Subgroups — C₃₁×#17905 #21474664

Order 7936.

698 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3101	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2960	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1585	C₂	1	4	yes	maximal, complemented
5	C₃₁×SD₁₆⋊C₈	C₂	1	4	yes	maximal, complemented
6	C₃₁×#1571	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1486	C₂	1	1	yes	maximal, characteristic
8	C₃₁×#1481	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#1452	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×C₈×C₃₁	—	2	1	no	—
11	C₃₁×#533	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
13	C₃₁×#483	C₄	1	2	yes	—
14	C₃₁×#476	C₄	1	2	yes	—
15	C₃₁×#461	C₄	1	2	yes	—
16	C₃₁×#450	C₄	1	2	yes	—
17	C₃₁×#446	—	2	1	no	—
18	C₃₁×#446	C₂²	1	2	yes	complemented
19	C₈×Q₈×C₃₁	—	2	1	no	—
20	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
21	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	—
22	C₈×D₄×C₃₁	—	2	1	no	—
23	C₈×D₄×C₃₁	—	2	1	no	—
24	C₈×D₄×C₃₁	C₂²	1	2	yes	—
25	C₈×D₄×C₃₁	C₂²	1	2	yes	—
26	C₃₁×#431	C₂²	1	1	yes	characteristic
27	C₃₁×#431	C₂²	1	1	yes	characteristic
28	C₃₁×#424	—	2	1	no	—
29	C₃₁×#423	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×C₂²⋊C₈	—	2	1	no	—
32	C₃₁×#405	—	2	1	no	—
33	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
34	C₃₁×#335	C₂²	1	4	yes	complemented
35	C₃₁×Q₈⋊C₈	C₂²	1	4	yes	complemented
36	C₃₁×D₄⋊C₈	C₂²	1	4	yes	—
37	C₃₁×#322	C₂²	1	2	yes	complemented
38	C₃₁×#322	C₂²	1	2	yes	complemented
39	C₂²×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₃₁	—	2	1	no	—
41	C₂×SD₁₆×C₃₁	C₂×C₄	1	4	yes	—
42	C₂×M₁₆×C₃₁	—	2	1	no	—
43	C₂²×C₈×C₃₁	—	2	1	no	—
44	C₂²×C₈×C₃₁	—	2	2	no	—
45	C₂²×C₈×C₃₁	—	2	2	no	—
46	C₂²×C₈×C₃₁	—	4	4	no	—
47	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
48	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
49	C₃₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
50	C₃₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
51	C₃₁×#125	—	2	1	no	—
52	C₃₁×C₂²⋊Q₈	—	2	1	no	—
53	C₃₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
54	C₄×Q₈×C₃₁	—	2	1	no	—
55	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
56	C₄×D₄×C₃₁	—	2	1	no	—
57	C₄×D₄×C₃₁	—	2	1	no	—
58	C₄×D₄×C₃₁	C₂×C₄	1	2	yes	—
59	C₄×D₄×C₃₁	C₂³	1	2	yes	—
60	C₃₁×#117	—	2	1	no	—
61	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
62	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
63	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
64	C₃₁×#106	C₂×C₄	1	4	yes	—
65	C₃₁×C₄⋊C₈	—	2	2	no	—
66	C₃₁×C₄⋊C₈	—	2	2	no	—
67	C₃₁×C₄⋊C₈	—	2	1	no	—
68	C₃₁×C₄⋊C₈	—	2	1	no	—
69	C₃₁×C₄⋊C₈	—	2	1	no	—
70	C₃₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
71	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
72	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
73	C₃₁×#103	C₂×C₄	1	4	yes	—
74	C₃₁×#102	C₂×C₄	1	4	yes	—
75	C₃₁×C₂²⋊C₈	—	2	1	no	—
76	C₃₁×C₂²⋊C₈	—	2	2	no	—
77	C₃₁×C₂²⋊C₈	—	2	2	no	—
78	C₃₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
79	C₃₁×#97	—	2	2	no	—
80	C₄×C₈×C₃₁	—	2	2	no	—
81	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
82	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
83	C₄×C₈×C₃₁	C₂³	1	2	yes	—
84	C₄×C₈×C₃₁	C₂³	1	2	yes	—
