Subgroups — C₃₁×#33031 #21489790

Order 7936.

978 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#477	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#460	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2858	C₂	1	1	yes	maximal, characteristic
4	C₄²×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1987	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1982	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#1925	C₂	1	4	yes	maximal, complemented
8	C₃₁×#1880	C₂	1	4	yes	maximal, complemented
9	C₃₁×#1831	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
11	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#124	—	2	2	no	—
14	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
16	C₃₁×#477	—	2	4	no	—
17	C₃₁×#460	—	2	4	no	—
18	C₂×C₃₁×#107	C₂²	1	2	yes	—
19	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×#103	C₂²	1	2	yes	—
22	C₂×C₃₁×#102	C₂²	1	4	yes	—
23	C₂×C₃₁×#102	C₂²	1	2	yes	—
24	C₃₁×#390	—	2	1	no	—
25	C₃₁×#390	—	2	1	no	—
26	C₃₁×#390	C₂²	1	4	yes	—
27	C₄×C₄⋊C₄×C₃₁	—	2	2	no	—
28	C₄×C₄⋊C₄×C₃₁	—	2	1	no	—
29	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
30	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
31	C₄³×C₃₁	—	2	1	no	—
32	C₄³×C₃₁	C₂²	1	1	yes	characteristic
33	C₃₁×#340	C₂²	1	4	yes	—
34	C₃₁×#336	C₂²	1	4	yes	—
35	C₂²×Q₈×C₃₁	—	2	1	no	—
36	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
37	C₂²×D₄×C₃₁	—	2	1	no	—
38	C₂²×D₄×C₃₁	—	2	1	no	—
39	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
40	C₂×SD₁₆×C₃₁	—	2	4	no	—
41	C₂×SD₁₆×C₃₁	—	2	8	no	—
42	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
44	C₃₁×C₄⋊Q₈	—	2	2	no	—
45	C₃₁×C₄⋊Q₈	—	2	2	no	—
46	C₃₁×#127	—	2	2	no	—
47	C₃₁×#127	—	2	2	no	—
48	C₃₁×#124	—	4	8	no	—
49	C₄×Q₈×C₃₁	—	2	4	no	—
50	C₄×Q₈×C₃₁	—	2	4	no	—
51	C₄×Q₈×C₃₁	—	2	2	no	—
52	C₄×Q₈×C₃₁	D₄	1	4	yes	—
53	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
54	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
55	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
56	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
59	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
60	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
61	C₂×C₄²×C₃₁	—	2	2	no	—
62	C₂×C₄²×C₃₁	—	2	1	no	—
63	C₂×C₄²×C₃₁	—	2	1	no	—
64	C₂×C₄²×C₃₁	—	2	2	no	—
65	C₂×C₄²×C₃₁	D₄	1	2	yes	—
66	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
69	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
70	C₃₁×#107	—	2	4	no	—
71	C₃₁×C₄⋊C₈	—	2	2	no	—
72	C₃₁×C₄⋊C₈	—	2	2	no	—
73	C₃₁×#103	—	2	4	no	—
74	C₃₁×#102	—	2	4	no	—
75	C₃₁×#102	—	2	8	no	—
76	C₃₁×#95	—	2	2	no	—
77	C₃₁×#95	—	2	1	no	—
78	C₂⁴×C₃₁	—	2	2	no	—
79	C₂×Q₈×C₃₁	—	2	1	no	—
80	C₂×Q₈×C₃₁	—	2	2	no	—
81	C₂×Q₈×C₃₁	—	4	4	no	—
82	C₂×Q₈×C₃₁	—	4	2	no	—
83	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
84	C₂×Q₈×C₃₁	#41	1	4	yes	—
85	C₂×D₄×C₃₁	—	2	2	no	—
86	C₂×D₄×C₃₁	—	2	4	no	—
87	C₂×D₄×C₃₁	—	2	2	no	—
88	C₂×D₄×C₃₁	—	2	4	no	—
89	C₂×D₄×C₃₁	—	4	4	no	—
90	C₂×D₄×C₃₁	—	4	2	no	—
91	C₂×D₄×C₃₁	—	4	2	no	—
92	C₂×D₄×C₃₁	—	4	2	no	—
93	C₂×D₄×C₃₁	—	4	2	no	—
94	C₂²×C₄×C₃₁	—	2	1	no	—
