—
399	#436	C₂²×C₃₁	1	2	yes	—
400	#428	C₂²×C₃₁	1	4	yes	complemented
401	#428	C₂²×C₃₁	1	4	yes	complemented
402	#428	C₂²×C₃₁	1	4	yes	complemented
403	#428	C₂²×C₃₁	1	4	yes	complemented
404	#427	C₂²×C₃₁	1	4	yes	—
405	#427	C₂²×C₃₁	1	2	yes	—
406	#427	C₂²×C₃₁	1	2	yes	—
407	#427	C₂²×C₃₁	1	1	yes	characteristic
408	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
409	#416	C₂²×C₃₁	1	4	yes	—
410	#416	C₂²×C₃₁	1	2	yes	—
411	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
412	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
413	C₂×C₃₁	—	2	2	no	—
414	C₂×C₃₁	—	4	4	no	—
415	C₂×C₃₁	—	8	2	no	—
416	C₂×C₃₁	C₂×#547	1	1	yes	characteristic
417	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
418	C₂×C₃₁	#3584	1	1	yes	characteristic
419	C₂×#41	—	2	2	no	—
420	C₂×#41	C₂³×C₃₁	1	2	yes	—
421	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
422	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
423	#135	—	2	4	no	—
424	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
425	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
426	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
427	C₂×M₁₆	—	2	8	no	—
428	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
429	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
430	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
431	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
432	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
433	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
434	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
435	#126	—	2	4	no	—
436	#126	—	2	4	no	—
437	#126	—	2	4	no	—
438	#125	—	2	4	no	—
439	#125	—	2	2	no	—
440	#125	C₂³×C₃₁	1	4	yes	—
441	#124	—	2	2	no	—
442	#124	—	2	4	no	—
443	#123	—	2	4	no	—
444	#123	—	2	4	no	—
445	#123	—	2	4	no	—
446	#123	—	2	4	no	—
447	C₂²⋊Q₈	—	2	2	no	—
448	C₂²⋊Q₈	—	2	2	no	—
449	C₂²⋊Q₈	—	2	2	no	—
450	C₂²⋊Q₈	—	2	4	no	—
451	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
452	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
453	#121	—	2	4	no	—
454	#121	—	2	2	no	—
455	#121	C₂³×C₃₁	1	4	yes	—
456	#121	C₂³×C₃₁	1	4	yes	—
457	#120	—	2	4	no	—
458	C₄×Q₈	—	2	2	no	—
459	C₄×Q₈	—	2	2	no	—
460	C₄×Q₈	—	2	2	no	—
461	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
462	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
463	C₄×D₄	—	2	2	no	—
464	C₄×D₄	—	2	4	no	—
465	C₄×D₄	—	2	2	no	—
466	C₄×D₄	—	2	2	no	—
467	C₄×D₄	—	2	4	no	—
468	C₄×D₄	—	2	4	no	—
469	C₄×D₄	D₄×C₃₁	1	2	yes	—
470	C₄×D₄	D₄×C₃₁	1	2	yes	—
471	C₄×D₄	C₂³×C₃₁	1	2	yes	—
472	C₄×D₄	C₂³×C₃₁	1	2	yes	—
473	C₄×D₄	C₂³×C₃₁	1	2	yes	—
474	C₄×D₄	C₂³×C₃₁	1	2	yes	—
475	#117	—	2	4	no	—
476	#117	—	2	4	no	—
477	#117	—	2	2	no	—
478	#117	—	2	4	no	—
479	#117	—	2	2	no	—
480	#117	C₂³×C₃₁	1	2	yes	—
481	#117	C₂³×C₃₁	1	4	yes	—
482	#117	C₂³×C₃₁	1	4	yes	—
483	#117	C₂³×C₃₁	1	4	yes	—
484	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
485	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
486	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
487	C₂×C₂²⋊C₄	—	2	4	no	—
488	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
489	C₂×C₄²	—	2	4	no	—
