Subgroups — C₂×C₃₁×#1686 #21475902

Order 7936.

766 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#492	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁×#460	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃₁×#446	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1686	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×SD₁₆×C₃₁	—	2	1	no	—
10	C₂²×SD₁₆×C₃₁	—	2	1	no	—
11	C₂²×SD₁₆×C₃₁	—	2	1	no	—
12	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
15	C₃₁×#492	—	2	2	no	—
16	C₃₁×#492	C₂²	1	4	yes	—
17	C₃₁×#475	—	2	2	no	—
18	C₃₁×#475	C₂²	1	4	yes	complemented
19	C₃₁×#460	—	2	2	no	—
20	C₃₁×#460	C₂²	1	4	yes	—
21	C₃₁×#446	—	2	2	no	—
22	C₃₁×#446	C₂²	1	4	yes	complemented
23	C₂×C₃₁×#106	—	2	1	no	—
24	C₂×C₃₁×C₄⋊C₈	—	2	1	no	—
25	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#103	—	2	1	no	—
29	C₂×C₃₁×#102	—	2	1	no	—
30	C₂×C₃₁×#97	—	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×SD₁₆×C₃₁	—	2	4	no	—
41	C₂×SD₁₆×C₃₁	—	2	4	no	—
42	C₂×SD₁₆×C₃₁	—	2	4	no	—
43	C₂×SD₁₆×C₃₁	—	4	4	no	—
44	C₂×SD₁₆×C₃₁	—	4	4	no	—
45	C₂×SD₁₆×C₃₁	—	4	4	no	—
46	C₂²×C₈×C₃₁	—	2	1	no	—
47	C₂²×C₈×C₃₁	—	2	1	no	—
48	C₂²×C₈×C₃₁	—	2	1	no	—
49	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
51	C₃₁×C₄⋊Q₈	—	2	1	no	—
52	C₃₁×C₄⋊Q₈	—	2	1	no	—
53	C₃₁×C₄⋊Q₈	—	2	1	no	—
54	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
55	C₃₁×#127	—	2	1	no	—
56	C₃₁×#127	—	2	1	no	—
57	C₃₁×#127	—	2	1	no	—
58	C₃₁×#127	C₂³	1	2	yes	—
59	C₄×Q₈×C₃₁	—	2	1	no	—
60	C₄×Q₈×C₃₁	—	2	1	no	—
61	C₄×Q₈×C₃₁	D₄	1	2	yes	—
62	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₃₁	—	2	1	no	—
68	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
69	C₃₁×#106	—	2	4	no	—
70	C₃₁×C₄⋊C₈	—	2	4	no	—
71	C₃₁×C₄⋊C₈	—	2	1	no	—
72	C₃₁×C₄⋊C₈	—	2	1	no	—
73	C₃₁×C₄⋊C₈	—	2	1	no	—
74	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
75	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
76	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
77	C₃₁×#103	—	2	4	no	—
78	C₃₁×#102	—	2	4	no	—
79	C₃₁×#97	—	2	4	no	—
80	C₄×C₈×C₃₁	D₄	1	2	yes	—
81	C₄×C₈×C₃₁	C₂³	1	2	yes	—
82	C₂⁴×C₃₁	—	4	1	no	—
83	C₂×Q₈×C₃₁	—	2	1	no	—
84	C₂×Q₈×C₃₁	—	2	2	no	—
85	C₂×Q₈×C₃₁	—	2	2	no	—
86	C₂×Q₈×C₃₁	—	2	2	no	—
87	C₂×Q₈×C₃₁	—	4	1	no	—
88	C₂×Q₈×C₃₁	—	4	2	no	—
89	C₂×Q₈×C₃₁	—	4	2	no	—
90	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
91	C₂×D₄×C₃₁	—	2	2	no	—
92	C₂×D₄×C₃₁	—	2	2	no	—
93	C₂×D₄×C₃₁	—	2	2	no	—
94	C₂×D₄×C₃₁	—	4	1	no	—
95	C₂×D₄×C₃₁	—	4	1	no	—
96	C₂×D₄×C₃₁	—	4	1	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	—	4	2	no	—
101	C₂×D₄×C₃₁	—	8	2	no	—
102	C₂²×C₄×C₃₁	—	2	1	no	—
103	C₂²×C₄×C₃₁	—	2	1	no	—
104	C₂²×C₄×C₃₁	—	4	1	no	—
105	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
108	SD₁₆×C₃₁	—	4	8	no	—
109	SD₁₆×C₃₁	—	4	8	no	—
110	SD₁₆×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	2	no	—
115	C₂×C₈×C₃₁	—	4	2	no	—
116	C₂×C₈×C₃₁	—	4	2	no	—
117	C₂×C₈×C₃₁	—	4	2	no	—
