Subgroups — C₃₁×#9225 #21465984

Order 7936.

578 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#461	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#436	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#1990	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#1802	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃₁×#332	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1296	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1277	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×SD₁₆×C₃₁	—	2	1	no	—
9	C₂²×M₁₆×C₃₁	—	2	1	no	—
10	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
12	C₃₁×#461	—	2	2	no	—
13	C₃₁×#461	C₄	1	4	yes	complemented
14	C₃₁×#436	—	2	2	no	—
15	C₃₁×#436	—	2	2	no	—
16	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×#103	—	2	1	no	—
20	C₂×C₃₁×#102	—	2	1	no	—
21	C₂×C₃₁×C₂²⋊C₈	—	2	1	no	—
22	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
23	C₃₁×#384	C₂²	1	1	yes	characteristic
24	C₃₁×#340	—	2	1	no	—
25	C₃₁×#340	—	2	1	no	—
26	C₃₁×#340	—	2	1	no	—
27	C₃₁×#332	—	2	2	no	—
28	C₂²×Q₈×C₃₁	—	2	1	no	—
29	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₃₁	—	2	1	no	—
31	C₂×SD₁₆×C₃₁	—	2	4	no	—
32	C₂×SD₁₆×C₃₁	—	4	2	no	—
33	C₂×SD₁₆×C₃₁	—	4	2	no	—
34	C₂×M₁₆×C₃₁	—	2	4	no	—
35	C₂×M₁₆×C₃₁	—	4	2	no	—
36	C₂×M₁₆×C₃₁	—	4	2	no	—
37	C₂²×C₈×C₃₁	—	2	1	no	—
38	C₂²×C₈×C₃₁	—	2	1	no	—
39	C₂²×C₈×C₃₁	—	2	1	no	—
40	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
42	C₃₁×C₄⋊Q₈	—	2	1	no	—
43	C₃₁×C₄⋊Q₈	—	2	1	no	—
44	C₃₁×C₄⋊Q₈	—	2	1	no	—
45	C₃₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
46	C₄×D₄×C₃₁	—	2	1	no	—
47	C₄×D₄×C₃₁	—	2	1	no	—
48	C₄×D₄×C₃₁	C₂×C₄	1	2	yes	—
49	C₄×D₄×C₃₁	D₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
51	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
52	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
53	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
54	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
55	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
56	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
57	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
58	C₃₁×C₄⋊C₈	—	2	1	no	—
59	C₃₁×C₄⋊C₈	—	2	1	no	—
60	C₃₁×C₄⋊C₈	—	2	1	no	—
61	C₃₁×C₄⋊C₈	—	2	1	no	—
62	C₃₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
63	C₃₁×C₄⋊C₈	D₄	1	2	yes	—
64	C₃₁×#103	—	2	4	no	—
65	C₃₁×#102	—	4	2	no	—
66	C₃₁×C₂²⋊C₈	—	2	4	no	—
67	C₄×C₈×C₃₁	—	2	1	no	—
68	C₄×C₈×C₃₁	—	2	1	no	—
69	C₂⁴×C₃₁	—	2	1	no	—
70	C₂×Q₈×C₃₁	—	2	2	no	—
71	C₂×Q₈×C₃₁	—	4	1	no	—
72	C₂×Q₈×C₃₁	—	4	1	no	—
