Subgroups — C₃₁×#25936 #21482695

Order 7936.

1034 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈²×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#487	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₁×#462	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2568	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#2024	C₂	1	4	yes	maximal
6	C₃₁×#1987	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#1984	C₂	1	1	yes	maximal, characteristic
8	C₃₁×#1878	C₂	1	4	yes	maximal
9	C₄×C₃₁×#103	C₂	1	1	yes	maximal, characteristic
10	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	—
11	Q₈²×C₃₁	—	2	4	no	—
12	Q₈²×C₃₁	—	2	4	no	—
13	C₂×C₃₁×C₄⋊Q₈	—	2	2	no	—
14	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
15	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₃₁	—	2	1	no	—
19	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
22	C₃₁×#487	—	2	4	no	—
23	C₃₁×#462	—	2	4	no	—
24	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#103	C₂²	1	4	yes	—
26	C₂×C₃₁×#103	C₂²	1	2	yes	—
27	C₂×C₃₁×#103	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
29	C₃₁×#400	—	2	2	no	—
30	C₃₁×#391	—	2	1	no	—
31	C₃₁×#391	C₂²	1	4	yes	—
32	C₃₁×#382	—	2	1	no	—
33	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
34	C₃₁×#340	C₂²	1	4	yes	—
35	C₃₁×#340	C₂²	1	2	yes	—
36	C₃₁×#336	C₂²	1	4	yes	—
37	C₂²×Q₈×C₃₁	—	2	2	no	—
38	C₂²×Q₈×C₃₁	—	2	1	no	—
39	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
40	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
41	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
42	C₂×Q₁₆×C₃₁	—	2	4	no	—
43	C₂×Q₁₆×C₃₁	—	2	8	no	—
44	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
45	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
46	C₃₁×C₄⋊Q₈	—	2	16	no	—
47	C₃₁×C₄⋊Q₈	—	2	8	no	—
48	C₃₁×C₄⋊Q₈	—	2	4	no	—
49	C₃₁×C₄⋊Q₈	—	2	4	no	—
50	C₃₁×C₄⋊Q₈	—	2	2	no	—
51	C₃₁×C₄⋊Q₈	—	2	2	no	—
52	C₃₁×C₄⋊Q₈	—	2	2	no	—
53	C₃₁×C₄⋊Q₈	D₄	1	4	yes	—
54	C₄×Q₈×C₃₁	—	2	8	no	—
55	C₄×Q₈×C₃₁	—	2	4	no	—
56	C₄×Q₈×C₃₁	—	2	4	no	—
57	C₄×Q₈×C₃₁	—	2	2	no	—
58	C₄×Q₈×C₃₁	—	2	2	no	—
59	C₄×Q₈×C₃₁	—	2	2	no	—
60	C₄×Q₈×C₃₁	D₄	1	4	yes	—
61	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
64	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
68	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₃₁	—	2	2	no	—
73	C₂×C₄²×C₃₁	—	2	1	no	—
74	C₂×C₄²×C₃₁	—	2	1	no	—
75	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
76	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
77	C₃₁×C₄⋊C₈	—	2	2	no	—
78	C₃₁×#103	—	2	4	no	—
79	C₃₁×#103	—	2	4	no	—
80	C₃₁×#103	—	2	8	no	—
81	C₄×C₈×C₃₁	—	2	2	no	—
82	C₃₁×#95	—	2	1	no	—
83	C₃₁×#95	—	2	4	no	—
84	C₃₁×#95	—	2	4	no	—
85	C₂×Q₈×C₃₁	—	2	8	no	—
86	C₂×Q₈×C₃₁	—	2	2	no	—
87	C₂×Q₈×C₃₁	—	2	4	no	—
88	C₂×Q₈×C₃₁	—	2	2	no	—
89	C₂×Q₈×C₃₁	—	2	1	no	—
90	C₂×Q₈×C₃₁	—	2	2	no	—
91	C₂×Q₈×C₃₁	—	2	2	no	—
