Subgroups — C₃₁×#7961 #21464720

Order 7936.

606 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2920	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2920	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2285	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1286	C₂	1	4	yes	maximal, complemented
5	C₂×C₃₁×#117	—	2	1	no	—
6	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
7	C₃₁×#432	—	2	1	no	—
8	C₃₁×#432	—	2	1	no	—
9	C₃₁×#432	—	2	1	no	—
10	C₃₁×#432	C₄	1	2	yes	complemented
11	C₃₁×#431	—	2	1	no	—
12	C₃₁×#431	C₄	1	2	yes	complemented
13	C₃₁×#431	C₄	1	2	yes	complemented
14	C₃₁×#431	C₂²	1	2	yes	—
15	C₃₁×#423	—	2	1	no	—
16	C₃₁×#423	C₂²	1	2	yes	—
17	C₃₁×#407	—	2	1	no	—
18	C₃₁×#407	—	2	1	no	—
19	C₄×M₁₆×C₃₁	—	2	1	no	—
20	C₄×M₁₆×C₃₁	C₄	1	2	yes	complemented
21	C₃₁×#384	—	2	1	no	—
22	C₃₁×#382	C₂²	1	2	yes	—
23	C₃₁×#380	—	2	1	no	—
24	C₃₁×#380	C₄	1	2	yes	—
25	C₄×C₄⋊C₄×C₃₁	—	2	1	no	—
26	C₄×C₄⋊C₄×C₃₁	C₄	1	2	yes	—
27	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
30	C₂×M₁₆×C₃₁	—	2	2	no	—
31	C₂×M₁₆×C₃₁	—	2	2	no	—
32	C₃₁×#117	—	4	4	no	—
33	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
34	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
35	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
36	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
37	C₂×C₄²×C₃₁	—	2	2	no	—
38	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₃₁	Q₈	1	1	yes	characteristic
48	C₂×C₄²×C₃₁	Q₈	1	1	yes	characteristic
49	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
50	C₃₁×C₄⋊C₈	—	2	2	no	—
51	C₃₁×C₄⋊C₈	—	2	2	no	—
52	C₃₁×C₄⋊C₈	—	2	2	no	—
53	C₃₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
54	C₃₁×C₂²⋊C₈	—	2	2	no	—
55	C₃₁×C₂²⋊C₈	—	2	2	no	—
56	C₃₁×C₂²⋊C₈	—	2	2	no	—
57	C₃₁×C₂²⋊C₈	—	2	2	no	—
58	C₃₁×#97	—	2	2	no	—
59	C₃₁×#97	—	2	2	no	—
60	C₄×C₈×C₃₁	—	2	2	no	—
61	C₄×C₈×C₃₁	C₂×C₄	1	4	yes	—
62	C₃₁×#95	—	2	2	no	—
63	C₃₁×#95	C₂×C₄	1	4	yes	—
64	C₂⁴×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₃₁	—	2	2	no	—
66	C₂²×C₄×C₃₁	—	2	2	no	—
67	C₂²×C₄×C₃₁	—	2	4	no	—
68	C₂²×C₄×C₃₁	—	4	2	no	—
69	C₂²×C₄×C₃₁	—	4	2	no	—
70	C₂²×C₄×C₃₁	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₃₁	C₄²	1	1	yes	characteristic
72	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
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	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
88	M₁₆×C₃₁	—	4	4	no	—
89	M₁₆×C₃₁	—	4	2	no	—
90	M₁₆×C₃₁	—	4	2	no	—
91	C₂×C₈×C₃₁	—	2	4	no	—
92	C₂×C₈×C₃₁	—	2	4	no	—
93	C₄⋊C₄×C₃₁	—	4	4	no	—
94	C₄⋊C₄×C₃₁	—	4	4	no	—
95	C₄⋊C₄×C₃₁	—	4	4	no	—
96	C₂²⋊C₄×C₃₁	—	4	4	no	—
97	C₄²×C₃₁	—	4	4	no	—
98	C₄²×C₃₁	C₄²	1	1	yes	characteristic
99	C₄²×C₃₁	C₄²	1	1	yes	characteristic
100	C₄²×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
101	C₄²×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
102	C₄²×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
103	C₄²×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
104	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₃₁	C₂×Q₈	1	1	yes	characteristic