95	C₂²×C₄×C₃₁	—	2	1	no	—
96	C₂²×C₄×C₃₁	—	2	2	no	—
97	C₂²×C₄×C₃₁	—	2	2	no	—
98	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
103	SD₁₆×C₃₁	—	4	8	no	—
104	C₂×C₈×C₃₁	—	2	2	no	—
105	C₂×C₈×C₃₁	—	2	2	no	—
106	C₂×C₈×C₃₁	—	2	4	no	—
107	C₂×C₈×C₃₁	—	2	4	no	—
108	C₄⋊C₄×C₃₁	—	2	8	no	—
109	C₄⋊C₄×C₃₁	—	2	4	no	—
110	C₄⋊C₄×C₃₁	—	2	1	no	—
111	C₄⋊C₄×C₃₁	—	2	2	no	—
112	C₄⋊C₄×C₃₁	—	2	2	no	—
113	C₄⋊C₄×C₃₁	—	2	2	no	—
114	C₄⋊C₄×C₃₁	—	4	2	no	—
115	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
116	C₄⋊C₄×C₃₁	#41	1	4	yes	—
117	C₂²⋊C₄×C₃₁	—	4	8	no	—
118	C₂²⋊C₄×C₃₁	—	4	8	no	—
119	C₄²×C₃₁	—	2	8	no	—
120	C₄²×C₃₁	—	2	4	no	—
121	C₄²×C₃₁	—	2	2	no	—
122	C₄²×C₃₁	—	2	4	no	—
123	C₄²×C₃₁	—	2	2	no	—
124	C₄²×C₃₁	—	2	2	no	—
125	C₄²×C₃₁	—	2	2	no	—
126	C₄²×C₃₁	—	4	2	no	—
127	C₄²×C₃₁	—	4	4	no	—
128	C₄²×C₃₁	C₂×D₄	1	2	yes	—
129	C₄²×C₃₁	#41	1	2	yes	—
130	#33031	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂³×C₃₁	—	4	2	no	—
132	C₂³×C₃₁	—	4	4	no	—
133	C₂³×C₃₁	—	4	2	no	—
134	C₂³×C₃₁	—	4	4	no	—
135	C₂³×C₃₁	—	4	2	no	—
136	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
137	Q₈×C₃₁	—	2	4	no	—
138	Q₈×C₃₁	—	2	2	no	—
139	Q₈×C₃₁	—	8	4	no	—
140	Q₈×C₃₁	#124	1	4	yes	complemented
141	D₄×C₃₁	—	4	2	no	—
142	D₄×C₃₁	—	4	4	no	—
143	D₄×C₃₁	—	4	2	no	—
144	D₄×C₃₁	—	8	4	no	—
145	D₄×C₃₁	—	8	4	no	—
146	C₂×C₄×C₃₁	—	2	2	no	—
147	C₂×C₄×C₃₁	—	2	2	no	—
148	C₂×C₄×C₃₁	—	2	4	no	—
149	C₂×C₄×C₃₁	—	2	2	no	—
150	C₂×C₄×C₃₁	—	2	2	no	—
151	C₂×C₄×C₃₁	—	2	2	no	—
152	C₂×C₄×C₃₁	—	2	2	no	—
153	C₂×C₄×C₃₁	—	2	4	no	—
154	C₂×C₄×C₃₁	—	2	2	no	—
155	C₂×C₄×C₃₁	—	2	2	no	—
156	C₂×C₄×C₃₁	—	4	2	no	—
157	C₂×C₄×C₃₁	—	4	2	no	—
158	C₂×C₄×C₃₁	—	4	2	no	—
159	C₂×C₄×C₃₁	—	4	2	no	—
160	C₂×C₄×C₃₁	—	4	4	no	—
161	C₂×C₄×C₃₁	#121	1	2	yes	—
162	C₂×C₄×C₃₁	#121	1	2	yes	—
163	C₂×C₄×C₃₁	#135	1	2	yes	—
164	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	4	yes	—
165	C₂×C₄×C₃₁	#137	1	2	yes	—
166	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
168	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
169	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
170	C₈×C₃₁	—	4	2	no	—
171	C₈×C₃₁	—	4	2	no	—
172	C₂×#477	C₂×C₃₁	1	1	yes	characteristic, complemented
173	C₂×#460	C₂×C₃₁	1	1	yes	characteristic
174	#2858	C₂×C₃₁	1	1	yes	characteristic
175	C₄²×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
176	#1987	C₂×C₃₁	1	1	yes	characteristic, complemented
177	#1982	C₂×C₃₁	1	1	yes	characteristic
178	#1925	C₂×C₃₁	1	4	yes	complemented
179	#1880	C₂×C₃₁	1	4	yes	complemented
180	#1831	C₂×C₃₁	1	1	yes	characteristic, complemented
181	C₂²×C₃₁	—	8	2	no	—
182	C₂²×C₃₁	—	8	4	no	—
183	C₂²×C₃₁	—	8	4	no	—
184	C₂²×C₃₁	—	8	2	no	—
185	C₂²×C₃₁	—	8	2	no	—
186	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
187	C₂²×C₃₁	#525	1	2	yes	—
188	C₂²×C₃₁	C₂×#135	1	1	yes	characteristic
189	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
190	C₂²×C₃₁	C₂×#137	1	1	yes	characteristic
191	C₄×C₃₁	—	2	4	no	—
192	C₄×C₃₁	—	2	4	no	—
193	C₄×C₃₁	—	2	2	no	—
194	C₄×C₃₁	—	4	2	no	—
195	C₄×C₃₁	—	4	4	no	—
196	C₄×C₃₁	—	4	2	no	—
197	C₄×C₃₁	—	8	2	no	—
198	C₄×C₃₁	#464	1	4	yes	—