92	C₂×Q₈×C₃₁	—	2	2	no	—
93	C₂×Q₈×C₃₁	—	2	4	no	—
94	C₂×Q₈×C₃₁	—	2	4	no	—
95	C₂×Q₈×C₃₁	—	8	2	no	—
96	C₂×Q₈×C₃₁	—	8	4	no	—
97	C₂×Q₈×C₃₁	Q₁₆	1	4	yes	complemented
98	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
99	C₂×Q₈×C₃₁	#41	1	4	yes	—
100	C₂²×C₄×C₃₁	—	2	1	no	—
101	C₂²×C₄×C₃₁	—	2	2	no	—
102	C₂²×C₄×C₃₁	—	2	1	no	—
103	C₂²×C₄×C₃₁	—	2	2	no	—
104	C₂²×C₄×C₃₁	—	2	2	no	—
105	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
110	Q₁₆×C₃₁	—	4	8	no	—
111	C₂×C₈×C₃₁	—	2	2	no	—
112	C₂×C₈×C₃₁	—	2	2	no	—
113	C₂×C₈×C₃₁	—	2	2	no	—
114	C₂×C₈×C₃₁	—	2	4	no	—
115	C₂×C₈×C₃₁	—	2	2	no	—
116	C₄⋊C₄×C₃₁	—	2	8	no	—
117	C₄⋊C₄×C₃₁	—	2	8	no	—
118	C₄⋊C₄×C₃₁	—	2	4	no	—
119	C₄⋊C₄×C₃₁	—	2	4	no	—
120	C₄⋊C₄×C₃₁	—	2	4	no	—
121	C₄⋊C₄×C₃₁	—	2	2	no	—
122	C₄⋊C₄×C₃₁	—	2	2	no	—
123	C₄⋊C₄×C₃₁	—	2	1	no	—
124	C₄⋊C₄×C₃₁	—	2	2	no	—
125	C₄⋊C₄×C₃₁	—	2	2	no	—
126	C₄⋊C₄×C₃₁	—	4	2	no	—
127	C₄⋊C₄×C₃₁	—	4	2	no	—
128	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
129	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
130	C₄²×C₃₁	—	2	8	no	—
131	C₄²×C₃₁	—	2	4	no	—
132	C₄²×C₃₁	—	2	2	no	—
133	C₄²×C₃₁	—	2	2	no	—
134	C₄²×C₃₁	—	4	2	no	—
135	C₄²×C₃₁	C₂×D₄	1	2	yes	—
136	C₄²×C₃₁	C₂×D₄	1	2	yes	—
137	#25936	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
139	Q₈×C₃₁	—	2	2	no	—
140	Q₈×C₃₁	—	2	4	no	—
141	Q₈×C₃₁	—	2	8	no	—
142	Q₈×C₃₁	—	4	2	no	—
143	Q₈×C₃₁	—	4	2	no	—
144	Q₈×C₃₁	—	4	4	no	—
145	Q₈×C₃₁	—	8	4	no	—
146	Q₈×C₃₁	—	8	8	no	—
147	Q₈×C₃₁	#124	1	4	yes	—
148	C₂×C₄×C₃₁	—	2	2	no	—
149	C₂×C₄×C₃₁	—	2	2	no	—
150	C₂×C₄×C₃₁	—	2	4	no	—
151	C₂×C₄×C₃₁	—	2	2	no	—
152	C₂×C₄×C₃₁	—	2	2	no	—
153	C₂×C₄×C₃₁	—	2	2	no	—
154	C₂×C₄×C₃₁	—	2	4	no	—
155	C₂×C₄×C₃₁	—	2	2	no	—
156	C₂×C₄×C₃₁	—	2	4	no	—
157	C₂×C₄×C₃₁	—	4	4	no	—
158	C₂×C₄×C₃₁	—	4	2	no	—
159	C₂×C₄×C₃₁	—	4	2	no	—
160	C₂×C₄×C₃₁	—	4	2	no	—
161	C₂×C₄×C₃₁	—	4	4	no	—
162	C₂×C₄×C₃₁	—	4	2	no	—
163	C₂×C₄×C₃₁	—	4	2	no	—
164	C₂×C₄×C₃₁	#120	1	2	yes	—
165	C₂×C₄×C₃₁	#120	1	2	yes	—
166	C₂×C₄×C₃₁	C₂×Q₁₆	1	4	yes	—
167	C₂×C₄×C₃₁	C₂×Q₁₆	1	2	yes	—
168	C₂×C₄×C₃₁	#137	1	2	yes	—
169	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
172	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
173	C₈×C₃₁	—	4	2	no	—
174	C₈×C₃₁	—	4	2	no	—
175	C₂×Q₈²	C₂×C₃₁	1	1	yes	characteristic
176	C₂×#487	C₂×C₃₁	1	1	yes	characteristic
177	C₂×#462	C₂×C₃₁	1	1	yes	characteristic
178	#2568	C₂×C₃₁	1	1	yes	characteristic
179	#2024	C₂×C₃₁	1	4	yes	—
180	#1987	C₂×C₃₁	1	1	yes	characteristic
181	#1984	C₂×C₃₁	1	1	yes	characteristic
182	#1878	C₂×C₃₁	1	4	yes	—
183	C₄×#103	C₂×C₃₁	1	1	yes	characteristic
184	C₂²×C₃₁	C₂×#120	1	1	yes	characteristic
185	C₂²×C₃₁	#548	1	2	yes	—
186	C₂²×C₃₁	C₂²×Q₁₆	1	1	yes	characteristic
187	C₂²×C₃₁	C₂×#137	1	1	yes	characteristic
188	C₂²×C₃₁	#577	1	2	yes	—
189	C₄×C₃₁	—	2	4	no	—
190	C₄×C₃₁	—	2	4	no	—
191	C₄×C₃₁	—	2	2	no	—