114	#7961	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂³×C₃₁	—	2	1	no	—
116	C₂³×C₃₁	—	2	1	no	—
117	C₂³×C₃₁	—	4	1	no	—
118	C₂³×C₃₁	—	4	1	no	—
119	C₂³×C₃₁	#95	1	1	yes	characteristic
120	C₂³×C₃₁	#95	1	1	yes	characteristic
121	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
122	C₂×C₄×C₃₁	—	2	1	no	—
123	C₂×C₄×C₃₁	—	2	1	no	—
124	C₂×C₄×C₃₁	—	2	2	no	—
125	C₂×C₄×C₃₁	—	2	2	no	—
126	C₂×C₄×C₃₁	—	2	2	no	—
127	C₂×C₄×C₃₁	—	2	2	no	—
128	C₂×C₄×C₃₁	—	2	2	no	—
129	C₂×C₄×C₃₁	—	2	2	no	—
130	C₂×C₄×C₃₁	—	2	2	no	—
131	C₂×C₄×C₃₁	—	2	2	no	—
132	C₂×C₄×C₃₁	—	2	2	no	—
133	C₂×C₄×C₃₁	—	2	2	no	—
134	C₂×C₄×C₃₁	—	4	1	no	—
135	C₂×C₄×C₃₁	—	4	1	no	—
136	C₂×C₄×C₃₁	—	4	1	no	—
137	C₂×C₄×C₃₁	—	4	1	no	—
138	C₂×C₄×C₃₁	—	4	1	no	—
139	C₂×C₄×C₃₁	—	4	1	no	—
140	C₂×C₄×C₃₁	—	4	4	no	—
141	C₂×C₄×C₃₁	—	4	4	no	—
142	C₂×C₄×C₃₁	—	4	4	no	—
143	C₂×C₄×C₃₁	#95	1	1	yes	characteristic
144	C₂×C₄×C₃₁	#95	1	1	yes	characteristic
145	C₂×C₄×C₃₁	#95	1	1	yes	characteristic
146	C₂×C₄×C₃₁	#95	1	1	yes	characteristic
147	C₂×C₄×C₃₁	#95	1	1	yes	characteristic
148	C₂×C₄×C₃₁	#95	1	1	yes	characteristic
149	C₂×C₄×C₃₁	C₂×C₄²	1	1	yes	characteristic
150	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
156	C₂×C₄×C₃₁	#137	1	2	yes	—
157	C₈×C₃₁	—	4	4	no	—
158	C₈×C₃₁	—	4	4	no	—
159	#2920	C₂×C₃₁	1	1	yes	characteristic
160	#2920	C₂×C₃₁	1	1	yes	characteristic
161	#2285	C₂×C₃₁	1	1	yes	characteristic
162	#1286	C₂×C₃₁	1	4	yes	complemented
163	C₂²×C₃₁	—	2	1	no	—
164	C₂²×C₃₁	—	2	1	no	—
165	C₂²×C₃₁	—	2	1	no	—
166	C₂²×C₃₁	—	2	1	no	—
167	C₂²×C₃₁	—	2	1	no	—
168	C₂²×C₃₁	—	2	1	no	—
169	C₂²×C₃₁	—	2	1	no	—
170	C₂²×C₃₁	—	2	1	no	—
171	C₂²×C₃₁	—	4	2	no	—
172	C₂²×C₃₁	—	4	2	no	—
173	C₂²×C₃₁	C₂×#95	1	1	yes	characteristic
174	C₂²×C₃₁	#418	1	1	yes	characteristic
175	C₂²×C₃₁	#419	1	1	yes	characteristic
176	C₄×C₃₁	—	2	1	no	—
177	C₄×C₃₁	—	2	1	no	—
178	C₄×C₃₁	—	2	1	no	—
179	C₄×C₃₁	—	2	1	no	—
180	C₄×C₃₁	—	2	1	no	—
181	C₄×C₃₁	—	2	1	no	—
182	C₄×C₃₁	—	2	1	no	—
183	C₄×C₃₁	—	2	1	no	—
184	C₄×C₃₁	—	8	4	no	—
185	C₄×C₃₁	H(3,ℤ/4)	1	2	yes	—
186	C₄×C₃₁	#344	1	2	yes	—
187	C₄×C₃₁	#417	1	2	yes	—
188	C₄×C₃₁	#428	1	2	yes	—
189	C₂×#117	—	2	1	no	—
190	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
191	#432	—	2	1	no	—
192	#432	—	2	1	no	—
193	#432	—	2	1	no	—
194	#432	C₄×C₃₁	1	2	yes	complemented
195	#431	—	2	1	no	—
196	#431	C₄×C₃₁	1	2	yes	complemented
197	#431	C₄×C₃₁	1	2	yes	complemented
198	#431	C₂²×C₃₁	1	2	yes	—
199	#423	—	2	1	no	—
200	#423	C₂²×C₃₁	1	2	yes	—
201	#407	—	2	1	no	—
202	#407	—	2	1	no	—
203	C₄×M₁₆	—	2	1	no	—
204	C₄×M₁₆	C₄×C₃₁	1	2	yes	complemented
205	#384	—	2	1	no	—
206	#382	C₂²×C₃₁	1	2	yes	—
207	#380	—	2	1	no	—
208	#380	C₄×C₃₁	1	2	yes	—
209	C₄×C₄⋊C₄	—	2	1	no	—
210	C₄×C₄⋊C₄	C₄×C₃₁	1	2	yes	—
211	C₂×C₃₁	—	2	1	no	—
212	C₂×C₃₁	—	2	1	no	—
213	C₂×C₃₁	—	4	1	no	—
214	C₂×C₃₁	—	4	1	no	—
215	C₂×C₃₁	C₂×H(3,ℤ/4)	1	1	yes	characteristic
216	C₂×C₃₁	#1736	1	1	yes	characteristic
217	C₂×C₃₁	C₂×#344	1	1	yes	characteristic