73	C₂×Q₈×C₃₁	—	4	1	no	—
74	C₂×Q₈×C₃₁	—	4	1	no	—
75	C₂×Q₈×C₃₁	—	4	1	no	—
76	C₂×D₄×C₃₁	—	2	1	no	—
77	C₂×D₄×C₃₁	—	2	1	no	—
78	C₂×D₄×C₃₁	—	2	1	no	—
79	C₂×D₄×C₃₁	—	2	1	no	—
80	C₂×D₄×C₃₁	—	2	1	no	—
81	C₂×D₄×C₃₁	C₂²⋊C₄	1	2	yes	—
82	C₂²×C₄×C₃₁	—	2	1	no	—
83	C₂²×C₄×C₃₁	—	2	2	no	—
84	C₂²×C₄×C₃₁	—	2	2	no	—
85	C₂²×C₄×C₃₁	—	4	1	no	—
86	C₂²×C₄×C₃₁	—	4	1	no	—
87	C₂²×C₄×C₃₁	—	4	1	no	—
88	C₂²×C₄×C₃₁	—	4	1	no	—
89	C₂²×C₄×C₃₁	—	4	1	no	—
90	C₂²×C₄×C₃₁	—	4	1	no	—
91	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
94	SD₁₆×C₃₁	—	4	8	no	—
95	M₁₆×C₃₁	—	4	8	no	—
96	C₂×C₈×C₃₁	—	2	1	no	—
97	C₂×C₈×C₃₁	—	2	1	no	—
98	C₂×C₈×C₃₁	—	2	2	no	—
99	C₂×C₈×C₃₁	—	2	1	no	—
100	C₂×C₈×C₃₁	—	2	2	no	—
101	C₂×C₈×C₃₁	—	2	1	no	—
102	C₂×C₈×C₃₁	—	2	1	no	—
103	C₂×C₈×C₃₁	—	4	1	no	—
104	C₂×C₈×C₃₁	—	4	1	no	—
105	C₂×C₈×C₃₁	—	4	1	no	—
106	C₂×C₈×C₃₁	—	4	1	no	—
107	C₂×C₈×C₃₁	—	4	1	no	—
108	C₂×C₈×C₃₁	—	4	1	no	—
109	C₂×C₈×C₃₁	—	4	1	no	—
110	C₂×C₈×C₃₁	SD₁₆	1	2	yes	complemented
111	C₄⋊C₄×C₃₁	—	2	1	no	—
112	C₄⋊C₄×C₃₁	—	2	2	no	—
113	C₄⋊C₄×C₃₁	—	2	2	no	—
114	C₄⋊C₄×C₃₁	—	4	1	no	—
115	C₄⋊C₄×C₃₁	—	4	1	no	—
116	C₄⋊C₄×C₃₁	—	4	1	no	—
117	C₄⋊C₄×C₃₁	—	4	1	no	—
118	C₄⋊C₄×C₃₁	—	4	1	no	—
119	C₄⋊C₄×C₃₁	—	4	1	no	—
120	C₄⋊C₄×C₃₁	—	8	1	no	—
121	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
122	C₂²⋊C₄×C₃₁	—	2	2	no	—
123	C₂²⋊C₄×C₃₁	—	2	2	no	—
124	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₃₁	#41	1	1	yes	characteristic
128	#9225	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂³×C₃₁	—	2	2	no	—
130	C₂³×C₃₁	—	4	1	no	—
131	C₂³×C₃₁	—	4	1	no	—
132	C₂³×C₃₁	—	4	1	no	—
133	C₂³×C₃₁	—	4	1	no	—
134	C₂³×C₃₁	—	4	1	no	—
135	C₂³×C₃₁	—	4	1	no	—
136	C₂³×C₃₁	#121	1	1	yes	characteristic
137	Q₈×C₃₁	—	4	2	no	—
138	Q₈×C₃₁	—	4	2	no	—
139	Q₈×C₃₁	—	8	1	no	—
140	Q₈×C₃₁	—	8	1	no	—
141	D₄×C₃₁	—	2	2	no	—
142	D₄×C₃₁	—	2	2	no	—
143	D₄×C₃₁	—	4	1	no	—
144	D₄×C₃₁	—	4	1	no	—
145	C₂×C₄×C₃₁	—	2	1	no	—
146	C₂×C₄×C₃₁	—	2	1	no	—
147	C₂×C₄×C₃₁	—	2	2	no	—
148	C₂×C₄×C₃₁	—	4	1	no	—
149	C₂×C₄×C₃₁	—	4	1	no	—
150	C₂×C₄×C₃₁	—	4	2	no	—
151	C₂×C₄×C₃₁	—	4	2	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	—	8	1	no	—
156	C₂×C₄×C₃₁	—	8	1	no	—
157	C₂×C₄×C₃₁	—	8	1	no	—
158	C₂×C₄×C₃₁	—	8	1	no	—
159	C₂×C₄×C₃₁	—	8	1	no	—
160	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₃₁	#120	1	1	yes	characteristic
164	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
165	C₂×C₄×C₃₁	#123	1	1	yes	characteristic
166	C₂×C₄×C₃₁	C₂×SD₁₆	1	1	yes	characteristic
167	C₂×C₄×C₃₁	#135	1	1	yes	characteristic
168	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