118	C₂×C₈×C₃₁	SD₁₆	1	4	yes	complemented
119	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
121	C₄⋊C₄×C₃₁	—	2	2	no	—
122	C₄⋊C₄×C₃₁	—	2	1	no	—
123	C₄⋊C₄×C₃₁	—	2	2	no	—
124	C₄⋊C₄×C₃₁	—	2	2	no	—
125	C₄⋊C₄×C₃₁	—	2	2	no	—
126	C₄⋊C₄×C₃₁	—	4	1	no	—
127	C₄⋊C₄×C₃₁	—	4	1	no	—
128	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
129	C₄²×C₃₁	—	2	2	no	—
130	C₄²×C₃₁	—	2	2	no	—
131	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₃₁	#41	1	1	yes	characteristic
134	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
135	C₂×#1686	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂³×C₃₁	—	4	2	no	—
137	C₂³×C₃₁	—	8	2	no	—
138	C₂³×C₃₁	—	8	2	no	—
139	C₂³×C₃₁	—	8	2	no	—
140	C₂³×C₃₁	#121	1	1	yes	characteristic
141	Q₈×C₃₁	—	2	2	no	—
142	Q₈×C₃₁	—	2	2	no	—
143	Q₈×C₃₁	—	4	2	no	—
144	Q₈×C₃₁	—	4	2	no	—
145	Q₈×C₃₁	—	4	2	no	—
146	Q₈×C₃₁	—	8	2	no	—
147	D₄×C₃₁	—	4	2	no	—
148	D₄×C₃₁	—	4	2	no	—
149	D₄×C₃₁	—	4	2	no	—
150	D₄×C₃₁	—	4	2	no	—
151	D₄×C₃₁	—	8	2	no	—
152	D₄×C₃₁	—	8	2	no	—
153	D₄×C₃₁	—	8	2	no	—
154	D₄×C₃₁	—	8	2	no	—
155	C₂×C₄×C₃₁	—	2	2	no	—
156	C₂×C₄×C₃₁	—	2	2	no	—
157	C₂×C₄×C₃₁	—	2	2	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	—	8	2	no	—
162	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
163	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
164	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
165	C₂×C₄×C₃₁	C₂×SD₁₆	1	2	yes	—
166	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
167	C₂×C₄×C₃₁	AGL(1,ℤ/8)	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	1	yes	characteristic
172	C₈×C₃₁	—	2	2	no	—
173	C₈×C₃₁	—	4	2	no	—
174	C₈×C₃₁	—	4	2	no	—
175	C₈×C₃₁	—	4	2	no	—
176	C₈×C₃₁	C₂×SD₁₆	1	4	yes	complemented
177	C₂×#492	C₂×C₃₁	1	1	yes	characteristic
178	C₂×#475	C₂×C₃₁	1	1	yes	characteristic, complemented
179	C₂×#460	C₂×C₃₁	1	1	yes	characteristic
180	C₂×#446	C₂×C₃₁	1	1	yes	characteristic, complemented
181	#1686	C₂×C₃₁	1	8	yes	direct product factor
182	C₂×#335	C₂×C₃₁	1	1	yes	characteristic, complemented
183	C₂×#332	C₂×C₃₁	1	1	yes	characteristic, complemented
184	C₂×#331	C₂×C₃₁	1	1	yes	characteristic
185	C₂²×C₃₁	—	8	2	no	—
186	C₂²×C₃₁	—	8	2	no	—
187	C₂²×C₃₁	—	8	2	no	—
188	C₂²×C₃₁	—	16	4	no	—
189	C₂²×C₃₁	#460	1	2	yes	—
190	C₂²×C₃₁	#468	1	2	yes	—
191	C₂²×C₃₁	#471	1	2	yes	—
192	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
193	C₄×C₃₁	—	2	1	no	—
194	C₄×C₃₁	—	2	1	no	—
195	C₄×C₃₁	—	4	2	no	—
196	C₄×C₃₁	—	4	2	no	—
197	C₄×C₃₁	—	8	2	no	—
198	C₄×C₃₁	#460	1	2	yes	—
199	C₄×C₃₁	#468	1	2	yes	—
200	C₄×C₃₁	C₂²×SD₁₆	1	1	yes	characteristic
201	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
202	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
203	C₄×C₃₁	C₂×#137	1	1	yes	characteristic
204	C₂²×SD₁₆	—	2	1	no	—
205	C₂²×SD₁₆	—	2	1	no	—
206	C₂²×SD₁₆	—	2	1	no	—
207	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
208	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