199	C₄×C₃₁	C₂×#124	1	1	yes	characteristic
200	C₄×C₃₁	#529	1	2	yes	—
201	C₄×C₃₁	#532	1	1	yes	characteristic
202	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
203	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
204	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
205	C₂×#124	—	2	2	no	—
206	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
207	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
208	#477	—	2	4	no	—
209	#460	—	2	4	no	—
210	C₂×#107	C₂²×C₃₁	1	2	yes	—
211	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
212	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
213	C₂×#103	C₂²×C₃₁	1	2	yes	—
214	C₂×#102	C₂²×C₃₁	1	4	yes	—
215	C₂×#102	C₂²×C₃₁	1	2	yes	—
216	#390	—	2	1	no	—
217	#390	—	2	1	no	—
218	#390	C₂²×C₃₁	1	4	yes	—
219	C₄×C₄⋊C₄	—	2	2	no	—
220	C₄×C₄⋊C₄	—	2	1	no	—
221	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
222	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
223	C₄³	—	2	1	no	—
224	C₄³	C₂²×C₃₁	1	1	yes	characteristic
225	#340	C₂²×C₃₁	1	4	yes	—
226	#336	C₂²×C₃₁	1	4	yes	—
227	C₂×C₃₁	—	16	2	no	—
228	C₂×C₃₁	#2850	1	1	yes	characteristic
229	C₂×C₃₁	C₂×#464	1	1	yes	characteristic
230	C₂×C₃₁	#3038	1	1	yes	characteristic
231	C₂×C₃₁	#3106	1	2	yes	—
232	C₂×C₃₁	#3112	1	2	yes	—
233	C₂²×Q₈	—	2	1	no	—
234	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
235	C₂²×D₄	—	2	1	no	—
236	C₂²×D₄	—	2	1	no	—
237	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
238	C₂×SD₁₆	—	2	4	no	—
239	C₂×SD₁₆	—	2	8	no	—
240	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
241	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
242	C₄⋊Q₈	—	2	2	no	—
243	C₄⋊Q₈	—	2	2	no	—
244	#127	—	2	2	no	—
245	#127	—	2	2	no	—
246	#124	—	4	8	no	—
247	C₄×Q₈	—	2	4	no	—
248	C₄×Q₈	—	2	4	no	—
249	C₄×Q₈	—	2	2	no	—
250	C₄×Q₈	D₄×C₃₁	1	4	yes	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
257	C₂×C₂²⋊C₄	—	2	4	no	—
258	C₂×C₂²⋊C₄	—	2	4	no	—
259	C₂×C₄²	—	2	2	no	—
260	C₂×C₄²	—	2	1	no	—
261	C₂×C₄²	—	2	1	no	—
262	C₂×C₄²	—	2	2	no	—
263	C₂×C₄²	D₄×C₃₁	1	2	yes	—
264	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
265	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
266	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
267	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
268	#107	—	2	4	no	—
269	C₄⋊C₈	—	2	2	no	—
270	C₄⋊C₈	—	2	2	no	—
271	#103	—	2	4	no	—
272	#102	—	2	4	no	—
273	#102	—	2	8	no	—
274	#95	—	2	2	no	—
275	#95	—	2	1	no	—
276	C₃₁	#33031	1	1	yes	characteristic, direct product factor, Sylow
277	C₂⁴	—	2	2	no	—
278	C₂×Q₈	—	2	1	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	4	4	no	—
281	C₂×Q₈	—	4	2	no	—
282	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
283	C₂×Q₈	#41×C₃₁	1	4	yes	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	4	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	4	no	—
288	C₂×D₄	—	4	4	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
298	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
300	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