169	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
170	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
171	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
172	C₂×C₄×C₃₁	#137	1	1	yes	characteristic
173	C₂×C₄×C₃₁	#137	1	1	yes	characteristic
174	C₈×C₃₁	—	2	2	no	—
175	C₈×C₃₁	—	4	2	no	—
176	C₈×C₃₁	—	4	2	no	—
177	C₈×C₃₁	—	4	1	no	—
178	C₈×C₃₁	—	8	1	no	—
179	C₂×#461	C₂×C₃₁	1	1	yes	characteristic
180	C₂×#436	C₂×C₃₁	1	1	yes	characteristic
181	#1990	C₂×C₃₁	1	1	yes	characteristic, complemented
182	#1802	C₂×C₃₁	1	1	yes	characteristic
183	C₂×#332	C₂×C₃₁	1	1	yes	characteristic, complemented
184	#1296	C₂×C₃₁	1	1	yes	characteristic, complemented
185	#1277	C₂×C₃₁	1	1	yes	characteristic, complemented
186	C₂²×C₃₁	—	4	2	no	—
187	C₂²×C₃₁	—	4	2	no	—
188	C₂²×C₃₁	—	4	2	no	—
189	C₂²×C₃₁	—	8	1	no	—
190	C₂²×C₃₁	—	8	1	no	—
191	C₂²×C₃₁	—	8	1	no	—
192	C₂²×C₃₁	—	8	1	no	—
193	C₂²×C₃₁	#386	1	1	yes	characteristic
194	C₂²×C₃₁	#461	1	1	yes	characteristic
195	C₂²×C₃₁	#463	1	1	yes	characteristic
196	C₂²×C₃₁	#468	1	1	yes	characteristic
197	C₂²×C₃₁	#469	1	1	yes	characteristic
198	C₂²×C₃₁	#471	1	1	yes	characteristic
199	C₂²×C₃₁	#473	1	1	yes	characteristic
200	C₄×C₃₁	—	2	1	no	—
201	C₄×C₃₁	—	2	1	no	—
202	C₄×C₃₁	—	4	2	no	—
203	C₄×C₃₁	—	8	2	no	—
204	C₄×C₃₁	—	16	1	no	—
205	C₄×C₃₁	#417	1	1	yes	characteristic
206	C₄×C₃₁	#418	1	1	yes	characteristic
207	C₄×C₃₁	C₄×SD₁₆	1	1	yes	characteristic
208	C₄×C₃₁	#440	1	1	yes	characteristic
209	C₄×C₃₁	#450	1	1	yes	characteristic
210	C₄×C₃₁	#452	1	1	yes	characteristic
211	C₄×C₃₁	#468	1	1	yes	characteristic
212	C₄×C₃₁	#469	1	1	yes	characteristic
213	C₂²×SD₁₆	—	2	1	no	—
214	C₂²×M₁₆	—	2	1	no	—
215	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
216	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
217	#461	—	2	2	no	—
218	#461	C₄×C₃₁	1	4	yes	complemented
219	#436	—	2	2	no	—
220	#436	—	2	2	no	—
221	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
222	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
223	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
224	C₂×#103	—	2	1	no	—
225	C₂×#102	—	2	1	no	—
226	C₂×C₂²⋊C₈	—	2	1	no	—
227	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
228	#384	C₂²×C₃₁	1	1	yes	characteristic
229	#340	—	2	1	no	—
230	#340	—	2	1	no	—
231	#340	—	2	1	no	—
232	#332	—	2	2	no	—
233	C₂×C₃₁	—	8	2	no	—
234	C₂×C₃₁	#1691	1	1	yes	characteristic
235	C₂×C₃₁	#1693	1	1	yes	characteristic
236	C₂×C₃₁	#1699	1	1	yes	characteristic
237	C₂×C₃₁	#1701	1	1	yes	characteristic
238	C₂×C₃₁	#1877	1	1	yes	characteristic