192	C₄×C₃₁	—	4	2	no	—
193	C₄×C₃₁	—	4	4	no	—
194	C₄×C₃₁	—	4	2	no	—
195	C₄×C₃₁	—	8	2	no	—
196	C₄×C₃₁	—	8	2	no	—
197	C₄×C₃₁	#451	1	4	yes	—
198	C₄×C₃₁	C₂×#124	1	1	yes	characteristic
199	C₄×C₃₁	#536	1	1	yes	characteristic
200	C₄×C₃₁	#548	1	2	yes	—
201	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	—
202	Q₈²	—	2	4	no	—
203	Q₈²	—	2	4	no	—
204	C₂×C₄⋊Q₈	—	2	1	no	—
205	C₂×C₄⋊Q₈	—	2	2	no	—
206	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
207	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
208	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
209	C₂×C₄×Q₈	—	2	1	no	—
210	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
211	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
212	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
213	#487	—	2	4	no	—
214	#462	—	2	4	no	—
215	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
216	C₂×#103	C₂²×C₃₁	1	4	yes	—
217	C₂×#103	C₂²×C₃₁	1	2	yes	—
218	C₂×#103	C₂²×C₃₁	1	2	yes	—
219	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
220	#400	—	2	2	no	—
221	#391	—	2	1	no	—
222	#391	C₂²×C₃₁	1	4	yes	—
223	#382	—	2	1	no	—
224	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
225	#340	C₂²×C₃₁	1	4	yes	—
226	#340	C₂²×C₃₁	1	2	yes	—
227	#336	C₂²×C₃₁	1	4	yes	—
228	C₂×C₃₁	#2436	1	1	yes	characteristic
229	C₂×C₃₁	C₂×#451	1	1	yes	characteristic
230	C₂×C₃₁	#3009	1	1	yes	characteristic
231	C₂×C₃₁	#3363	1	2	yes	—
232	C₂×C₃₁	#3369	1	2	yes	—
233	C₂²×Q₈	—	2	2	no	—
234	C₂²×Q₈	—	2	1	no	—
235	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
236	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
237	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
238	C₂×Q₁₆	—	2	4	no	—
239	C₂×Q₁₆	—	2	8	no	—
240	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
241	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
242	C₄⋊Q₈	—	2	16	no	—
243	C₄⋊Q₈	—	2	8	no	—
244	C₄⋊Q₈	—	2	4	no	—
245	C₄⋊Q₈	—	2	4	no	—
246	C₄⋊Q₈	—	2	2	no	—
247	C₄⋊Q₈	—	2	2	no	—
248	C₄⋊Q₈	—	2	2	no	—
249	C₄⋊Q₈	D₄×C₃₁	1	4	yes	—
250	C₄×Q₈	—	2	8	no	—
251	C₄×Q₈	—	2	4	no	—
252	C₄×Q₈	—	2	4	no	—
253	C₄×Q₈	—	2	2	no	—
254	C₄×Q₈	—	2	2	no	—
255	C₄×Q₈	—	2	2	no	—
256	C₄×Q₈	D₄×C₃₁	1	4	yes	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
264	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
265	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
266	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
267	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
268	C₂×C₄²	—	2	2	no	—
269	C₂×C₄²	—	2	1	no	—
270	C₂×C₄²	—	2	1	no	—
271	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
272	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
273	C₄⋊C₈	—	2	2	no	—
274	#103	—	2	4	no	—
275	#103	—	2	4	no	—
276	#103	—	2	8	no	—
277	C₄×C₈	—	2	2	no	—
278	#95	—	2	1	no	—
279	#95	—	2	4	no	—
280	#95	—	2	4	no	—
