Subgroups — C₂×C₃₁×#1682 #21475880

Order 7936.

754 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×#486	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#462	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁×#460	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1682	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃₁×#335	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃₁×#332	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#331	C₂	1	1	yes	maximal, characteristic
9	C₂²×Q₁₆×C₃₁	—	2	1	no	—
10	C₂²×SD₁₆×C₃₁	—	2	1	no	—
11	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
14	C₃₁×#486	—	2	2	no	—
15	C₃₁×#486	C₂²	1	4	yes	—
16	C₃₁×#462	—	2	2	no	—
17	C₃₁×#462	C₂²	1	4	yes	complemented
18	C₃₁×#460	—	2	2	no	—
19	C₃₁×#460	C₂²	1	4	yes	—
20	C₈×Q₈×C₃₁	—	2	2	no	—
21	C₈×Q₈×C₃₁	C₂²	1	4	yes	complemented
22	C₂×C₃₁×C₄⋊C₈	—	2	1	no	—
23	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#103	—	2	1	no	—
27	C₂×C₃₁×#102	—	2	1	no	—
28	C₂×C₃₁×#102	—	2	1	no	—
29	C₂×C₃₁×#102	—	2	1	no	—
30	C₂×C₄×C₈×C₃₁	—	2	1	no	—
31	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
32	C₃₁×#335	C₂²	1	4	yes	complemented
33	C₃₁×#332	C₂²	1	4	yes	complemented
34	C₃₁×#331	C₂²	1	4	yes	—
35	C₂²×Q₈×C₃₁	—	2	1	no	—
36	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
37	C₂²×D₄×C₃₁	—	2	1	no	—
38	C₂²×D₄×C₃₁	—	2	1	no	—
39	C₂²×D₄×C₃₁	—	2	1	no	—
40	C₂×Q₁₆×C₃₁	—	2	4	no	—
41	C₂×Q₁₆×C₃₁	—	4	4	no	—
42	C₂×SD₁₆×C₃₁	—	2	4	no	—
43	C₂×SD₁₆×C₃₁	—	4	4	no	—
44	C₂²×C₈×C₃₁	—	2	1	no	—
45	C₂²×C₈×C₃₁	—	2	1	no	—
46	C₂²×C₈×C₃₁	—	2	1	no	—
47	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
48	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
49	C₃₁×C₄⋊Q₈	—	2	1	no	—
50	C₃₁×C₄⋊Q₈	—	2	1	no	—
51	C₃₁×C₄⋊Q₈	—	2	1	no	—
52	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
53	C₃₁×#127	—	2	1	no	—
54	C₃₁×#127	—	2	1	no	—
55	C₃₁×#127	—	2	1	no	—
56	C₃₁×#127	C₂³	1	2	yes	—
57	C₄×Q₈×C₃₁	—	2	1	no	—
58	C₄×Q₈×C₃₁	—	2	1	no	—
59	C₄×Q₈×C₃₁	D₄	1	2	yes	—
60	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₃₁	—	2	1	no	—
66	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
67	C₃₁×C₄⋊C₈	—	2	4	no	—
68	C₃₁×C₄⋊C₈	—	2	1	no	—
69	C₃₁×C₄⋊C₈	—	2	1	no	—
70	C₃₁×C₄⋊C₈	—	2	1	no	—
71	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
72	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
73	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
74	C₃₁×#103	—	2	4	no	—
75	C₃₁×#102	—	2	4	no	—
76	C₃₁×#102	—	2	4	no	—
77	C₃₁×#102	—	2	4	no	—
78	C₄×C₈×C₃₁	—	2	4	no	—
79	C₄×C₈×C₃₁	D₄	1	2	yes	—
80	C₄×C₈×C₃₁	C₂³	1	2	yes	—
81	C₂⁴×C₃₁	—	4	1	no	—
82	C₂×Q₈×C₃₁	—	2	1	no	—
83	C₂×Q₈×C₃₁	—	2	2	no	—
84	C₂×Q₈×C₃₁	—	2	2	no	—
85	C₂×Q₈×C₃₁	—	4	1	no	—
86	C₂×Q₈×C₃₁	—	4	2	no	—
87	C₂×Q₈×C₃₁	—	4	2	no	—
88	C₂×Q₈×C₃₁	D₈	1	4	yes	—
89	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
90	C₂×D₄×C₃₁	—	2	2	no	—
91	C₂×D₄×C₃₁	—	2	2	no	—
92	C₂×D₄×C₃₁	—	2	2	no	—
93	C₂×D₄×C₃₁	—	4	1	no	—
94	C₂×D₄×C₃₁	—	4	1	no	—
95	C₂×D₄×C₃₁	—	4	1	no	—
96	C₂×D₄×C₃₁	—	4	2	no	—
97	C₂×D₄×C₃₁	—	4	2	no	—
98	C₂×D₄×C₃₁	—	4	2	no	—
99	C₂×D₄×C₃₁	—	4	2	no	—