209	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
210	#492	—	2	2	no	—
211	#492	C₂²×C₃₁	1	4	yes	—
212	#475	—	2	2	no	—
213	#475	C₂²×C₃₁	1	4	yes	complemented
214	#460	—	2	2	no	—
215	#460	C₂²×C₃₁	1	4	yes	—
216	#446	—	2	2	no	—
217	#446	C₂²×C₃₁	1	4	yes	complemented
218	C₂×#106	—	2	1	no	—
219	C₂×C₄⋊C₈	—	2	1	no	—
220	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
221	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
222	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
223	C₂×#103	—	2	1	no	—
224	C₂×#102	—	2	1	no	—
225	C₂×#97	—	2	1	no	—
226	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
227	#335	C₂²×C₃₁	1	4	yes	complemented
228	#332	C₂²×C₃₁	1	4	yes	complemented
229	#331	C₂²×C₃₁	1	4	yes	—
230	C₂×C₃₁	—	16	2	no	—
231	C₂×C₃₁	#1686	1	4	yes	direct product factor
232	C₂×C₃₁	C₂×#460	1	1	yes	characteristic
233	C₂×C₃₁	C₂×#468	1	1	yes	characteristic
234	C₂×C₃₁	C₂×#471	1	1	yes	characteristic
235	C₂²×Q₈	—	2	1	no	—
236	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
237	C₂²×D₄	—	2	1	no	—
238	C₂²×D₄	—	2	1	no	—
239	C₂²×D₄	—	2	1	no	—
240	C₂×SD₁₆	—	2	4	no	—
241	C₂×SD₁₆	—	2	4	no	—
242	C₂×SD₁₆	—	2	4	no	—
243	C₂×SD₁₆	—	4	4	no	—
244	C₂×SD₁₆	—	4	4	no	—
245	C₂×SD₁₆	—	4	4	no	—
246	C₂²×C₈	—	2	1	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	—	2	1	no	—
249	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
250	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
251	C₄⋊Q₈	—	2	1	no	—
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
255	#127	—	2	1	no	—
256	#127	—	2	1	no	—
257	#127	—	2	1	no	—
258	#127	C₂³×C₃₁	1	2	yes	—
259	C₄×Q₈	—	2	1	no	—
260	C₄×Q₈	—	2	1	no	—
261	C₄×Q₈	D₄×C₃₁	1	2	yes	—
262	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
269	#106	—	2	4	no	—
270	C₄⋊C₈	—	2	4	no	—
271	C₄⋊C₈	—	2	1	no	—
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
275	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
276	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
277	#103	—	2	4	no	—
278	#102	—	2	4	no	—
279	#97	—	2	4	no	—
280	C₄×C₈	D₄×C₃₁	1	2	yes	—
281	C₄×C₈	C₂³×C₃₁	1	2	yes	—
282	C₃₁	C₂×#1686	1	1	yes	characteristic, direct product factor, Sylow
283	C₂⁴	—	4	1	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	4	1	no	—
289	C₂×Q₈	—	4	2	no	—
290	C₂×Q₈	—	4	2	no	—
291	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	8	2	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
308	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
309	SD₁₆	—	4	8	no	—
310	SD₁₆	—	4	8	no	—
311	SD₁₆	—	4	8	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	4	2	no	—
317	C₂×C₈	—	4	2	no	—
318	C₂×C₈	—	4	2	no	—
319	C₂×C₈	SD₁₆×C₃₁	1	4	yes	complemented
320	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
321	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
333	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
334	C₄²	#41×C₃₁	1	1	yes	characteristic
