Subgroups — C₃₁×#21200 #21477959

Order 7936.

1726 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	C₂×C₃₁×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#417	C₂	1	4	yes	maximal, complemented
3	C₂×C₄×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₁×#384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1959	C₂	1	4	yes	maximal, complemented
6	C₃₁×#1957	C₂	1	2	yes	maximal, complemented
7	C₃₁×#1956	C₂	1	2	yes	maximal, complemented
8	C₂²×#41×C₃₁	C₂²	1	2	yes	—
9	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
10	C₃₁×#532	—	2	4	no	—
11	C₃₁×#532	C₄	1	8	yes	complemented
12	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
14	C₂×C₃₁×#124	C₂²	1	2	yes	—
15	C₂×C₃₁×#121	—	2	2	no	—
16	C₂×C₄×D₄×C₃₁	—	2	2	no	—
17	C₂²×C₄⋊C₄×C₃₁	—	2	2	no	—
18	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
19	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
20	C₃₁×#417	—	2	16	no	—
21	C₂×C₃₁×#103	C₂²	1	8	yes	—
22	C₂×C₃₁×#102	C₂²	1	8	yes	—
23	C₄×M₁₆×C₃₁	—	2	4	no	—
24	C₂×C₃₁×#97	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
26	C₃₁×#384	—	2	2	no	—
27	C₃₁×#384	C₂²	1	2	yes	—
28	C₃₁×#384	C₂²	1	2	yes	—
29	C₂×#41×C₃₁	—	2	4	no	—
30	C₂×#41×C₃₁	—	2	8	no	—
31	C₂×#41×C₃₁	—	2	8	no	—
32	C₂×#41×C₃₁	C₂×C₄	1	8	yes	—
33	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
34	C₂²×D₄×C₃₁	—	2	2	no	—
35	C₂²×D₄×C₃₁	—	2	2	no	—
36	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
37	C₂³×C₄×C₃₁	—	2	2	no	—
38	C₂³×C₄×C₃₁	—	2	2	no	—
39	C₂³×C₄×C₃₁	D₄	1	2	yes	—
40	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
41	C₂×M₁₆×C₃₁	—	2	4	no	—
42	C₂×M₁₆×C₃₁	—	2	4	no	—
43	C₂×M₁₆×C₃₁	D₄	1	8	yes	complemented
44	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
45	C₃₁×C₄⋊Q₈	—	2	2	no	—
46	C₃₁×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
47	C₃₁×#127	—	2	2	no	—
48	C₃₁×#127	C₂×C₄	1	4	yes	complemented
49	C₃₁×#124	—	2	4	no	—
50	C₃₁×#124	C₂×C₄	1	8	yes	complemented
51	C₃₁×#121	—	2	16	no	—
52	C₄×D₄×C₃₁	—	2	16	no	—
53	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
54	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
55	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
56	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
57	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₃₁	—	4	8	no	—
59	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
60	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
61	C₂×C₄²×C₃₁	C₂×C₄	1	4	yes	—
62	C₂×C₄²×C₃₁	D₄	1	2	yes	—
63	C₂×C₄²×C₃₁	D₄	1	4	yes	—
64	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
66	C₃₁×#103	—	2	16	no	—
67	C₃₁×#102	—	2	16	no	—
68	C₃₁×#97	—	2	4	no	—
69	C₄×C₈×C₃₁	—	2	4	no	—
70	C₂⁴×C₃₁	—	2	2	no	—
71	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
