Subgroups — C₃₁×#33201 #21489960

Order 7936.

946 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#476	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#474	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2862	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄²×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#1988	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1987	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1949	C₂	1	4	yes	maximal, complemented
8	C₃₁×#1842	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#1804	C₂	1	4	yes	maximal
10	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
14	C₂²×C₄²×C₃₁	—	2	1	no	—
15	C₃₁×#476	—	2	4	no	—
16	C₃₁×#474	—	2	4	no	—
17	C₂×C₃₁×#107	C₂²	1	2	yes	—
18	C₂×C₃₁×#106	C₂²	1	2	yes	—
19	C₂×C₃₁×C₄⋊C₈	C₂²	1	4	yes	—
20	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×#102	C₂²	1	2	yes	—
23	C₂×C₃₁×#102	C₂²	1	2	yes	—
24	C₃₁×#391	—	2	1	no	—
25	C₃₁×#391	—	2	1	no	—
26	C₃₁×#391	—	2	2	no	—
27	C₃₁×#382	C₂²	1	4	yes	—
28	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
30	C₄×C₂²⋊C₄×C₃₁	—	2	1	no	—
31	C₄×C₂²⋊C₄×C₃₁	—	2	2	no	—
32	C₄³×C₃₁	C₂²	1	1	yes	characteristic
33	C₃₁×#340	C₂²	1	4	yes	—
34	C₃₁×#340	C₂²	1	4	yes	—
35	C₂²×Q₈×C₃₁	—	2	1	no	—
36	C₂²×Q₈×C₃₁	—	2	1	no	—
37	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₃₁	—	2	1	no	—
39	C₂³×C₄×C₃₁	—	2	2	no	—
40	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
41	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
42	C₃₁×C₄⋊Q₈	—	2	2	no	—
43	C₃₁×C₄⋊Q₈	—	2	2	no	—
44	C₃₁×C₄⋊Q₈	—	2	2	no	—
45	C₃₁×C₄⋊Q₈	—	2	2	no	—
46	C₄×D₄×C₃₁	—	2	2	no	—
47	C₄×D₄×C₃₁	—	2	4	no	—
48	C₄×D₄×C₃₁	D₄	1	4	yes	—
49	C₄×D₄×C₃₁	Q₈	1	8	yes	complemented
50	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
51	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
52	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
56	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
57	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
58	C₂×C₄²×C₃₁	—	2	2	no	—
59	C₂×C₄²×C₃₁	—	2	1	no	—
60	C₂×C₄²×C₃₁	—	4	4	no	—
61	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₃₁	D₄	1	2	yes	—
64	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
66	C₃₁×#107	—	2	4	no	—
67	C₃₁×#106	—	2	4	no	—
68	C₃₁×C₄⋊C₈	—	2	2	no	—
69	C₃₁×C₄⋊C₈	—	2	2	no	—
70	C₃₁×C₄⋊C₈	—	2	8	no	—
71	C₃₁×#102	—	2	4	no	—
72	C₃₁×#102	—	2	4	no	—
73	C₃₁×#95	—	2	1	no	—
74	C₃₁×#95	—	2	2	no	—
75	C₃₁×#95	—	2	4	no	—
76	C₃₁×#95	—	2	4	no	—
77	C₂⁴×C₃₁	—	2	1	no	—
78	C₂×Q₈×C₃₁	—	4	4	no	—
79	C₂×Q₈×C₃₁	—	4	2	no	—
80	C₂×Q₈×C₃₁	—	4	2	no	—
81	C₂×Q₈×C₃₁	—	4	2	no	—
82	C₂×Q₈×C₃₁	—	4	2	no	—
83	C₂×D₄×C₃₁	—	2	2	no	—
84	C₂×D₄×C₃₁	—	2	1	no	—
85	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
86	C₂×D₄×C₃₁	C₂×Q₈	1	4	yes	—
87	C₂²×C₄×C₃₁	—	2	1	no	—
88	C₂²×C₄×C₃₁	—	2	2	no	—
89	C₂²×C₄×C₃₁	—	2	4	no	—
90	C₂²×C₄×C₃₁	—	2	8	no	—
91	C₂²×C₄×C₃₁	—	2	2	no	—
92	C₂²×C₄×C₃₁	—	2	2	no	—
93	C₂²×C₄×C₃₁	—	4	4	no	—
94	C₂²×C₄×C₃₁	—	4	4	no	—
95	C₂²×C₄×C₃₁	—	4	2	no	—
96	C₂²×C₄×C₃₁	—	4	2	no	—