85	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
86	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
87	C₂⁴×C₃₁	—	2	1	no	—
88	C₂×Q₈×C₃₁	—	2	1	no	—
89	C₂×Q₈×C₃₁	C₂²×C₄	1	2	yes	—
90	C₂×D₄×C₃₁	—	2	4	no	—
91	C₂×D₄×C₃₁	—	2	1	no	—
92	C₂×D₄×C₃₁	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₃₁	—	2	1	no	—
94	C₂²×C₄×C₃₁	—	2	2	no	—
95	C₂²×C₄×C₃₁	—	2	2	no	—
96	C₂²×C₄×C₃₁	—	4	2	no	—
97	C₂²×C₄×C₃₁	—	4	2	no	—
98	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
101	SD₁₆×C₃₁	—	2	8	no	—
102	M₁₆×C₃₁	—	4	2	no	—
103	C₂×C₈×C₃₁	—	2	2	no	—
104	C₂×C₈×C₃₁	—	2	2	no	—
105	C₂×C₈×C₃₁	—	2	2	no	—
106	C₂×C₈×C₃₁	—	2	2	no	—
107	C₂×C₈×C₃₁	—	2	2	no	—
108	C₂×C₈×C₃₁	—	4	4	no	—
109	C₂×C₈×C₃₁	—	4	4	no	—
110	C₂×C₈×C₃₁	—	4	2	no	—
111	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
112	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
116	C₄⋊C₄×C₃₁	—	2	1	no	—
117	C₄⋊C₄×C₃₁	—	2	1	no	—
118	C₄⋊C₄×C₃₁	—	2	1	no	—
119	C₄⋊C₄×C₃₁	—	2	1	no	—
120	C₄⋊C₄×C₃₁	—	2	2	no	—
121	C₄⋊C₄×C₃₁	—	2	2	no	—
122	C₄⋊C₄×C₃₁	C₂²×C₄	1	2	yes	—
123	C₄⋊C₄×C₃₁	C₂²×C₄	1	2	yes	—
124	C₂²⋊C₄×C₃₁	—	2	2	no	—
125	C₂²⋊C₄×C₃₁	—	2	2	no	—
126	C₂²⋊C₄×C₃₁	—	2	2	no	—
127	C₄²×C₃₁	—	2	2	no	—
128	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₃₁	#41	1	1	yes	characteristic
131	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
132	#17905	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂³×C₃₁	—	2	4	no	—
134	C₂³×C₃₁	—	2	2	no	—
135	C₂³×C₃₁	—	4	2	no	—
136	C₂³×C₃₁	—	4	2	no	—
137	C₂³×C₃₁	C₄×D₄	1	1	yes	characteristic
138	Q₈×C₃₁	—	2	4	no	—
139	Q₈×C₃₁	—	4	2	no	—
140	D₄×C₃₁	—	2	4	no	—
141	D₄×C₃₁	—	2	2	no	—
142	D₄×C₃₁	#131	1	4	yes	—
143	C₂×C₄×C₃₁	—	2	2	no	—
144	C₂×C₄×C₃₁	—	2	2	no	—
145	C₂×C₄×C₃₁	—	2	2	no	—
146	C₂×C₄×C₃₁	—	2	2	no	—
147	C₂×C₄×C₃₁	—	4	1	no	—
148	C₂×C₄×C₃₁	—	4	2	no	—
149	C₂×C₄×C₃₁	—	4	2	no	—
150	C₂×C₄×C₃₁	—	4	2	no	—
151	C₂×C₄×C₃₁	—	4	4	no	—
152	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
156	C₂×C₄×C₃₁	#137	1	2	yes	—
157	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
160	C₈×C₃₁	—	2	4	no	—
161	C₈×C₃₁	—	2	1	no	—
162	C₈×C₃₁	—	2	1	no	—
163	C₈×C₃₁	—	2	1	no	—
164	C₈×C₃₁	—	2	1	no	—
165	C₈×C₃₁	—	4	2	no	—
166	C₈×C₃₁	—	4	2	no	—
167	C₈×C₃₁	—	4	2	no	—
168	#3101	C₂×C₃₁	1	1	yes	characteristic
169	#2960	C₂×C₃₁	1	1	yes	characteristic, complemented
170	C₂×C₈×D₄	C₂×C₃₁	1	1	yes	characteristic
171	#1585	C₂×C₃₁	1	4	yes	complemented
172	SD₁₆⋊C₈	C₂×C₃₁	1	4	yes	complemented
173	#1571	C₂×C₃₁	1	1	yes	characteristic, complemented
174	#1486	C₂×C₃₁	1	1	yes	characteristic
175	#1481	C₂×C₃₁	1	1	yes	characteristic, complemented
176	#1452	C₂×C₃₁	1	1	yes	characteristic, complemented
177	C₂²×C₃₁	—	2	1	no	—
178	C₂²×C₃₁	—	2	1	no	—
179	C₂²×C₃₁	—	2	4	no	—
180	C₂²×C₃₁	—	4	8	no	—
181	C₂²×C₃₁	—	4	2	no	—
182	C₂²×C₃₁	—	4	2	no	—
183	C₂²×C₃₁	#440	1	2	yes	—
184	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
185	C₄×C₃₁	—	2	1	no	—
186	C₄×C₃₁	—	2	1	no	—
187	C₄×C₃₁	—	2	1	no	—
188	C₄×C₃₁	—	4	2	no	—
189	C₄×C₃₁	—	4	2	no	—
190	C₄×C₃₁	—	4	2	no	—
191	C₄×C₃₁	#440	1	2	yes	—
192	C₄×C₃₁	C₂×#131	1	2	yes	—
193	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
194	C₄×C₃₁	C₂×#137	1	1	yes	characteristic
195	C₂³×C₈	—	2	1	no	—
196	#533	C₂²×C₃₁	1	1	yes	characteristic
197	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