100	C₂×D₄×C₃₁	—	8	2	no	—
101	C₂²×C₄×C₃₁	—	2	1	no	—
102	C₂²×C₄×C₃₁	—	2	1	no	—
103	C₂²×C₄×C₃₁	—	4	1	no	—
104	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
107	Q₁₆×C₃₁	—	4	8	no	—
108	SD₁₆×C₃₁	—	4	8	no	—
109	C₂×C₈×C₃₁	—	2	2	no	—
110	C₂×C₈×C₃₁	—	2	2	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	—	4	2	no	—
115	C₂×C₈×C₃₁	—	4	2	no	—
116	C₂×C₈×C₃₁	—	4	2	no	—
117	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
119	C₄⋊C₄×C₃₁	—	2	2	no	—
120	C₄⋊C₄×C₃₁	—	2	1	no	—
121	C₄⋊C₄×C₃₁	—	2	2	no	—
122	C₄⋊C₄×C₃₁	—	2	2	no	—
123	C₄⋊C₄×C₃₁	—	2	2	no	—
124	C₄⋊C₄×C₃₁	—	4	1	no	—
125	C₄⋊C₄×C₃₁	—	4	1	no	—
126	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
127	C₄²×C₃₁	—	2	2	no	—
128	C₄²×C₃₁	—	2	2	no	—
129	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₃₁	#41	1	1	yes	characteristic
132	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
133	C₂×#1682	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂³×C₃₁	—	4	2	no	—
135	C₂³×C₃₁	—	8	2	no	—
136	C₂³×C₃₁	—	8	2	no	—
137	C₂³×C₃₁	—	8	2	no	—
138	C₂³×C₃₁	#121	1	1	yes	characteristic
139	Q₈×C₃₁	—	2	2	no	—
140	Q₈×C₃₁	—	2	4	no	—
141	Q₈×C₃₁	—	4	2	no	—
142	Q₈×C₃₁	—	4	2	no	—
143	Q₈×C₃₁	—	8	2	no	—
144	Q₈×C₃₁	C₂×D₈	1	4	yes	—
145	D₄×C₃₁	—	4	2	no	—
146	D₄×C₃₁	—	4	2	no	—
147	D₄×C₃₁	—	4	2	no	—
148	D₄×C₃₁	—	4	2	no	—
149	D₄×C₃₁	—	8	2	no	—
150	D₄×C₃₁	—	8	2	no	—
151	D₄×C₃₁	—	8	2	no	—
152	D₄×C₃₁	—	8	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	2	no	—
157	C₂×C₄×C₃₁	—	4	2	no	—
158	C₂×C₄×C₃₁	—	4	2	no	—
159	C₂×C₄×C₃₁	—	8	2	no	—
160	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
161	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
162	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
163	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
164	C₂×C₄×C₃₁	#135	1	2	yes	—
165	C₂×C₄×C₃₁	#135	1	2	yes	—
166	C₂×C₄×C₃₁	#137	1	2	yes	—
167	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
170	C₈×C₃₁	—	2	2	no	—
171	C₈×C₃₁	—	2	2	no	—
172	C₈×C₃₁	—	4	2	no	—
173	C₈×C₃₁	—	4	2	no	—
174	C₈×C₃₁	—	4	2	no	—
175	C₂×#486	C₂×C₃₁	1	1	yes	characteristic
176	C₂×#462	C₂×C₃₁	1	1	yes	characteristic, complemented
177	C₂×#460	C₂×C₃₁	1	1	yes	characteristic
178	C₂×C₈×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
179	#1682	C₂×C₃₁	1	8	yes	direct product factor
180	C₂×#335	C₂×C₃₁	1	1	yes	characteristic, complemented
181	C₂×#332	C₂×C₃₁	1	1	yes	characteristic, complemented
182	C₂×#331	C₂×C₃₁	1	1	yes	characteristic
183	C₂²×C₃₁	—	8	2	no	—
184	C₂²×C₃₁	—	8	2	no	—
185	C₂²×C₃₁	—	8	2	no	—
186	C₂²×C₃₁	—	16	4	no	—
187	C₂²×C₃₁	#464	1	2	yes	—
188	C₂²×C₃₁	#466	1	2	yes	—
189	C₂²×C₃₁	#471	1	2	yes	—
190	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
191	C₄×C₃₁	—	2	4	no	—
192	C₄×C₃₁	—	2	1	no	—
193	C₄×C₃₁	—	2	1	no	—
194	C₄×C₃₁	—	4	2	no	—
195	C₄×C₃₁	—	8	2	no	—
196	C₄×C₃₁	#464	1	2	yes	—
197	C₄×C₃₁	#466	1	2	yes	—
198	C₄×C₃₁	C₂²×D₈	1	1	yes	characteristic
199	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
200	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
201	C₄×C₃₁	C₂×#137	1	1	yes	characteristic
202	C₂²×Q₁₆	—	2	1	no	—