72	#41×C₃₁	—	2	32	no	—
73	#41×C₃₁	—	4	16	no	—
74	C₂×Q₈×C₃₁	—	2	2	no	—
75	C₂×Q₈×C₃₁	—	2	4	no	—
76	C₂×Q₈×C₃₁	—	2	4	no	—
77	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
78	C₂×D₄×C₃₁	—	2	8	no	—
79	C₂×D₄×C₃₁	—	2	8	no	—
80	C₂×D₄×C₃₁	—	2	4	no	—
81	C₂×D₄×C₃₁	—	2	2	no	—
82	C₂×D₄×C₃₁	—	2	4	no	—
83	C₂×D₄×C₃₁	—	4	4	no	—
84	C₂×D₄×C₃₁	—	4	4	no	—
85	C₂×D₄×C₃₁	—	4	4	no	—
86	C₂×D₄×C₃₁	—	4	4	no	—
87	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₃₁	—	2	4	no	—
89	C₂²×C₄×C₃₁	—	2	4	no	—
90	C₂²×C₄×C₃₁	—	2	2	no	—
91	C₂²×C₄×C₃₁	—	2	8	no	—
92	C₂²×C₄×C₃₁	—	2	4	no	—
93	C₂²×C₄×C₃₁	—	4	4	no	—
94	C₂²×C₄×C₃₁	—	4	4	no	—
95	C₂²×C₄×C₃₁	—	4	8	no	—
96	C₂²×C₄×C₃₁	—	4	4	no	—
97	C₂²×C₄×C₃₁	C₂²⋊C₄	1	8	yes	—
98	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
104	C₂²×C₄×C₃₁	#41	1	4	yes	—
105	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
106	M₁₆×C₃₁	—	2	16	no	—
107	C₂×C₈×C₃₁	—	2	4	no	—
108	C₂×C₈×C₃₁	—	2	4	no	—
109	C₂×C₈×C₃₁	C₂×D₄	1	8	yes	—
110	C₄⋊C₄×C₃₁	—	2	8	no	—
111	C₄⋊C₄×C₃₁	—	2	8	no	—
112	C₄⋊C₄×C₃₁	—	4	8	no	—
113	C₄⋊C₄×C₃₁	—	4	4	no	—
114	C₄⋊C₄×C₃₁	—	4	8	no	—
115	C₂²⋊C₄×C₃₁	—	2	16	no	—
116	C₄²×C₃₁	C₂²⋊C₄	1	8	yes	—
117	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
118	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
119	C₄²×C₃₁	C₂×D₄	1	2	yes	—
120	C₄²×C₃₁	C₂×D₄	1	2	yes	—
121	#21200	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
122	C₂³×C₃₁	—	2	2	no	—
123	C₂³×C₃₁	—	2	2	no	—
124	C₂³×C₃₁	—	2	4	no	—
125	C₂³×C₃₁	—	4	2	no	—
126	C₂³×C₃₁	—	4	2	no	—
127	C₂³×C₃₁	—	4	4	no	—
128	C₂³×C₃₁	—	4	4	no	—
129	C₂³×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
130	C₂³×C₃₁	#124	1	2	yes	—
131	C₂³×C₃₁	#127	1	2	yes	—
132	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
133	Q₈×C₃₁	—	2	8	no	—
134	Q₈×C₃₁	—	4	4	no	—
135	D₄×C₃₁	—	2	8	no	—
136	D₄×C₃₁	—	4	16	no	—
137	D₄×C₃₁	—	4	4	no	—
138	D₄×C₃₁	—	4	16	no	—
139	C₂×C₄×C₃₁	—	2	2	no	—
140	C₂×C₄×C₃₁	—	2	2	no	—
141	C₂×C₄×C₃₁	—	2	16	no	—
142	C₂×C₄×C₃₁	—	2	4	no	—
143	C₂×C₄×C₃₁	—	4	2	no	—
144	C₂×C₄×C₃₁	—	4	2	no	—
145	C₂×C₄×C₃₁	—	4	16	no	—
146	C₂×C₄×C₃₁	—	4	4	no	—
147	C₂×C₄×C₃₁	—	4	8	no	—
148	C₂×C₄×C₃₁	—	8	8	no	—
149	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	4	yes	—
150	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	4	yes	—
152	C₂×C₄×C₃₁	C₄×D₄	1	8	yes	—
153	C₂×C₄×C₃₁	#121	1	8	yes	—
154	C₂×C₄×C₃₁	#124	1	2	yes	—
155	C₂×C₄×C₃₁	#127	1	2	yes	—
156	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	4	yes	—
157	C₂×C₄×C₃₁	#137	1	4	yes	—
158	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
160	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
162	C₈×C₃₁	—	2	8	no	—
163	C₂×#532	C₂×C₃₁	1	1	yes	characteristic