281	C₃₁	#25936	1	1	yes	characteristic, direct product factor, Sylow
282	C₂×Q₈	—	2	8	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	2	4	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	1	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	4	no	—
291	C₂×Q₈	—	2	4	no	—
292	C₂×Q₈	—	8	2	no	—
293	C₂×Q₈	—	8	4	no	—
294	C₂×Q₈	Q₁₆×C₃₁	1	4	yes	complemented
295	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
296	C₂×Q₈	#41×C₃₁	1	4	yes	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
306	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
307	Q₁₆	—	4	8	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	4	no	—
312	C₂×C₈	—	2	2	no	—
313	C₄⋊C₄	—	2	8	no	—
314	C₄⋊C₄	—	2	8	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
326	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
327	C₄²	—	2	8	no	—
328	C₄²	—	2	4	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	4	2	no	—
332	C₄²	C₂×D₄×C₃₁	1	2	yes	—
333	C₄²	C₂×D₄×C₃₁	1	2	yes	—
334	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
335	Q₈	—	2	8	no	—
336	Q₈	—	2	2	no	—
337	Q₈	—	2	4	no	—
338	Q₈	—	4	2	no	—
339	Q₈	—	4	2	no	—
340	Q₈	—	4	4	no	—
341	Q₈	—	8	4	no	—
342	Q₈	—	8	8	no	—
343	Q₈	C₃₁×#124	1	4	yes	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	C₃₁×#120	1	2	yes	—
361	C₂×C₄	C₃₁×#120	1	2	yes	—
362	C₂×C₄	C₂×Q₁₆×C₃₁	1	4	yes	—
363	C₂×C₄	C₂×Q₁₆×C₃₁	1	2	yes	—
364	C₂×C₄	C₃₁×#137	1	2	yes	—
365	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
366	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
367	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
368	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
369	C₈	—	4	2	no	—
370	C₈	—	4	2	no	—
371	C₂²	C₂×C₃₁×#120	1	1	yes	characteristic
372	C₂²	C₃₁×#548	1	2	yes	—
373	C₂²	C₂²×Q₁₆×C₃₁	1	1	yes	characteristic
374	C₂²	C₂×C₃₁×#137	1	1	yes	characteristic
375	C₂²	C₃₁×#577	1	2	yes	—
376	C₄	—	2	4	no	—
377	C₄	—	2	4	no	—
378	C₄	—	2	2	no	—
379	C₄	—	4	2	no	—
380	C₄	—	4	4	no	—
381	C₄	—	4	2	no	—
382	C₄	—	8	2	no	—
383	C₄	—	8	2	no	—
384	C₄	C₃₁×#451	1	4	yes	—
385	C₄	C₂×C₃₁×#124	1	1	yes	characteristic
386	C₄	C₃₁×#536	1	1	yes	characteristic
387	C₄	C₃₁×#548	1	2	yes	—
388	C₂	C₃₁×#2436	1	1	yes	characteristic
389	C₂	C₂×C₃₁×#451	1	1	yes	characteristic
390	C₂	C₃₁×#3009	1	1	yes	characteristic
391	C₂	C₃₁×#3363	1	2	yes	—
392	C₂	C₃₁×#3369	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂×C₄×Q₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
97. C₂×Q₈×C₃₁	Q₁₆	semidirect
137. #25936	C₃₁	direct (N × H)
281. C₃₁	#25936	direct (N × H)
294. C₂×Q₈	Q₁₆×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈²×C₃₁	2
C₂×C₃₁×#487	2
C₂×C₃₁×#462	2
C₃₁×#2568	2
C₃₁×#2024	2
C₃₁×#1987	2
C₃₁×#1984	2
C₃₁×#1878	2
C₄×C₃₁×#103	2
#25936	31

Subgroups — C31×#25936 #21482695

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#25936 #21482695