203	C₂²×SD₁₆	—	2	1	no	—
204	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
205	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
206	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
207	#486	—	2	2	no	—
208	#486	C₂²×C₃₁	1	4	yes	—
209	#462	—	2	2	no	—
210	#462	C₂²×C₃₁	1	4	yes	complemented
211	#460	—	2	2	no	—
212	#460	C₂²×C₃₁	1	4	yes	—
213	C₈×Q₈	—	2	2	no	—
214	C₈×Q₈	C₂²×C₃₁	1	4	yes	complemented
215	C₂×C₄⋊C₈	—	2	1	no	—
216	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
217	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
218	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
219	C₂×#103	—	2	1	no	—
220	C₂×#102	—	2	1	no	—
221	C₂×#102	—	2	1	no	—
222	C₂×#102	—	2	1	no	—
223	C₂×C₄×C₈	—	2	1	no	—
224	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
225	#335	C₂²×C₃₁	1	4	yes	complemented
226	#332	C₂²×C₃₁	1	4	yes	complemented
227	#331	C₂²×C₃₁	1	4	yes	—
228	C₂×C₃₁	—	16	2	no	—
229	C₂×C₃₁	#1682	1	4	yes	direct product factor
230	C₂×C₃₁	C₂×#464	1	1	yes	characteristic
231	C₂×C₃₁	C₂×#466	1	1	yes	characteristic
232	C₂×C₃₁	C₂×#471	1	1	yes	characteristic
233	C₂²×Q₈	—	2	1	no	—
234	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
235	C₂²×D₄	—	2	1	no	—
236	C₂²×D₄	—	2	1	no	—
237	C₂²×D₄	—	2	1	no	—
238	C₂×Q₁₆	—	2	4	no	—
239	C₂×Q₁₆	—	4	4	no	—
240	C₂×SD₁₆	—	2	4	no	—
241	C₂×SD₁₆	—	4	4	no	—
242	C₂²×C₈	—	2	1	no	—
243	C₂²×C₈	—	2	1	no	—
244	C₂²×C₈	—	2	1	no	—
245	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
246	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
247	C₄⋊Q₈	—	2	1	no	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
251	#127	—	2	1	no	—
252	#127	—	2	1	no	—
253	#127	—	2	1	no	—
254	#127	C₂³×C₃₁	1	2	yes	—
255	C₄×Q₈	—	2	1	no	—
256	C₄×Q₈	—	2	1	no	—
257	C₄×Q₈	D₄×C₃₁	1	2	yes	—
258	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
263	C₂×C₄²	—	2	1	no	—
264	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
265	C₄⋊C₈	—	2	4	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	—	2	1	no	—
268	C₄⋊C₈	—	2	1	no	—
269	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
270	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
271	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
272	#103	—	2	4	no	—
273	#102	—	2	4	no	—
274	#102	—	2	4	no	—
275	#102	—	2	4	no	—
276	C₄×C₈	—	2	4	no	—
277	C₄×C₈	D₄×C₃₁	1	2	yes	—
278	C₄×C₈	C₂³×C₃₁	1	2	yes	—
279	C₃₁	C₂×#1682	1	1	yes	characteristic, direct product factor, Sylow
280	C₂⁴	—	4	1	no	—
281	C₂×Q₈	—	2	1	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	4	1	no	—
285	C₂×Q₈	—	4	2	no	—
286	C₂×Q₈	—	4	2	no	—
287	C₂×Q₈	D₈×C₃₁	1	4	yes	—
288	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂×D₄	—	4	1	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	—	4	2	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	—	8	2	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	4	1	no	—
303	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
305	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
306	Q₁₆	—	4	8	no	—
307	SD₁₆	—	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	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	4	2	no	—