164	C₂×#417	C₂×C₃₁	1	4	yes	complemented
165	C₂×C₄×M₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
166	C₂×#384	C₂×C₃₁	1	1	yes	characteristic, complemented
167	#1959	C₂×C₃₁	1	4	yes	complemented
168	#1957	C₂×C₃₁	1	2	yes	complemented
169	#1956	C₂×C₃₁	1	2	yes	complemented
170	C₂²×C₃₁	—	2	4	no	—
171	C₂²×C₃₁	—	2	4	no	—
172	C₂²×C₃₁	—	2	2	no	—
173	C₂²×C₃₁	—	2	2	no	—
174	C₂²×C₃₁	—	4	8	no	—
175	C₂²×C₃₁	—	4	4	no	—
176	C₂²×C₃₁	—	8	4	no	—
177	C₂²×C₃₁	—	8	2	no	—
178	C₂²×C₃₁	—	8	2	no	—
179	C₂²×C₃₁	#390	1	4	yes	—
180	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
181	C₂²×C₃₁	C₂×#124	1	1	yes	characteristic
182	C₂²×C₃₁	C₂×#127	1	1	yes	characteristic
183	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
184	C₂²×C₃₁	C₂×#137	1	2	yes	—
185	C₄×C₃₁	—	2	4	no	—
186	C₄×C₃₁	—	4	4	no	—
187	C₄×C₃₁	—	8	4	no	—
188	C₄×C₃₁	#390	1	4	yes	—
189	C₄×C₃₁	#417	1	8	yes	complemented
190	C₄×C₃₁	C₂×C₄×D₄	1	2	yes	—
191	C₄×C₃₁	C₂×#121	1	2	yes	—
192	C₂²×#41	C₂²×C₃₁	1	2	yes	—
193	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
194	#532	—	2	4	no	—
195	#532	C₄×C₃₁	1	8	yes	complemented
196	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
197	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
198	C₂×#124	C₂²×C₃₁	1	2	yes	—
199	C₂×#121	—	2	2	no	—
200	C₂×C₄×D₄	—	2	2	no	—
201	C₂²×C₄⋊C₄	—	2	2	no	—
202	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
203	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
204	#417	—	2	16	no	—
205	C₂×#103	C₂²×C₃₁	1	8	yes	—
206	C₂×#102	C₂²×C₃₁	1	8	yes	—
207	C₄×M₁₆	—	2	4	no	—
208	C₂×#97	C₂²×C₃₁	1	2	yes	—
209	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
210	#384	—	2	2	no	—
211	#384	C₂²×C₃₁	1	2	yes	—
212	#384	C₂²×C₃₁	1	2	yes	—
213	C₂×C₃₁	—	2	4	no	—
214	C₂×C₃₁	—	8	4	no	—
215	C₂×C₃₁	C₂×#390	1	1	yes	characteristic
216	C₂×C₃₁	C₂×#417	1	2	yes	—
217	C₂×C₃₁	#3141	1	2	yes	—
218	C₂×C₃₁	#3151	1	1	yes	characteristic
219	C₂×C₃₁	#3152	1	1	yes	characteristic
220	C₂×#41	—	2	4	no	—
221	C₂×#41	—	2	8	no	—
222	C₂×#41	—	2	8	no	—
223	C₂×#41	C₂×C₄×C₃₁	1	8	yes	—
224	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
225	C₂²×D₄	—	2	2	no	—
226	C₂²×D₄	—	2	2	no	—
227	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
228	C₂³×C₄	—	2	2	no	—
229	C₂³×C₄	—	2	2	no	—
230	C₂³×C₄	D₄×C₃₁	1	2	yes	—
231	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
232	C₂×M₁₆	—	2	4	no	—
233	C₂×M₁₆	—	2	4	no	—
234	C₂×M₁₆	D₄×C₃₁	1	8	yes	complemented
235	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
236	C₄⋊Q₈	—	2	2	no	—
237	C₄⋊Q₈	C₂×C₄×C₃₁	1	4	yes	complemented
238	#127	—	2	2	no	—
239	#127	C₂×C₄×C₃₁	1	4	yes	complemented
240	#124	—	2	4	no	—
241	#124	C₂×C₄×C₃₁	1	8	yes	complemented
242	#121	—	2	16	no	—