490	C₂×C₄²	—	2	2	no	—
491	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
492	#107	C₂³×C₃₁	1	1	yes	characteristic
493	#107	C₂³×C₃₁	1	1	yes	characteristic
494	#107	C₂³×C₃₁	1	2	yes	—
495	#107	C₂³×C₃₁	1	2	yes	—
496	#107	C₂³×C₃₁	1	4	yes	—
497	#107	C₂³×C₃₁	1	4	yes	—
498	#107	C₂³×C₃₁	1	2	yes	—
499	#107	C₂³×C₃₁	1	2	yes	—
500	#106	C₂³×C₃₁	1	2	yes	—
501	#106	C₂³×C₃₁	1	4	yes	—
502	#106	C₂³×C₃₁	1	4	yes	—
503	#106	C₂³×C₃₁	1	4	yes	—
504	#106	C₂³×C₃₁	1	4	yes	—
505	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
506	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
507	#103	C₂³×C₃₁	1	2	yes	—
508	#103	C₂³×C₃₁	1	2	yes	—
509	#103	C₂³×C₃₁	1	4	yes	—
510	#103	C₂³×C₃₁	1	4	yes	—
511	#102	C₂³×C₃₁	1	2	yes	—
512	#102	C₂³×C₃₁	1	2	yes	—
513	#102	C₂³×C₃₁	1	4	yes	—
514	#102	C₂³×C₃₁	1	4	yes	—
515	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
516	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
517	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
518	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
519	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
520	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
521	C₃₁	#61251	1	1	yes	characteristic, direct product factor, Sylow
522	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
523	#41	—	2	4	no	—
524	#41	—	2	4	no	—
525	#41	—	4	8	no	—
526	C₂×Q₈	—	2	2	no	—
527	C₂×Q₈	—	2	2	no	—
528	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
529	C₂×D₄	—	2	2	no	—
530	C₂×D₄	—	2	4	no	—
531	C₂×D₄	—	2	4	no	—
532	C₂×D₄	—	4	2	no	—
533	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
534	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
535	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	2	4	no	—
539	C₂²×C₄	—	2	4	no	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
544	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
545	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
546	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
547	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
548	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
549	Q₁₆	—	2	2	no	—
550	SD₁₆	—	2	4	no	—
551	D₈	—	2	2	no	—
552	M₁₆	—	2	8	no	—
553	M₁₆	—	2	8	no	—
554	C₂×C₈	—	2	4	no	—
555	C₂×C₈	—	2	2	no	—
556	C₂×C₈	#41×C₃₁	1	4	yes	complemented
557	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
558	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
559	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
560	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
561	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
562	C₄⋊C₄	—	2	4	no	—
563	C₄⋊C₄	—	2	4	no	—
564	C₄⋊C₄	—	2	2	no	—
565	C₄⋊C₄	—	2	4	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	4	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	2	2	no	—
572	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
573	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
574	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
575	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
576	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
577	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
