Subgroups — C₃₁×#10714 #21467473

Order 7936.

1670 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₈×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃₁×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃₁×#336	C₂	1	4	yes	maximal, complemented
5	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
6	C₂³×C₈×C₃₁	—	2	2	no	—
7	C₂³×C₈×C₃₁	—	2	2	no	—
8	C₂³×C₈×C₃₁	—	2	8	no	—
9	C₂³×C₈×C₃₁	C₄	1	4	yes	complemented
10	C₂³×C₈×C₃₁	C₂²	1	2	yes	—
11	C₂³×C₈×C₃₁	C₂²	1	2	yes	—
12	C₂²×C₂²⋊C₄×C₃₁	C₄	1	2	yes	—
13	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
14	C₂×C₃₁×C₂²⋊C₈	—	2	2	no	—
15	C₂×C₃₁×C₂²⋊C₈	—	2	2	no	—
16	C₂×C₃₁×C₂²⋊C₈	C₄	1	4	yes	complemented
17	C₄×C₂²⋊C₄×C₃₁	—	2	2	no	—
18	C₄×C₂²⋊C₄×C₃₁	—	2	2	no	—
19	C₂×C₃₁×#95	C₄	1	2	yes	—
20	C₃₁×#336	—	2	8	no	—
21	C₂⁵×C₃₁	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₃₁	—	2	4	no	—
23	C₂³×C₄×C₃₁	—	2	4	no	—
24	C₂³×C₄×C₃₁	C₂×C₄	1	4	yes	—
25	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₃₁	C₂×C₄	1	2	yes	—
27	C₂³×C₄×C₃₁	C₂×C₄	1	2	yes	—
28	C₂³×C₄×C₃₁	D₄	1	2	yes	—
29	C₂³×C₄×C₃₁	D₄	1	2	yes	—
30	C₂³×C₄×C₃₁	D₄	1	2	yes	—
31	C₂³×C₄×C₃₁	Q₈	1	2	yes	—
32	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
33	C₂²×C₈×C₃₁	—	2	16	no	—
34	C₂²×C₈×C₃₁	—	2	16	no	—
35	C₂²×C₈×C₃₁	—	2	8	no	—
36	C₂²×C₈×C₃₁	—	2	2	no	—
37	C₂²×C₈×C₃₁	—	2	2	no	—
38	C₂²×C₈×C₃₁	—	2	4	no	—
39	C₂²×C₈×C₃₁	—	2	16	no	—
40	C₂²×C₈×C₃₁	—	2	2	no	—
41	C₂²×C₈×C₃₁	—	2	2	no	—
42	C₂²×C₈×C₃₁	—	2	4	no	—
43	C₂²×C₈×C₃₁	—	2	4	no	—
44	C₂²×C₈×C₃₁	C₂×C₄	1	4	yes	—
45	C₂²×C₈×C₃₁	C₂×C₄	1	4	yes	—
46	C₂²×C₈×C₃₁	D₄	1	8	yes	—
47	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
48	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
49	C₂×C₂²⋊C₄×C₃₁	C₈	1	8	yes	complemented
50	C₂×C₄²×C₃₁	—	2	4	no	—
51	C₂×C₄²×C₃₁	—	2	2	no	—
52	C₂×C₄²×C₃₁	—	2	2	no	—
53	C₂×C₄²×C₃₁	—	2	4	no	—
54	C₃₁×C₂²⋊C₈	—	2	8	no	—
55	C₃₁×#95	—	2	4	no	—
56	C₂⁴×C₃₁	—	2	4	no	—
57	C₂⁴×C₃₁	—	2	4	no	—
58	C₂⁴×C₃₁	C₄²	1	2	yes	—
59	C₂⁴×C₃₁	C₂²⋊C₄	1	2	yes	—
60	C₂⁴×C₃₁	C₄⋊C₄	1	2	yes	—
61	C₂⁴×C₃₁	C₂×C₈	1	4	yes	—
62	C₂⁴×C₃₁	M₁₆	1	4	yes	—