301	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
302	SD₁₆	—	4	8	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	4	no	—
306	C₂×C₈	—	2	4	no	—
307	C₄⋊C₄	—	2	8	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
315	C₄⋊C₄	#41×C₃₁	1	4	yes	—
316	C₂²⋊C₄	—	4	8	no	—
317	C₂²⋊C₄	—	4	8	no	—
318	C₄²	—	2	8	no	—
319	C₄²	—	2	4	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	4	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	4	2	no	—
326	C₄²	—	4	4	no	—
327	C₄²	C₂×D₄×C₃₁	1	2	yes	—
328	C₄²	#41×C₃₁	1	2	yes	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	4	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	4	no	—
333	C₂³	—	4	2	no	—
334	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
335	Q₈	—	2	4	no	—
336	Q₈	—	2	2	no	—
337	Q₈	—	8	4	no	—
338	Q₈	C₃₁×#124	1	4	yes	complemented
339	D₄	—	4	2	no	—
340	D₄	—	4	4	no	—
341	D₄	—	4	2	no	—
342	D₄	—	8	4	no	—
343	D₄	—	8	4	no	—
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	2	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	C₃₁×#121	1	2	yes	—
360	C₂×C₄	C₃₁×#121	1	2	yes	—
361	C₂×C₄	C₃₁×#135	1	2	yes	—
362	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	4	yes	—
363	C₂×C₄	C₃₁×#137	1	2	yes	—
364	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
365	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
366	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
367	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
368	C₈	—	4	2	no	—
369	C₈	—	4	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	4	no	—
372	C₂²	—	8	4	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
376	C₂²	C₃₁×#525	1	2	yes	—
377	C₂²	C₂×C₃₁×#135	1	1	yes	characteristic
378	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
379	C₂²	C₂×C₃₁×#137	1	1	yes	characteristic
380	C₄	—	2	4	no	—
381	C₄	—	2	4	no	—
382	C₄	—	2	2	no	—
383	C₄	—	4	2	no	—
384	C₄	—	4	4	no	—
385	C₄	—	4	2	no	—
386	C₄	—	8	2	no	—
387	C₄	C₃₁×#464	1	4	yes	—
388	C₄	C₂×C₃₁×#124	1	1	yes	characteristic
389	C₄	C₃₁×#529	1	2	yes	—
390	C₄	C₃₁×#532	1	1	yes	characteristic
391	C₂	—	16	2	no	—
392	C₂	C₃₁×#2850	1	1	yes	characteristic
393	C₂	C₂×C₃₁×#464	1	1	yes	characteristic
394	C₂	C₃₁×#3038	1	1	yes	characteristic
395	C₂	C₃₁×#3106	1	2	yes	—
396	C₂	C₃₁×#3112	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂×C₃₁×#127	C₂²
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
1. C₂×C₃₁×#477	C₂	semidirect
4. C₄²×Q₈×C₃₁	C₂	semidirect
5. C₃₁×#1987	C₂	semidirect
7. C₃₁×#1925	C₂	semidirect
8. C₃₁×#1880	C₂	semidirect
9. C₃₁×#1831	C₂	semidirect
130. #33031	C₃₁	direct (N × H)
140. Q₈×C₃₁	#124	semidirect
172. C₂×#477	C₂×C₃₁	semidirect
175. C₄²×Q₈	C₂×C₃₁	semidirect
176. #1987	C₂×C₃₁	semidirect
178. #1925	C₂×C₃₁	semidirect
179. #1880	C₂×C₃₁	semidirect
180. #1831	C₂×C₃₁	semidirect
276. C₃₁	#33031	direct (N × H)
338. Q₈	C₃₁×#124	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#477	2
C₂×C₃₁×#460	2
C₃₁×#2858	2
C₄²×Q₈×C₃₁	2
C₃₁×#1987	2
C₃₁×#1982	2
C₃₁×#1925	2
C₃₁×#1880	2
C₃₁×#1831	2
#33031	31

Subgroups — C31×#33031 #21489790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33031 #21489790