198	#483	C₄×C₃₁	1	2	yes	—
199	#476	C₄×C₃₁	1	2	yes	—
200	#461	C₄×C₃₁	1	2	yes	—
201	#450	C₄×C₃₁	1	2	yes	—
202	#446	—	2	1	no	—
203	#446	C₂²×C₃₁	1	2	yes	complemented
204	C₈×Q₈	—	2	1	no	—
205	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
206	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	—
207	C₈×D₄	—	2	1	no	—
208	C₈×D₄	—	2	1	no	—
209	C₈×D₄	C₂²×C₃₁	1	2	yes	—
210	C₈×D₄	C₂²×C₃₁	1	2	yes	—
211	#431	C₂²×C₃₁	1	1	yes	characteristic
212	#431	C₂²×C₃₁	1	1	yes	characteristic
213	#424	—	2	1	no	—
214	#423	C₂²×C₃₁	1	1	yes	characteristic
215	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
216	C₂×C₂²⋊C₈	—	2	1	no	—
217	#405	—	2	1	no	—
218	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
219	#335	C₂²×C₃₁	1	4	yes	complemented
220	Q₈⋊C₈	C₂²×C₃₁	1	4	yes	complemented
221	D₄⋊C₈	C₂²×C₃₁	1	4	yes	—
222	#322	C₂²×C₃₁	1	2	yes	complemented
223	#322	C₂²×C₃₁	1	2	yes	complemented
224	C₂×C₃₁	—	2	2	no	—
225	C₂×C₃₁	—	4	4	no	—
226	C₂×C₃₁	#2929	1	1	yes	characteristic
227	C₂×C₃₁	C₂×#440	1	1	yes	characteristic
228	C₂×C₃₁	#2955	1	1	yes	characteristic
229	C₂²×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
230	C₂³×C₄	—	2	1	no	—
231	C₂×SD₁₆	C₂×C₄×C₃₁	1	4	yes	—
232	C₂×M₁₆	—	2	1	no	—
233	C₂²×C₈	—	2	1	no	—
234	C₂²×C₈	—	2	2	no	—
235	C₂²×C₈	—	2	2	no	—
236	C₂²×C₈	—	4	4	no	—
237	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
238	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
239	C₄⋊Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic
240	C₄⋊Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic
241	#125	—	2	1	no	—
242	C₂²⋊Q₈	—	2	1	no	—
243	C₂²⋊Q₈	C₂×C₄×C₃₁	1	2	yes	—
244	C₄×Q₈	—	2	1	no	—
245	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	—	2	1	no	—
248	C₄×D₄	C₂×C₄×C₃₁	1	2	yes	—
249	C₄×D₄	C₂³×C₃₁	1	2	yes	—
250	#117	—	2	1	no	—
251	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
252	C₂×C₂²⋊C₄	—	2	1	no	—
253	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
254	#106	C₂×C₄×C₃₁	1	4	yes	—
255	C₄⋊C₈	—	2	2	no	—
256	C₄⋊C₈	—	2	2	no	—
257	C₄⋊C₈	—	2	1	no	—
258	C₄⋊C₈	—	2	1	no	—
259	C₄⋊C₈	—	2	1	no	—
260	C₄⋊C₈	C₂×C₄×C₃₁	1	2	yes	—
261	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
262	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
263	#103	C₂×C₄×C₃₁	1	4	yes	—
264	#102	C₂×C₄×C₃₁	1	4	yes	—
265	C₂²⋊C₈	—	2	1	no	—
266	C₂²⋊C₈	—	2	2	no	—
267	C₂²⋊C₈	—	2	2	no	—
268	C₂²⋊C₈	C₂×C₄×C₃₁	1	2	yes	—
269	#97	—	2	2	no	—
270	C₄×C₈	—	2	2	no	—
271	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
272	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
273	C₄×C₈	C₂³×C₃₁	1	2	yes	—
274	C₄×C₈	C₂³×C₃₁	1	2	yes	—
275	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
276	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
277	C₃₁	#17905	1	1	yes	characteristic, direct product factor, Sylow
278	C₂⁴	—	2	1	no	—
279	C₂×Q₈	—	2	1	no	—
280	C₂×Q₈	C₂²×C₄×C₃₁	1	2	yes	—
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	C₂²×C₄×C₃₁	1	2	yes	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
291	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
292	SD₁₆	—	2	8	no	—
293	M₁₆	—	4	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	4	4	no	—
300	C₂×C₈	—	4	4	no	—
301	C₂×C₈	—	4	2	no	—