63	C₂⁴×C₃₁	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₃₁	—	2	4	no	—
65	C₂²×C₄×C₃₁	—	2	4	no	—
66	C₂²×C₄×C₃₁	—	2	4	no	—
67	C₂²×C₄×C₃₁	—	2	8	no	—
68	C₂²×C₄×C₃₁	—	2	4	no	—
69	C₂²×C₄×C₃₁	—	2	4	no	—
70	C₂²×C₄×C₃₁	—	2	8	no	—
71	C₂²×C₄×C₃₁	—	2	8	no	—
72	C₂²×C₄×C₃₁	—	2	4	no	—
73	C₂²×C₄×C₃₁	—	2	4	no	—
74	C₂²×C₄×C₃₁	—	2	4	no	—
75	C₂²×C₄×C₃₁	—	2	8	no	—
76	C₂²×C₄×C₃₁	—	2	4	no	—
77	C₂²×C₄×C₃₁	—	2	8	no	—
78	C₂²×C₄×C₃₁	C₄²	1	2	yes	—
79	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
80	C₂²×C₄×C₃₁	C₂²⋊C₄	1	4	yes	—
81	C₂²×C₄×C₃₁	C₂²⋊C₄	1	4	yes	—
82	C₂²×C₄×C₃₁	C₄⋊C₄	1	2	yes	—
83	C₂²×C₄×C₃₁	C₄⋊C₄	1	4	yes	—
84	C₂²×C₄×C₃₁	C₄⋊C₄	1	4	yes	—
85	C₂²×C₄×C₃₁	C₂×C₈	1	8	yes	complemented
86	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
92	C₂²×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₄×C₃₁	#41	1	4	yes	—
94	C₂×C₈×C₃₁	—	2	32	no	—
95	C₂×C₈×C₃₁	—	2	4	no	—
96	C₂×C₈×C₃₁	—	2	4	no	—
97	C₂×C₈×C₃₁	—	2	8	no	—
98	C₂×C₈×C₃₁	—	2	8	no	—
99	C₂×C₈×C₃₁	—	2	4	no	—
100	C₂×C₈×C₃₁	—	2	8	no	—
101	C₂×C₈×C₃₁	—	4	2	no	—
102	C₂×C₈×C₃₁	—	4	4	no	—
103	C₂×C₈×C₃₁	—	4	2	no	—
104	C₂×C₈×C₃₁	C₂²⋊C₄	1	8	yes	complemented
105	C₂²⋊C₄×C₃₁	—	2	16	no	—
106	C₄²×C₃₁	—	4	2	no	—
107	C₄²×C₃₁	—	4	4	no	—
108	C₄²×C₃₁	—	4	2	no	—
109	#10714	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂³×C₃₁	—	2	4	no	—
111	C₂³×C₃₁	—	2	4	no	—
112	C₂³×C₃₁	—	2	4	no	—
113	C₂³×C₃₁	—	2	4	no	—
114	C₂³×C₃₁	—	2	4	no	—
115	C₂³×C₃₁	—	2	4	no	—
116	C₂³×C₃₁	—	2	16	no	—
117	C₂³×C₃₁	—	2	16	no	—
118	C₂³×C₃₁	#95	1	4	yes	—
119	C₂³×C₃₁	C₄×C₈	1	4	yes	—
120	C₂³×C₃₁	#97	1	4	yes	—
121	C₂³×C₃₁	C₂²⋊C₈	1	8	yes	—
122	C₂³×C₃₁	C₄⋊C₈	1	8	yes	—
123	C₂³×C₃₁	C₂×C₄²	1	1	yes	characteristic
124	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
125	C₂³×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
126	C₂³×C₃₁	C₄×D₄	1	4	yes	—
127	C₂³×C₃₁	C₂²×C₈	1	2	yes	—
128	C₂³×C₃₁	C₂×M₁₆	1	2	yes	—
129	C₂³×C₃₁	#131	1	4	yes	—
130	C₂×C₄×C₃₁	—	2	4	no	—
131	C₂×C₄×C₃₁	—	2	4	no	—
132	C₂×C₄×C₃₁	—	2	4	no	—
133	C₂×C₄×C₃₁	—	2	4	no	—
134	C₂×C₄×C₃₁	—	2	8	no	—
135	C₂×C₄×C₃₁	—	2	4	no	—