314	C₂×C₈	—	4	2	no	—
315	C₂×C₈	—	4	2	no	—
316	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
317	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
329	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
330	C₄²	#41×C₃₁	1	1	yes	characteristic
331	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
332	C₂³	—	4	2	no	—
333	C₂³	—	8	2	no	—
334	C₂³	—	8	2	no	—
335	C₂³	—	8	2	no	—
336	C₂³	C₃₁×#121	1	1	yes	characteristic
337	Q₈	—	2	4	no	—
338	Q₈	—	2	2	no	—
339	Q₈	—	4	2	no	—
340	Q₈	—	4	2	no	—
341	Q₈	—	8	2	no	—
342	Q₈	C₂×D₈×C₃₁	1	4	yes	—
343	D₄	—	4	2	no	—
344	D₄	—	4	2	no	—
345	D₄	—	4	2	no	—
346	D₄	—	4	2	no	—
347	D₄	—	8	2	no	—
348	D₄	—	8	2	no	—
349	D₄	—	8	2	no	—
350	D₄	—	8	2	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	8	2	no	—
358	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
359	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
360	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
361	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
362	C₂×C₄	C₃₁×#135	1	2	yes	—
363	C₂×C₄	C₃₁×#135	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	1	yes	characteristic
368	C₈	—	2	2	no	—
369	C₈	—	2	2	no	—
370	C₈	—	4	2	no	—
371	C₈	—	4	2	no	—
372	C₈	—	4	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	16	4	no	—
377	C₂²	C₃₁×#464	1	2	yes	—
378	C₂²	C₃₁×#466	1	2	yes	—
379	C₂²	C₃₁×#471	1	2	yes	—
380	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
381	C₄	—	2	4	no	—
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	4	2	no	—
385	C₄	—	8	2	no	—
386	C₄	C₃₁×#464	1	2	yes	—
387	C₄	C₃₁×#466	1	2	yes	—
388	C₄	C₂²×D₈×C₃₁	1	1	yes	characteristic
389	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
390	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
391	C₄	C₂×C₃₁×#137	1	1	yes	characteristic
392	C₂	—	16	2	no	—
393	C₂	C₃₁×#1682	1	4	yes	direct product factor
394	C₂	C₂×C₃₁×#464	1	1	yes	characteristic
395	C₂	C₂×C₃₁×#466	1	1	yes	characteristic
396	C₂	C₂×C₃₁×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₁
prime radical	C₂×C₃₁×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₁×#462	C₂	semidirect
4. C₂×C₈×Q₈×C₃₁	C₂	semidirect
5. C₃₁×#1682	C₂	direct (N × H)
6. C₂×C₃₁×#335	C₂	semidirect
7. C₂×C₃₁×#332	C₂	semidirect
17. C₃₁×#462	C₂²	semidirect
21. C₈×Q₈×C₃₁	C₂²	semidirect
32. C₃₁×#335	C₂²	semidirect
33. C₃₁×#332	C₂²	semidirect
133. C₂×#1682	C₃₁	direct (N × H)
176. C₂×#462	C₂×C₃₁	semidirect
178. C₂×C₈×Q₈	C₂×C₃₁	semidirect
179. #1682	C₂×C₃₁	direct (N × H)
180. C₂×#335	C₂×C₃₁	semidirect
181. C₂×#332	C₂×C₃₁	semidirect
210. #462	C₂²×C₃₁	semidirect
214. C₈×Q₈	C₂²×C₃₁	semidirect
225. #335	C₂²×C₃₁	semidirect
226. #332	C₂²×C₃₁	semidirect
229. C₂×C₃₁	#1682	direct (N × H)
279. C₃₁	C₂×#1682	direct (N × H)
393. C₂	C₃₁×#1682	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×#486	2
C₂×C₃₁×#462	2
C₂×C₃₁×#460	2
C₂×C₈×Q₈×C₃₁	2
C₃₁×#1682	2
C₂×C₃₁×#335	2
C₂×C₃₁×#332	2
C₂×C₃₁×#331	2
C₂×#1682	31

Subgroups — C2×C31×#1682 #21475880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#1682 #21475880