218	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
219	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
220	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
221	C₂×M₁₆	—	2	2	no	—
222	C₂×M₁₆	—	2	2	no	—
223	#117	—	4	4	no	—
224	C₂×C₄⋊C₄	—	2	2	no	—
225	C₂×C₄⋊C₄	—	2	2	no	—
226	C₂×C₄⋊C₄	—	2	2	no	—
227	C₂×C₂²⋊C₄	—	2	2	no	—
228	C₂×C₄²	—	2	2	no	—
229	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
230	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
231	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
232	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
233	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
234	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
235	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
236	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
237	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
238	C₂×C₄²	Q₈×C₃₁	1	1	yes	characteristic
239	C₂×C₄²	Q₈×C₃₁	1	1	yes	characteristic
240	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
241	C₄⋊C₈	—	2	2	no	—
242	C₄⋊C₈	—	2	2	no	—
243	C₄⋊C₈	—	2	2	no	—
244	C₄⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
245	C₂²⋊C₈	—	2	2	no	—
246	C₂²⋊C₈	—	2	2	no	—
247	C₂²⋊C₈	—	2	2	no	—
248	C₂²⋊C₈	—	2	2	no	—
249	#97	—	2	2	no	—
250	#97	—	2	2	no	—
251	C₄×C₈	—	2	2	no	—
252	C₄×C₈	C₂×C₄×C₃₁	1	4	yes	—
253	#95	—	2	2	no	—
254	#95	C₂×C₄×C₃₁	1	4	yes	—
255	C₃₁	#7961	1	1	yes	characteristic, direct product factor, Sylow
256	C₂⁴	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	4	2	no	—
261	C₂²×C₄	—	4	2	no	—
262	C₂²×C₄	C₄²×C₃₁	1	1	yes	characteristic
263	C₂²×C₄	C₄²×C₃₁	1	1	yes	characteristic
264	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
265	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
266	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
267	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
268	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
269	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
270	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
271	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
272	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
273	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
274	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
275	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
276	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
277	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
279	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
280	M₁₆	—	4	4	no	—
281	M₁₆	—	4	2	no	—
282	M₁₆	—	4	2	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	2	4	no	—
285	C₄⋊C₄	—	4	4	no	—
286	C₄⋊C₄	—	4	4	no	—
287	C₄⋊C₄	—	4	4	no	—
288	C₂²⋊C₄	—	4	4	no	—
289	C₄²	—	4	4	no	—
290	C₄²	C₄²×C₃₁	1	1	yes	characteristic
291	C₄²	C₄²×C₃₁	1	1	yes	characteristic
292	C₄²	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
293	C₄²	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
294	C₄²	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