335	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
336	C₂³	—	4	2	no	—
337	C₂³	—	8	2	no	—
338	C₂³	—	8	2	no	—
339	C₂³	—	8	2	no	—
340	C₂³	C₃₁×#121	1	1	yes	characteristic
341	Q₈	—	2	2	no	—
342	Q₈	—	2	2	no	—
343	Q₈	—	4	2	no	—
344	Q₈	—	4	2	no	—
345	Q₈	—	4	2	no	—
346	Q₈	—	8	2	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	2	no	—
351	D₄	—	8	2	no	—
352	D₄	—	8	2	no	—
353	D₄	—	8	2	no	—
354	D₄	—	8	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	8	2	no	—
362	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
363	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
364	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
365	C₂×C₄	C₂×SD₁₆×C₃₁	1	2	yes	—
366	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
367	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
368	C₂×C₄	C₃₁×#137	1	2	yes	—
369	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
370	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
371	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
372	C₈	—	2	2	no	—
373	C₈	—	4	2	no	—
374	C₈	—	4	2	no	—
375	C₈	—	4	2	no	—
376	C₈	C₂×SD₁₆×C₃₁	1	4	yes	complemented
377	C₂²	—	8	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	16	4	no	—
381	C₂²	C₃₁×#460	1	2	yes	—
382	C₂²	C₃₁×#468	1	2	yes	—
383	C₂²	C₃₁×#471	1	2	yes	—
384	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	4	2	no	—
388	C₄	—	4	2	no	—
389	C₄	—	8	2	no	—
390	C₄	C₃₁×#460	1	2	yes	—
391	C₄	C₃₁×#468	1	2	yes	—
392	C₄	C₂²×SD₁₆×C₃₁	1	1	yes	characteristic
393	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
394	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
395	C₄	C₂×C₃₁×#137	1	1	yes	characteristic
396	C₂	—	16	2	no	—
397	C₂	C₃₁×#1686	1	4	yes	direct product factor
398	C₂	C₂×C₃₁×#460	1	1	yes	characteristic
399	C₂	C₂×C₃₁×#468	1	1	yes	characteristic
400	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×#475	C₂	semidirect
4. C₂×C₃₁×#446	C₂	semidirect
5. C₃₁×#1686	C₂	direct (N × H)
6. C₂×C₃₁×#335	C₂	semidirect
7. C₂×C₃₁×#332	C₂	semidirect
18. C₃₁×#475	C₂²	semidirect
22. C₃₁×#446	C₂²	semidirect
32. C₃₁×#335	C₂²	semidirect
33. C₃₁×#332	C₂²	semidirect
118. C₂×C₈×C₃₁	SD₁₆	semidirect
135. C₂×#1686	C₃₁	direct (N × H)
176. C₈×C₃₁	C₂×SD₁₆	semidirect
178. C₂×#475	C₂×C₃₁	semidirect
180. C₂×#446	C₂×C₃₁	semidirect
181. #1686	C₂×C₃₁	direct (N × H)
182. C₂×#335	C₂×C₃₁	semidirect
183. C₂×#332	C₂×C₃₁	semidirect
213. #475	C₂²×C₃₁	semidirect
217. #446	C₂²×C₃₁	semidirect
227. #335	C₂²×C₃₁	semidirect
228. #332	C₂²×C₃₁	semidirect
231. C₂×C₃₁	#1686	direct (N × H)
282. C₃₁	C₂×#1686	direct (N × H)
319. C₂×C₈	SD₁₆×C₃₁	semidirect
376. C₈	C₂×SD₁₆×C₃₁	semidirect
397. C₂	C₃₁×#1686	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×#492	2
C₂×C₃₁×#475	2
C₂×C₃₁×#460	2
C₂×C₃₁×#446	2
C₃₁×#1686	2
C₂×C₃₁×#335	2
C₂×C₃₁×#332	2
C₂×C₃₁×#331	2
C₂×#1686	31

Subgroups — C2×C31×#1686 #21475902

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#1686 #21475902