97	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₃₁	C₂×D₄	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	C₂⁴	1	1	yes	characteristic
102	C₂×C₈×C₃₁	—	2	2	no	—
103	C₂×C₈×C₃₁	—	2	2	no	—
104	C₂×C₈×C₃₁	—	2	4	no	—
105	C₂×C₈×C₃₁	—	2	4	no	—
106	C₄⋊C₄×C₃₁	—	2	1	no	—
107	C₄⋊C₄×C₃₁	—	2	2	no	—
108	C₄⋊C₄×C₃₁	—	2	2	no	—
109	C₄⋊C₄×C₃₁	—	2	2	no	—
110	C₄⋊C₄×C₃₁	—	2	2	no	—
111	C₄⋊C₄×C₃₁	—	2	2	no	—
112	C₄⋊C₄×C₃₁	—	4	2	no	—
113	C₄⋊C₄×C₃₁	—	4	2	no	—
114	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
115	C₄⋊C₄×C₃₁	C₂×Q₈	1	4	yes	—
116	C₂²⋊C₄×C₃₁	—	2	4	no	—
117	C₂²⋊C₄×C₃₁	—	2	8	no	—
118	C₄²×C₃₁	—	2	2	no	—
119	C₄²×C₃₁	—	2	2	no	—
120	C₄²×C₃₁	—	4	2	no	—
121	C₄²×C₃₁	—	4	4	no	—
122	C₄²×C₃₁	—	4	2	no	—
123	C₄²×C₃₁	C₂×D₄	1	2	yes	—
124	C₄²×C₃₁	C₂×Q₈	1	4	yes	—
125	C₄²×C₃₁	#41	1	2	yes	—
126	C₄²×C₃₁	#41	1	4	yes	—
127	#33201	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂³×C₃₁	—	2	2	no	—
129	C₂³×C₃₁	—	2	4	no	—
130	C₂³×C₃₁	—	4	1	no	—
131	C₂³×C₃₁	—	4	1	no	—
132	C₂³×C₃₁	—	4	2	no	—
133	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
134	Q₈×C₃₁	—	8	4	no	—
135	Q₈×C₃₁	—	8	4	no	—
136	D₄×C₃₁	—	2	2	no	—
137	D₄×C₃₁	—	2	4	no	—
138	D₄×C₃₁	C₄⋊Q₈	1	4	yes	—
139	C₂×C₄×C₃₁	—	2	2	no	—
140	C₂×C₄×C₃₁	—	2	2	no	—
141	C₂×C₄×C₃₁	—	2	2	no	—
142	C₂×C₄×C₃₁	—	2	2	no	—
143	C₂×C₄×C₃₁	—	2	2	no	—
144	C₂×C₄×C₃₁	—	2	2	no	—
145	C₂×C₄×C₃₁	—	2	4	no	—
146	C₂×C₄×C₃₁	—	4	16	no	—
147	C₂×C₄×C₃₁	—	4	1	no	—
148	C₂×C₄×C₃₁	—	4	2	no	—
149	C₂×C₄×C₃₁	—	4	1	no	—
150	C₂×C₄×C₃₁	—	4	2	no	—
151	C₂×C₄×C₃₁	—	4	8	no	—
152	C₂×C₄×C₃₁	—	4	2	no	—
153	C₂×C₄×C₃₁	—	4	2	no	—
154	C₂×C₄×C₃₁	—	4	2	no	—
155	C₂×C₄×C₃₁	—	4	2	no	—
156	C₂×C₄×C₃₁	—	4	4	no	—
157	C₂×C₄×C₃₁	#121	1	2	yes	—
158	C₂×C₄×C₃₁	#121	1	2	yes	—
159	C₂×C₄×C₃₁	C₂²⋊Q₈	1	4	yes	—
160	C₂×C₄×C₃₁	C₂²⋊Q₈	1	4	yes	—
161	C₂×C₄×C₃₁	#135	1	2	yes	—
162	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
163	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
165	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
166	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
167	C₈×C₃₁	—	4	2	no	—
168	C₈×C₃₁	—	4	2	no	—
169	C₂×#476	C₂×C₃₁	1	1	yes	characteristic
170	C₂×#474	C₂×C₃₁	1	1	yes	characteristic
171	#2862	C₂×C₃₁	1	1	yes	characteristic, complemented
172	C₄²×D₄	C₂×C₃₁	1	1	yes	characteristic
173	#1988	C₂×C₃₁	1	1	yes	characteristic, complemented
174	#1987	C₂×C₃₁	1	1	yes	characteristic, complemented
175	#1949	C₂×C₃₁	1	4	yes	complemented
176	#1842	C₂×C₃₁	1	1	yes	characteristic, complemented
177	#1804	C₂×C₃₁	1	4	yes	—
178	C₂²×C₃₁	—	2	4	no	—
179	C₂²×C₃₁	—	4	4	no	—
180	C₂²×C₃₁	—	4	4	no	—
181	C₂²×C₃₁	—	4	2	no	—
182	C₂²×C₃₁	—	4	2	no	—
183	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
184	C₂²×C₃₁	C₂×C₂²⋊Q₈	1	2	yes	—
185	C₂²×C₃₁	C₂×#135	1	1	yes	characteristic
186	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₂²×C₃₁	#575	1	2	yes	—
188	C₄×C₃₁	—	2	4	no	—
189	C₄×C₃₁	—	2	4	no	—
190	C₄×C₃₁	—	2	2	no	—
191	C₄×C₃₁	—	4	4	no	—
192	C₄×C₃₁	—	4	2	no	—
193	C₄×C₃₁	—	8	2	no	—
194	C₄×C₃₁	—	8	2	no	—
195	C₄×C₃₁	#463	1	4	yes	—
196	C₄×C₃₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