136	C₂×C₄×C₃₁	—	2	8	no	—
137	C₂×C₄×C₃₁	—	2	8	no	—
138	C₂×C₄×C₃₁	—	2	8	no	—
139	C₂×C₄×C₃₁	—	2	16	no	—
140	C₂×C₄×C₃₁	—	4	4	no	—
141	C₂×C₄×C₃₁	—	4	4	no	—
142	C₂×C₄×C₃₁	—	4	8	no	—
143	C₂×C₄×C₃₁	#95	1	4	yes	—
144	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
145	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₃₁	#117	1	2	yes	—
150	C₂×C₄×C₃₁	C₄×D₄	1	4	yes	—
151	C₂×C₄×C₃₁	#120	1	2	yes	—
152	C₂×C₄×C₃₁	#120	1	2	yes	—
153	C₂×C₄×C₃₁	#121	1	4	yes	—
154	C₂×C₄×C₃₁	C₂²⋊Q₈	1	4	yes	—
155	C₂×C₄×C₃₁	#123	1	2	yes	—
156	C₂×C₄×C₃₁	#123	1	2	yes	—
157	C₈×C₃₁	—	2	8	no	—
158	C₈×C₃₁	—	4	4	no	—
159	C₂⁴×C₈	C₂×C₃₁	1	1	yes	characteristic
160	C₂²×C₂²⋊C₈	C₂×C₃₁	1	1	yes	characteristic
161	C₂×C₄×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic
162	C₂×#336	C₂×C₃₁	1	4	yes	complemented
163	C₂²×C₃₁	—	2	16	no	—
164	C₂²×C₃₁	—	2	16	no	—
165	C₂²×C₃₁	—	2	4	no	—
166	C₂²×C₃₁	—	2	4	no	—
167	C₂²×C₃₁	—	2	8	no	—
168	C₂²×C₃₁	—	2	8	no	—
169	C₂²×C₃₁	#336	1	8	yes	complemented
170	C₂²×C₃₁	C₂×#95	1	1	yes	characteristic
171	C₂²×C₃₁	C₄×C₂²⋊C₄	1	2	yes	—
172	C₂²×C₃₁	#385	1	2	yes	—
173	C₂²×C₃₁	#386	1	2	yes	—
174	C₂²×C₃₁	C₂×C₄×C₈	1	1	yes	characteristic
175	C₂²×C₃₁	C₂×#97	1	1	yes	characteristic
176	C₂²×C₃₁	#405	1	2	yes	—
177	C₂²×C₃₁	C₂×C₂²⋊C₈	1	2	yes	—
178	C₂²×C₃₁	#408	1	2	yes	—
179	C₂²×C₃₁	C₂×C₄⋊C₈	1	2	yes	—
180	C₂²×C₃₁	#424	1	2	yes	—
181	C₂²×C₃₁	C₈×D₄	1	8	yes	—
182	C₂²×C₃₁	#435	1	8	yes	—
183	C₄×C₃₁	—	2	4	no	—
184	C₄×C₃₁	—	4	8	no	—
185	C₄×C₃₁	#379	1	1	yes	characteristic
186	C₄×C₃₁	#380	1	2	yes	—
187	C₄×C₃₁	#381	1	1	yes	characteristic
188	C₄×C₃₁	#385	1	2	yes	—
189	C₄×C₃₁	#386	1	2	yes	—
190	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
191	C₂³×C₈	—	2	2	no	—
192	C₂³×C₈	—	2	2	no	—
193	C₂³×C₈	—	2	8	no	—
194	C₂³×C₈	C₄×C₃₁	1	4	yes	complemented
195	C₂³×C₈	C₂²×C₃₁	1	2	yes	—
196	C₂³×C₈	C₂²×C₃₁	1	2	yes	—
197	C₂²×C₂²⋊C₄	C₄×C₃₁	1	2	yes	—
198	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
199	C₂×C₂²⋊C₈	—	2	2	no	—
200	C₂×C₂²⋊C₈	—	2	2	no	—
201	C₂×C₂²⋊C₈	C₄×C₃₁	1	4	yes	complemented
202	C₄×C₂²⋊C₄	—	2	2	no	—
203	C₄×C₂²⋊C₄	—	2	2	no	—