243	C₄×D₄	—	2	16	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	2	8	no	—
246	C₂×C₄⋊C₄	—	2	4	no	—
247	C₂×C₄⋊C₄	—	2	4	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	4	8	no	—
250	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
251	C₂×C₂²⋊C₄	—	2	4	no	—
252	C₂×C₄²	C₂×C₄×C₃₁	1	4	yes	—
253	C₂×C₄²	D₄×C₃₁	1	2	yes	—
254	C₂×C₄²	D₄×C₃₁	1	4	yes	—
255	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
256	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
257	#103	—	2	16	no	—
258	#102	—	2	16	no	—
259	#97	—	2	4	no	—
260	C₄×C₈	—	2	4	no	—
261	C₃₁	#21200	1	1	yes	characteristic, direct product factor, Sylow
262	C₂⁴	—	2	2	no	—
263	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
264	#41	—	2	32	no	—
265	#41	—	4	16	no	—
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	2	4	no	—
268	C₂×Q₈	—	2	4	no	—
269	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
270	C₂×D₄	—	2	8	no	—
271	C₂×D₄	—	2	8	no	—
272	C₂×D₄	—	2	4	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	2	4	no	—
275	C₂×D₄	—	4	4	no	—
276	C₂×D₄	—	4	4	no	—
277	C₂×D₄	—	4	4	no	—
278	C₂×D₄	—	4	4	no	—
279	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	8	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	4	4	no	—
286	C₂²×C₄	—	4	4	no	—
287	C₂²×C₄	—	4	8	no	—
288	C₂²×C₄	—	4	4	no	—
289	C₂²×C₄	C₂²⋊C₄×C₃₁	1	8	yes	—
290	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
291	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
292	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
294	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
295	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
296	C₂²×C₄	#41×C₃₁	1	4	yes	—
297	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
298	M₁₆	—	2	16	no	—
299	C₂×C₈	—	2	4	no	—
300	C₂×C₈	—	2	4	no	—
301	C₂×C₈	C₂×D₄×C₃₁	1	8	yes	—
302	C₄⋊C₄	—	2	8	no	—
303	C₄⋊C₄	—	2	8	no	—
304	C₄⋊C₄	—	4	8	no	—
305	C₄⋊C₄	—	4	4	no	—
306	C₄⋊C₄	—	4	8	no	—
307	C₂²⋊C₄	—	2	16	no	—
308	C₄²	C₂²⋊C₄×C₃₁	1	8	yes	—
309	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
310	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
311	C₄²	C₂×D₄×C₃₁	1	2	yes	—
312	C₄²	C₂×D₄×C₃₁	1	2	yes	—
313	C₂³	—	2	2	no	—
314	C₂³	—	2	2	no	—
315	C₂³	—	2	4	no	—
316	C₂³	—	4	2	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	4	4	no	—
319	C₂³	—	4	4	no	—
320	C₂³	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
321	C₂³	C₃₁×#124	1	2	yes	—
322	C₂³	C₃₁×#127	1	2	yes	—
323	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
324	Q₈	—	2	8	no	—
325	Q₈	—	4	4	no	—
326	D₄	—	2	8	no	—
327	D₄	—	4	16	no	—
328	D₄	—	4	16	no	—
329	D₄	—	4	4	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	16	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	16	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	8	no	—