197	C₄×C₃₁	#532	1	1	yes	characteristic
198	C₄×C₃₁	#533	1	2	yes	—
199	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
200	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
201	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
202	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
203	C₂²×C₄²	—	2	1	no	—
204	#476	—	2	4	no	—
205	#474	—	2	4	no	—
206	C₂×#107	C₂²×C₃₁	1	2	yes	—
207	C₂×#106	C₂²×C₃₁	1	2	yes	—
208	C₂×C₄⋊C₈	C₂²×C₃₁	1	4	yes	—
209	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
210	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
211	C₂×#102	C₂²×C₃₁	1	2	yes	—
212	C₂×#102	C₂²×C₃₁	1	2	yes	—
213	#391	—	2	1	no	—
214	#391	—	2	1	no	—
215	#391	—	2	2	no	—
216	#382	C₂²×C₃₁	1	4	yes	—
217	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
218	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
219	C₄×C₂²⋊C₄	—	2	1	no	—
220	C₄×C₂²⋊C₄	—	2	2	no	—
221	C₄³	C₂²×C₃₁	1	1	yes	characteristic
222	#340	C₂²×C₃₁	1	4	yes	—
223	#340	C₂²×C₃₁	1	4	yes	—
224	C₂×C₃₁	—	4	4	no	—
225	C₂×C₃₁	#2857	1	1	yes	characteristic
226	C₂×C₃₁	C₂×#463	1	1	yes	characteristic
227	C₂×C₃₁	#3040	1	1	yes	characteristic
228	C₂×C₃₁	#3076	1	2	yes	—
229	C₂×C₃₁	#3077	1	2	yes	—
230	C₂²×Q₈	—	2	1	no	—
231	C₂²×Q₈	—	2	1	no	—
232	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
233	C₂³×C₄	—	2	1	no	—
234	C₂³×C₄	—	2	2	no	—
235	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
236	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
237	C₄⋊Q₈	—	2	2	no	—
238	C₄⋊Q₈	—	2	2	no	—
239	C₄⋊Q₈	—	2	2	no	—
240	C₄⋊Q₈	—	2	2	no	—
241	C₄×D₄	—	2	2	no	—
242	C₄×D₄	—	2	4	no	—
243	C₄×D₄	D₄×C₃₁	1	4	yes	—
244	C₄×D₄	Q₈×C₃₁	1	8	yes	complemented
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
248	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
249	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
251	C₂×C₂²⋊C₄	—	2	1	no	—
252	C₂×C₂²⋊C₄	—	2	2	no	—
253	C₂×C₄²	—	2	2	no	—
254	C₂×C₄²	—	2	1	no	—
255	C₂×C₄²	—	4	4	no	—
256	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
257	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
258	C₂×C₄²	D₄×C₃₁	1	2	yes	—
259	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
260	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
261	#107	—	2	4	no	—
262	#106	—	2	4	no	—
263	C₄⋊C₈	—	2	2	no	—
264	C₄⋊C₈	—	2	2	no	—
265	C₄⋊C₈	—	2	8	no	—
266	#102	—	2	4	no	—
267	#102	—	2	4	no	—
268	#95	—	2	1	no	—
269	#95	—	2	2	no	—
270	#95	—	2	4	no	—
271	#95	—	2	4	no	—
272	C₃₁	#33201	1	1	yes	characteristic, direct product factor, Sylow
273	C₂⁴	—	2	1	no	—
274	C₂×Q₈	—	4	4	no	—
275	C₂×Q₈	—	4	2	no	—
276	C₂×Q₈	—	4	2	no	—
277	C₂×Q₈	—	4	2	no	—
278	C₂×Q₈	—	4	2	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	1	no	—
281	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
282	C₂×D₄	C₂×Q₈×C₃₁	1	4	yes	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	8	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	4	4	no	—
290	C₂²×C₄	—	4	4	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
294	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