302	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
303	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
304	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
305	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
306	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
307	C₄⋊C₄	—	2	1	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
314	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₂²⋊C₄	—	2	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
320	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
321	C₄²	#41×C₃₁	1	1	yes	characteristic
322	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
323	C₂³	—	2	4	no	—
324	C₂³	—	2	2	no	—
325	C₂³	—	4	2	no	—
326	C₂³	—	4	2	no	—
327	C₂³	C₄×D₄×C₃₁	1	1	yes	characteristic
328	Q₈	—	2	4	no	—
329	Q₈	—	4	2	no	—
330	D₄	—	2	4	no	—
331	D₄	—	2	2	no	—
332	D₄	C₃₁×#131	1	4	yes	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
343	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
344	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
345	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
346	C₂×C₄	C₃₁×#137	1	2	yes	—
347	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
348	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
349	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
350	C₈	—	2	4	no	—
351	C₈	—	2	1	no	—
352	C₈	—	2	1	no	—
353	C₈	—	2	1	no	—
354	C₈	—	2	1	no	—
355	C₈	—	4	2	no	—
356	C₈	—	4	2	no	—
357	C₈	—	4	2	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	4	no	—
361	C₂²	—	4	8	no	—
362	C₂²	—	4	2	no	—
363	C₂²	—	4	2	no	—
364	C₂²	C₃₁×#440	1	2	yes	—
365	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	4	2	no	—
370	C₄	—	4	2	no	—
371	C₄	—	4	2	no	—
372	C₄	C₃₁×#440	1	2	yes	—
373	C₄	C₂×C₃₁×#131	1	2	yes	—
374	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
375	C₄	C₂×C₃₁×#137	1	1	yes	characteristic
376	C₂	—	2	2	no	—
377	C₂	—	4	4	no	—
378	C₂	C₃₁×#2929	1	1	yes	characteristic
379	C₂	C₂×C₃₁×#440	1	1	yes	characteristic
380	C₂	C₃₁×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₄²	C₂⁴×C₃₁
socle	C₂²×C₃₁	C₂×C₄×D₄
prime radical	C₂²×D₄×C₃₁	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₂×C₄×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2960	C₂	semidirect
4. C₃₁×#1585	C₂	semidirect
5. C₃₁×SD₁₆⋊C₈	C₂	semidirect
6. C₃₁×#1571	C₂	semidirect
8. C₃₁×#1481	C₂	semidirect
9. C₃₁×#1452	C₂	semidirect
18. C₃₁×#446	C₂²	semidirect
20. C₈×Q₈×C₃₁	C₂²	semidirect
34. C₃₁×#335	C₂²	semidirect
35. C₃₁×Q₈⋊C₈	C₂²	semidirect
37. C₃₁×#322	C₂²	semidirect
38. C₃₁×#322	C₂²	semidirect
132. #17905	C₃₁	direct (N × H)
169. #2960	C₂×C₃₁	semidirect
171. #1585	C₂×C₃₁	semidirect
172. SD₁₆⋊C₈	C₂×C₃₁	semidirect
173. #1571	C₂×C₃₁	semidirect
175. #1481	C₂×C₃₁	semidirect
176. #1452	C₂×C₃₁	semidirect
203. #446	C₂²×C₃₁	semidirect
205. C₈×Q₈	C₂²×C₃₁	semidirect
219. #335	C₂²×C₃₁	semidirect
220. Q₈⋊C₈	C₂²×C₃₁	semidirect
222. #322	C₂²×C₃₁	semidirect
223. #322	C₂²×C₃₁	semidirect
277. C₃₁	#17905	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×#3101	2
C₃₁×#2960	2
C₂×C₈×D₄×C₃₁	2
C₃₁×#1585	2
C₃₁×SD₁₆⋊C₈	2
C₃₁×#1571	2
C₃₁×#1486	2
C₃₁×#1481	2
C₃₁×#1452	2
#17905	31

Subgroups — C31×#17905 #21474664

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#17905 #21474664