578	C₂²⋊C₄	—	2	2	no	—
579	C₂²⋊C₄	—	2	4	no	—
580	C₂²⋊C₄	—	2	4	no	—
581	C₂²⋊C₄	—	2	4	no	—
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	2	no	—
586	C₂²⋊C₄	—	2	2	no	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
589	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
590	C₄²	—	2	2	no	—
591	C₄²	—	2	4	no	—
592	C₄²	—	2	2	no	—
593	C₄²	—	2	4	no	—
594	C₄²	—	2	4	no	—
595	C₄²	—	2	2	no	—
596	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
597	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
598	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
599	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
600	C₂³	—	2	4	no	—
601	C₂³	—	2	2	no	—
602	C₂³	—	4	2	no	—
603	C₂³	—	4	2	no	—
604	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
605	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
606	Q₈	—	2	2	no	—
607	Q₈	—	2	2	no	—
608	Q₈	—	4	4	no	—
609	Q₈	—	8	2	no	—
610	D₄	—	2	4	no	—
611	D₄	—	2	2	no	—
612	D₄	—	2	2	no	—
613	D₄	—	4	2	no	—
614	D₄	—	4	8	no	—
615	D₄	—	4	4	no	—
616	D₄	—	8	4	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	2	8	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	2	4	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	8	no	—
629	C₂×C₄	—	4	4	no	—
630	C₂×C₄	—	4	4	no	—
631	C₂×C₄	—	8	2	no	—
632	C₂×C₄	—	8	4	no	—
633	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
634	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
635	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
636	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
637	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
638	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
639	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
640	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
641	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
642	C₈	—	2	4	no	—
643	C₈	—	2	1	no	—
644	C₈	—	2	1	no	—
645	C₈	C₂×#41×C₃₁	1	2	yes	—
646	C₈	C₂×#41×C₃₁	1	2	yes	—
647	C₂²	—	2	1	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	2	4	no	—
650	C₂²	—	2	4	no	—
651	C₂²	—	2	4	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	2	no	—
654	C₂²	—	4	2	no	—
655	C₂²	—	8	4	no	—
656	C₂²	C₃₁×#547	1	2	yes	—
657	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
658	C₄	—	2	4	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	1	no	—
661	C₄	—	2	1	no	—
662	C₄	—	4	2	no	—
663	C₄	—	4	2	no	—
664	C₄	—	4	4	no	—
665	C₄	—	4	2	no	—
666	C₄	—	4	4	no	—
667	C₄	C₃₁×#547	1	2	yes	—
668	C₄	C₃₁×#575	1	2	yes	—
669	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
670	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
671	C₂	—	2	2	no	—
672	C₂	—	4	4	no	—
673	C₂	—	8	2	no	—
674	C₂	C₂×C₃₁×#547	1	1	yes	characteristic
675	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
676	C₂	C₃₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
socle	C₂²×C₃₁	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₂×C₄×D₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3475	C₂	semidirect
2. C₃₁×#3357	C₂	semidirect
3. C₃₁×#3356	C₂	semidirect
4. C₃₁×#3355	C₂	semidirect
5. C₃₁×#3354	C₂	semidirect
6. C₃₁×#3353	C₂	semidirect