295	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
296	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
297	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	4	no	—
301	C₂×C₈	—	2	4	no	—
302	C₄⋊C₄	—	2	1	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	4	2	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
311	C₄⋊C₄	C₂×Q₈×C₃₁	1	4	yes	—
312	C₂²⋊C₄	—	2	4	no	—
313	C₂²⋊C₄	—	2	8	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	4	2	no	—
317	C₄²	—	4	4	no	—
318	C₄²	—	4	2	no	—
319	C₄²	C₂×D₄×C₃₁	1	2	yes	—
320	C₄²	C₂×Q₈×C₃₁	1	4	yes	—
321	C₄²	#41×C₃₁	1	2	yes	—
322	C₄²	#41×C₃₁	1	4	yes	—
323	C₂³	—	2	2	no	—
324	C₂³	—	2	4	no	—
325	C₂³	—	4	1	no	—
326	C₂³	—	4	1	no	—
327	C₂³	—	4	2	no	—
328	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
329	Q₈	—	8	4	no	—
330	Q₈	—	8	4	no	—
331	D₄	—	2	2	no	—
332	D₄	—	2	4	no	—
333	D₄	C₃₁×C₄⋊Q₈	1	4	yes	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	4	16	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	8	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	C₃₁×#121	1	2	yes	—
353	C₂×C₄	C₃₁×#121	1	2	yes	—
354	C₂×C₄	C₃₁×C₂²⋊Q₈	1	4	yes	—
355	C₂×C₄	C₃₁×C₂²⋊Q₈	1	4	yes	—
356	C₂×C₄	C₃₁×#135	1	2	yes	—
357	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
358	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
359	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
360	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
361	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
362	C₈	—	4	2	no	—
363	C₈	—	4	2	no	—
364	C₂²	—	2	4	no	—
365	C₂²	—	4	4	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
370	C₂²	C₂×C₃₁×C₂²⋊Q₈	1	2	yes	—
371	C₂²	C₂×C₃₁×#135	1	1	yes	characteristic
372	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
373	C₂²	C₃₁×#575	1	2	yes	—
374	C₄	—	2	4	no	—
375	C₄	—	2	4	no	—
376	C₄	—	2	2	no	—
377	C₄	—	4	4	no	—
378	C₄	—	4	2	no	—
379	C₄	—	8	2	no	—
380	C₄	—	8	2	no	—
381	C₄	C₃₁×#463	1	4	yes	—
382	C₄	C₂×C₃₁×C₄⋊Q₈	1	1	yes	characteristic
383	C₄	C₃₁×#532	1	1	yes	characteristic
384	C₄	C₃₁×#533	1	2	yes	—
385	C₂	—	4	4	no	—
386	C₂	C₃₁×#2857	1	1	yes	characteristic
387	C₂	C₂×C₃₁×#463	1	1	yes	characteristic
388	C₂	C₃₁×#3040	1	1	yes	characteristic
389	C₂	C₃₁×#3076	1	2	yes	—
390	C₂	C₃₁×#3077	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂²×D₄×C₃₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₄³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃₁×#2862	C₂	semidirect
5. C₃₁×#1988	C₂	semidirect
6. C₃₁×#1987	C₂	semidirect
7. C₃₁×#1949	C₂	semidirect
8. C₃₁×#1842	C₂	semidirect
49. C₄×D₄×C₃₁	Q₈	semidirect
127. #33201	C₃₁	direct (N × H)
171. #2862	C₂×C₃₁	semidirect
173. #1988	C₂×C₃₁	semidirect
174. #1987	C₂×C₃₁	semidirect
175. #1949	C₂×C₃₁	semidirect
176. #1842	C₂×C₃₁	semidirect
244. C₄×D₄	Q₈×C₃₁	semidirect
272. C₃₁	#33201	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#476	2
C₂×C₃₁×#474	2
C₃₁×#2862	2
C₄²×D₄×C₃₁	2
C₃₁×#1988	2
C₃₁×#1987	2
C₃₁×#1949	2
C₃₁×#1842	2
C₃₁×#1804	2
#33201	31

Subgroups — C31×#33201 #21489960

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33201 #21489960