204	C₂×#95	C₄×C₃₁	1	2	yes	—
205	#336	—	2	8	no	—
206	C₂×C₃₁	—	2	8	no	—
207	C₂×C₃₁	C₂²⋊#95	1	1	yes	characteristic
208	C₂×C₃₁	C₂×#336	1	1	yes	characteristic
209	C₂×C₃₁	#1729	1	1	yes	characteristic
210	C₂×C₃₁	C₈×C₂²⋊C₄	1	2	yes	—
211	C₂×C₃₁	#1752	1	2	yes	—
212	C₂×C₃₁	#1850	1	4	yes	—
213	C₂×C₃₁	#1869	1	4	yes	—
214	C₂⁵	C₂×C₄×C₃₁	1	1	yes	characteristic
215	C₂³×C₄	—	2	4	no	—
216	C₂³×C₄	—	2	4	no	—
217	C₂³×C₄	C₂×C₄×C₃₁	1	4	yes	—
218	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
219	C₂³×C₄	C₂×C₄×C₃₁	1	2	yes	—
220	C₂³×C₄	C₂×C₄×C₃₁	1	2	yes	—
221	C₂³×C₄	D₄×C₃₁	1	2	yes	—
222	C₂³×C₄	D₄×C₃₁	1	2	yes	—
223	C₂³×C₄	D₄×C₃₁	1	2	yes	—
224	C₂³×C₄	Q₈×C₃₁	1	2	yes	—
225	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
226	C₂²×C₈	—	2	16	no	—
227	C₂²×C₈	—	2	16	no	—
228	C₂²×C₈	—	2	8	no	—
229	C₂²×C₈	—	2	2	no	—
230	C₂²×C₈	—	2	2	no	—
231	C₂²×C₈	—	2	4	no	—
232	C₂²×C₈	—	2	16	no	—
233	C₂²×C₈	—	2	4	no	—
234	C₂²×C₈	—	2	2	no	—
235	C₂²×C₈	—	2	2	no	—
236	C₂²×C₈	—	2	4	no	—
237	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
238	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
239	C₂²×C₈	D₄×C₃₁	1	8	yes	—
240	C₂×C₂²⋊C₄	—	2	4	no	—
241	C₂×C₂²⋊C₄	—	2	4	no	—
242	C₂×C₂²⋊C₄	C₈×C₃₁	1	8	yes	complemented
243	C₂×C₄²	—	2	4	no	—
244	C₂×C₄²	—	2	2	no	—
245	C₂×C₄²	—	2	2	no	—
246	C₂×C₄²	—	2	4	no	—
247	C₂²⋊C₈	—	2	8	no	—
248	#95	—	2	4	no	—
249	C₃₁	#10714	1	1	yes	characteristic, direct product factor, Sylow
250	C₂⁴	—	2	4	no	—
251	C₂⁴	—	2	4	no	—
252	C₂⁴	C₄²×C₃₁	1	2	yes	—
253	C₂⁴	C₂²⋊C₄×C₃₁	1	2	yes	—
254	C₂⁴	C₄⋊C₄×C₃₁	1	2	yes	—
255	C₂⁴	C₂×C₈×C₃₁	1	4	yes	—
256	C₂⁴	M₁₆×C₃₁	1	4	yes	—
257	C₂⁴	C₂²×C₄×C₃₁	1	1	yes	characteristic
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	8	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	8	no	—
265	C₂²×C₄	—	2	8	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	8	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	8	no	—
272	C₂²×C₄	C₄²×C₃₁	1	2	yes	—
273	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
274	C₂²×C₄	C₂²⋊C₄×C₃₁	1	4	yes	—
275	C₂²×C₄	C₂²⋊C₄×C₃₁	1	4	yes	—