339	C₂×C₄	—	8	8	no	—
340	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	4	yes	—
341	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	4	yes	—
342	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
343	C₂×C₄	C₄×D₄×C₃₁	1	8	yes	—
344	C₂×C₄	C₃₁×#121	1	8	yes	—
345	C₂×C₄	C₃₁×#124	1	2	yes	—
346	C₂×C₄	C₃₁×#127	1	2	yes	—
347	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	4	yes	—
348	C₂×C₄	C₃₁×#137	1	4	yes	—
349	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
350	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
351	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
352	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
353	C₈	—	2	8	no	—
354	C₂²	—	2	4	no	—
355	C₂²	—	2	4	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	4	8	no	—
359	C₂²	—	4	4	no	—
360	C₂²	—	8	4	no	—
361	C₂²	—	8	2	no	—
362	C₂²	—	8	2	no	—
363	C₂²	C₃₁×#390	1	4	yes	—
364	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
365	C₂²	C₂×C₃₁×#124	1	1	yes	characteristic
366	C₂²	C₂×C₃₁×#127	1	1	yes	characteristic
367	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
368	C₂²	C₂×C₃₁×#137	1	2	yes	—
369	C₄	—	2	4	no	—
370	C₄	—	4	4	no	—
371	C₄	—	8	4	no	—
372	C₄	C₃₁×#390	1	4	yes	—
373	C₄	C₃₁×#417	1	8	yes	complemented
374	C₄	C₂×C₄×D₄×C₃₁	1	2	yes	—
375	C₄	C₂×C₃₁×#121	1	2	yes	—
376	C₂	—	2	4	no	—
377	C₂	—	8	4	no	—
378	C₂	C₂×C₃₁×#390	1	1	yes	characteristic
379	C₂	C₂×C₃₁×#417	1	2	yes	—
380	C₂	C₃₁×#3141	1	2	yes	—
381	C₂	C₃₁×#3151	1	1	yes	characteristic
382	C₂	C₃₁×#3152	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂×C₃₁×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₁×#417	C₂	semidirect
3. C₂×C₄×M₁₆×C₃₁	C₂	semidirect
4. C₂×C₃₁×#384	C₂	semidirect
5. C₃₁×#1959	C₂	semidirect
6. C₃₁×#1957	C₂	semidirect
7. C₃₁×#1956	C₂	semidirect
11. C₃₁×#532	C₄	semidirect
43. C₂×M₁₆×C₃₁	D₄	semidirect
46. C₃₁×C₄⋊Q₈	C₂×C₄	semidirect
48. C₃₁×#127	C₂×C₄	semidirect
50. C₃₁×#124	C₂×C₄	semidirect
121. #21200	C₃₁	direct (N × H)
164. C₂×#417	C₂×C₃₁	semidirect
165. C₂×C₄×M₁₆	C₂×C₃₁	semidirect
166. C₂×#384	C₂×C₃₁	semidirect
167. #1959	C₂×C₃₁	semidirect
168. #1957	C₂×C₃₁	semidirect
169. #1956	C₂×C₃₁	semidirect
189. C₄×C₃₁	#417	semidirect
195. #532	C₄×C₃₁	semidirect
234. C₂×M₁₆	D₄×C₃₁	semidirect
237. C₄⋊Q₈	C₂×C₄×C₃₁	semidirect
239. #127	C₂×C₄×C₃₁	semidirect
241. #124	C₂×C₄×C₃₁	semidirect
261. C₃₁	#21200	direct (N × H)
373. C₄	C₃₁×#417	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#532	2
C₂×C₃₁×#417	2
C₂×C₄×M₁₆×C₃₁	2
C₂×C₃₁×#384	2
C₃₁×#1959	2
C₃₁×#1957	2
C₃₁×#1956	2
#21200	31

Subgroups — C31×#21200 #21477959

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#21200 #21477959