295	C₄²	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
296	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
297	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
298	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
299	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
300	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
301	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
302	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
303	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
304	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
305	C₄²	C₂×Q₈×C₃₁	1	1	yes	characteristic
306	C₂³	—	2	1	no	—
307	C₂³	—	2	1	no	—
308	C₂³	—	4	1	no	—
309	C₂³	—	4	1	no	—
310	C₂³	C₃₁×#95	1	1	yes	characteristic
311	C₂³	C₃₁×#95	1	1	yes	characteristic
312	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	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	—	4	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	C₃₁×#95	1	1	yes	characteristic
335	C₂×C₄	C₃₁×#95	1	1	yes	characteristic
336	C₂×C₄	C₃₁×#95	1	1	yes	characteristic
337	C₂×C₄	C₃₁×#95	1	1	yes	characteristic
338	C₂×C₄	C₃₁×#95	1	1	yes	characteristic
339	C₂×C₄	C₃₁×#95	1	1	yes	characteristic
340	C₂×C₄	C₂×C₄²×C₃₁	1	1	yes	characteristic
341	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
342	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
343	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
344	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
345	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
346	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
347	C₂×C₄	C₃₁×#137	1	2	yes	—
348	C₈	—	4	4	no	—
349	C₈	—	4	4	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	4	2	no	—
359	C₂²	—	4	2	no	—
360	C₂²	C₂×C₃₁×#95	1	1	yes	characteristic
361	C₂²	C₃₁×#418	1	1	yes	characteristic
362	C₂²	C₃₁×#419	1	1	yes	characteristic
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	8	4	no	—
372	C₄	C₃₁×H(3,ℤ/4)	1	2	yes	—
373	C₄	C₃₁×#344	1	2	yes	—
374	C₄	C₃₁×#417	1	2	yes	—
375	C₄	C₃₁×#428	1	2	yes	—
376	C₂	—	2	1	no	—
377	C₂	—	2	1	no	—
378	C₂	—	4	1	no	—
379	C₂	—	4	1	no	—
380	C₂	C₂×C₃₁×H(3,ℤ/4)	1	1	yes	characteristic
381	C₂	C₃₁×#1736	1	1	yes	characteristic
382	C₂	C₂×C₃₁×#344	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂×#95
commutator	C₂×C₄	C₂×C₄²×C₃₁
Frattini, cosocle	C₂×C₄²	C₂³×C₃₁
prime radical	C₂⁴×C₃₁	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₃₁×#1286	C₂	semidirect
10. C₃₁×#432	C₄	semidirect
12. C₃₁×#431	C₄	semidirect
13. C₃₁×#431	C₄	semidirect
20. C₄×M₁₆×C₃₁	C₄	semidirect
114. #7961	C₃₁	direct (N × H)
162. #1286	C₂×C₃₁	semidirect
194. #432	C₄×C₃₁	semidirect
196. #431	C₄×C₃₁	semidirect
197. #431	C₄×C₃₁	semidirect
204. C₄×M₁₆	C₄×C₃₁	semidirect
255. C₃₁	#7961	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×#2920	2
C₃₁×#2285	2
C₃₁×#1286	2
#7961	31

Subgroups — C31×#7961 #21464720

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#7961 #21464720