276	C₂²×C₄	C₄⋊C₄×C₃₁	1	2	yes	—
277	C₂²×C₄	C₄⋊C₄×C₃₁	1	4	yes	—
278	C₂²×C₄	C₄⋊C₄×C₃₁	1	4	yes	—
279	C₂²×C₄	C₂×C₈×C₃₁	1	8	yes	complemented
280	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
281	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
285	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
286	C₂²×C₄	C₂×Q₈×C₃₁	1	1	yes	characteristic
287	C₂²×C₄	#41×C₃₁	1	4	yes	—
288	C₂×C₈	—	2	32	no	—
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	—	2	4	no	—
291	C₂×C₈	—	2	8	no	—
292	C₂×C₈	—	2	8	no	—
293	C₂×C₈	—	2	4	no	—
294	C₂×C₈	—	2	8	no	—
295	C₂×C₈	—	4	2	no	—
296	C₂×C₈	—	4	4	no	—
297	C₂×C₈	—	4	2	no	—
298	C₂×C₈	C₂²⋊C₄×C₃₁	1	8	yes	complemented
299	C₂²⋊C₄	—	2	16	no	—
300	C₄²	—	4	2	no	—
301	C₄²	—	4	4	no	—
302	C₄²	—	4	2	no	—
303	C₂³	—	2	4	no	—
304	C₂³	—	2	4	no	—
305	C₂³	—	2	4	no	—
306	C₂³	—	2	16	no	—
307	C₂³	—	2	16	no	—
308	C₂³	—	2	4	no	—
309	C₂³	—	2	4	no	—
310	C₂³	—	2	4	no	—
311	C₂³	C₃₁×#95	1	4	yes	—
312	C₂³	C₄×C₈×C₃₁	1	4	yes	—
313	C₂³	C₃₁×#97	1	4	yes	—
314	C₂³	C₃₁×C₂²⋊C₈	1	8	yes	—
315	C₂³	C₃₁×C₄⋊C₈	1	8	yes	—
316	C₂³	C₂×C₄²×C₃₁	1	1	yes	characteristic
317	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
318	C₂³	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
319	C₂³	C₄×D₄×C₃₁	1	4	yes	—
320	C₂³	C₂²×C₈×C₃₁	1	2	yes	—
321	C₂³	C₂×M₁₆×C₃₁	1	2	yes	—
322	C₂³	C₃₁×#131	1	4	yes	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	2	16	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	8	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	C₃₁×#95	1	4	yes	—
337	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
338	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
339	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
340	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
341	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
342	C₂×C₄	C₃₁×#117	1	2	yes	—
343	C₂×C₄	C₄×D₄×C₃₁	1	4	yes	—
344	C₂×C₄	C₃₁×#120	1	2	yes	—
345	C₂×C₄	C₃₁×#120	1	2	yes	—
346	C₂×C₄	C₃₁×#121	1	4	yes	—
347	C₂×C₄	C₃₁×C₂²⋊Q₈	1	4	yes	—
348	C₂×C₄	C₃₁×#123	1	2	yes	—
349	C₂×C₄	C₃₁×#123	1	2	yes	—