7. C₃₁×#3352	C₂	semidirect
8. C₃₁×#3351	C₂	semidirect
9. C₃₁×#3160	C₂	semidirect
10. C₃₁×#3091	C₂	semidirect
11. C₃₁×#3076	C₂	semidirect
12. C₃₁×#3054	C₂	semidirect
13. C₄×C₃₁×#135	C₂	semidirect
14. C₂×C₃₁×#436	C₂	semidirect
15. C₃₁×#2911	C₂	semidirect
35. C₃₁×#500	C₂²	semidirect
36. C₃₁×#500	C₂²	semidirect
37. C₃₁×#499	C₂²	semidirect
38. C₃₁×#499	C₂²	semidirect
39. C₃₁×#498	C₂²	semidirect
40. C₃₁×#485	C₂²	semidirect
41. C₃₁×#485	C₂²	semidirect
42. C₃₁×#484	C₂²	semidirect
43. C₃₁×#483	C₂²	semidirect
44. C₃₁×#482	C₂²	semidirect
45. C₃₁×#482	C₂²	semidirect
46. C₃₁×#481	C₂²	semidirect
47. C₃₁×#480	C₂²	semidirect
48. C₃₁×#479	C₂²	semidirect
49. C₃₁×#478	C₂²	semidirect
50. C₃₁×#477	C₂²	semidirect
51. C₃₁×#476	C₂²	semidirect
52. C₃₁×#475	C₂²	semidirect
53. C₃₁×#474	C₂²	semidirect
54. C₃₁×#470	C₂²	semidirect
55. C₃₁×#469	C₂²	semidirect
56. C₃₁×#468	C₂²	semidirect
57. C₃₁×#468	C₂²	semidirect
58. C₄×Q₁₆×C₃₁	C₂²	semidirect
59. C₄×Q₁₆×C₃₁	C₂²	semidirect
60. C₄×SD₁₆×C₃₁	C₂²	semidirect
61. C₄×SD₁₆×C₃₁	C₂²	semidirect
62. C₄×D₈×C₃₁	C₂²	semidirect
63. C₄×D₈×C₃₁	C₂²	semidirect
68. C₃₁×#428	C₂²	semidirect
69. C₃₁×#428	C₂²	semidirect
70. C₃₁×#428	C₂²	semidirect
71. C₃₁×#428	C₂²	semidirect
217. C₂×C₈×C₃₁	#41	semidirect
261. #61251	C₃₁	direct (N × H)
309. #3475	C₂×C₃₁	semidirect
310. #3357	C₂×C₃₁	semidirect
311. #3356	C₂×C₃₁	semidirect
312. #3355	C₂×C₃₁	semidirect
313. #3354	C₂×C₃₁	semidirect
314. #3353	C₂×C₃₁	semidirect
315. #3352	C₂×C₃₁	semidirect
316. #3351	C₂×C₃₁	semidirect
317. #3160	C₂×C₃₁	semidirect
318. #3091	C₂×C₃₁	semidirect
319. #3076	C₂×C₃₁	semidirect
320. #3054	C₂×C₃₁	semidirect
321. C₄×#135	C₂×C₃₁	semidirect
322. C₂×#436	C₂×C₃₁	semidirect
323. #2911	C₂×C₃₁	semidirect
367. #500	C₂²×C₃₁	semidirect
368. #500	C₂²×C₃₁	semidirect
369. #499	C₂²×C₃₁	semidirect
370. #499	C₂²×C₃₁	semidirect
371. #498	C₂²×C₃₁	semidirect
372. #485	C₂²×C₃₁	semidirect
373. #485	C₂²×C₃₁	semidirect
374. #484	C₂²×C₃₁	semidirect
375. #483	C₂²×C₃₁	semidirect
376. #482	C₂²×C₃₁	semidirect
377. #482	C₂²×C₃₁	semidirect
378. #481	C₂²×C₃₁	semidirect
379. #480	C₂²×C₃₁	semidirect
380. #479	C₂²×C₃₁	semidirect
381. #478	C₂²×C₃₁	semidirect
382. #477	C₂²×C₃₁	semidirect
383. #476	C₂²×C₃₁	semidirect
384. #475	C₂²×C₃₁	semidirect
385. #474	C₂²×C₃₁	semidirect
386. #470	C₂²×C₃₁	semidirect
387. #469	C₂²×C₃₁	semidirect
388. #468	C₂²×C₃₁	semidirect
389. #468	C₂²×C₃₁	semidirect
390. C₄×Q₁₆	C₂²×C₃₁	semidirect
391. C₄×Q₁₆	C₂²×C₃₁	semidirect
392. C₄×SD₁₆	C₂²×C₃₁	semidirect
393. C₄×SD₁₆	C₂²×C₃₁	semidirect
394. C₄×D₈	C₂²×C₃₁	semidirect
395. C₄×D₈	C₂²×C₃₁	semidirect
400. #428	C₂²×C₃₁	semidirect
401. #428	C₂²×C₃₁	semidirect
402. #428	C₂²×C₃₁	semidirect
403. #428	C₂²×C₃₁	semidirect
521. C₃₁	#61251	direct (N × H)
556. C₂×C₈	#41×C₃₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₁×#3475	2
C₃₁×#3357	2
C₃₁×#3356	2
C₃₁×#3355	2
C₃₁×#3354	2
C₃₁×#3353	2
C₃₁×#3352	2
C₃₁×#3351	2
C₃₁×#3160	2
C₃₁×#3091	2
C₃₁×#3076	2
C₃₁×#3054	2
C₄×C₃₁×#135	2
C₂×C₃₁×#436	2
C₃₁×#2911	2
#61251	31

Subgroups — C31×#61251 #21518010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61251 #21518010