350	C₈	—	2	8	no	—
351	C₈	—	4	4	no	—
352	C₂²	—	2	16	no	—
353	C₂²	—	2	16	no	—
354	C₂²	—	2	4	no	—
355	C₂²	—	2	4	no	—
356	C₂²	—	2	8	no	—
357	C₂²	—	2	8	no	—
358	C₂²	C₃₁×#336	1	8	yes	complemented
359	C₂²	C₂×C₃₁×#95	1	1	yes	characteristic
360	C₂²	C₄×C₂²⋊C₄×C₃₁	1	2	yes	—
361	C₂²	C₃₁×#385	1	2	yes	—
362	C₂²	C₃₁×#386	1	2	yes	—
363	C₂²	C₂×C₄×C₈×C₃₁	1	1	yes	characteristic
364	C₂²	C₂×C₃₁×#97	1	1	yes	characteristic
365	C₂²	C₃₁×#405	1	2	yes	—
366	C₂²	C₂×C₃₁×C₂²⋊C₈	1	2	yes	—
367	C₂²	C₃₁×#408	1	2	yes	—
368	C₂²	C₂×C₃₁×C₄⋊C₈	1	2	yes	—
369	C₂²	C₃₁×#424	1	2	yes	—
370	C₂²	C₈×D₄×C₃₁	1	8	yes	—
371	C₂²	C₃₁×#435	1	8	yes	—
372	C₄	—	2	4	no	—
373	C₄	—	4	8	no	—
374	C₄	C₃₁×#379	1	1	yes	characteristic
375	C₄	C₃₁×#380	1	2	yes	—
376	C₄	C₃₁×#381	1	1	yes	characteristic
377	C₄	C₃₁×#385	1	2	yes	—
378	C₄	C₃₁×#386	1	2	yes	—
379	C₂	—	2	8	no	—
380	C₂	C₃₁×C₂²⋊#95	1	1	yes	characteristic
381	C₂	C₂×C₃₁×#336	1	1	yes	characteristic
382	C₂	C₃₁×#1729	1	1	yes	characteristic
383	C₂	C₈×C₂²⋊C₄×C₃₁	1	2	yes	—
384	C₂	C₃₁×#1752	1	2	yes	—
385	C₂	C₃₁×#1850	1	4	yes	—
386	C₂	C₃₁×#1869	1	4	yes	—

	subgroup	G/H
center	C₂³×C₄×C₃₁	C₂³
commutator	C₂²	C₂×C₄×C₈×C₃₁
Frattini, cosocle	C₂³×C₄	C₂³×C₃₁
socle	C₂⁴×C₃₁	C₂²×C₄
prime radical	C₂⁵×C₃₁	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₃₁×#336	C₂	semidirect
9. C₂³×C₈×C₃₁	C₄	semidirect
16. C₂×C₃₁×C₂²⋊C₈	C₄	semidirect
49. C₂×C₂²⋊C₄×C₃₁	C₈	semidirect
85. C₂²×C₄×C₃₁	C₂×C₈	semidirect
104. C₂×C₈×C₃₁	C₂²⋊C₄	semidirect
109. #10714	C₃₁	direct (N × H)
162. C₂×#336	C₂×C₃₁	semidirect
169. C₂²×C₃₁	#336	semidirect
194. C₂³×C₈	C₄×C₃₁	semidirect
201. C₂×C₂²⋊C₈	C₄×C₃₁	semidirect
242. C₂×C₂²⋊C₄	C₈×C₃₁	semidirect
249. C₃₁	#10714	direct (N × H)
279. C₂²×C₄	C₂×C₈×C₃₁	semidirect
298. C₂×C₈	C₂²⋊C₄×C₃₁	semidirect
358. C₂²	C₃₁×#336	semidirect

Maximal subgroups

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

subgroup	index
C₂⁴×C₈×C₃₁	2
C₂²×C₃₁×C₂²⋊C₈	2
C₂×C₄×C₂²⋊C₄×C₃₁	2
C₂×C₃₁×#336	2
#10714	31

Subgroups — C31×#10714 #21467473

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#10714 #21467473