239	C₂×C₃₁	#1895	1	1	yes	characteristic
240	C₂×C₃₁	#1908	1	1	yes	characteristic
241	C₂²×Q₈	—	2	1	no	—
242	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
243	C₂³×C₄	—	2	1	no	—
244	C₂×SD₁₆	—	2	4	no	—
245	C₂×SD₁₆	—	4	2	no	—
246	C₂×SD₁₆	—	4	2	no	—
247	C₂×M₁₆	—	2	4	no	—
248	C₂×M₁₆	—	4	2	no	—
249	C₂×M₁₆	—	4	2	no	—
250	C₂²×C₈	—	2	1	no	—
251	C₂²×C₈	—	2	1	no	—
252	C₂²×C₈	—	2	1	no	—
253	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
254	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
255	C₄⋊Q₈	—	2	1	no	—
256	C₄⋊Q₈	—	2	1	no	—
257	C₄⋊Q₈	—	2	1	no	—
258	C₄⋊Q₈	C₂×C₄×C₃₁	1	2	yes	—
259	C₄×D₄	—	2	1	no	—
260	C₄×D₄	—	2	1	no	—
261	C₄×D₄	C₂×C₄×C₃₁	1	2	yes	—
262	C₄×D₄	D₄×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	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	—	2	1	no	—
270	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
271	C₄⋊C₈	—	2	1	no	—
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	—	2	1	no	—
275	C₄⋊C₈	C₂×C₄×C₃₁	1	2	yes	—
276	C₄⋊C₈	D₄×C₃₁	1	2	yes	—
277	#103	—	2	4	no	—
278	#102	—	4	2	no	—
279	C₂²⋊C₈	—	2	4	no	—
280	C₄×C₈	—	2	1	no	—
281	C₄×C₈	—	2	1	no	—
282	C₃₁	#9225	1	1	yes	characteristic, direct product factor, Sylow
283	C₂⁴	—	2	1	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	4	1	no	—
286	C₂×Q₈	—	4	1	no	—
287	C₂×Q₈	—	4	1	no	—
288	C₂×Q₈	—	4	1	no	—
289	C₂×Q₈	—	4	1	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	—	2	1	no	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	C₂²⋊C₄×C₃₁	1	2	yes	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	4	1	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
307	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
308	SD₁₆	—	4	8	no	—
309	M₁₆	—	4	8	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	4	1	no	—
318	C₂×C₈	—	4	1	no	—
319	C₂×C₈	—	4	1	no	—
320	C₂×C₈	—	4	1	no	—
321	C₂×C₈	—	4	1	no	—
322	C₂×C₈	—	4	1	no	—
323	C₂×C₈	—	4	1	no	—
324	C₂×C₈	SD₁₆×C₃₁	1	2	yes	complemented
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₄⋊C₄	—	4	1	no	—
333	C₄⋊C₄	—	4	1	no	—
334	C₄⋊C₄	—	8	1	no	—
335	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
339	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
340	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
341	C₄²	#41×C₃₁	1	1	yes	characteristic
342	C₂³	—	2	2	no	—
343	C₂³	—	4	1	no	—
344	C₂³	—	4	1	no	—
345	C₂³	—	4	1	no	—
346	C₂³	—	4	1	no	—
347	C₂³	—	4	1	no	—
348	C₂³	—	4	1	no	—
349	C₂³	C₃₁×#121	1	1	yes	characteristic
350	Q₈	—	4	2	no	—
351	Q₈	—	4	2	no	—
352	Q₈	—	8	1	no	—
353	Q₈	—	8	1	no	—
354	D₄	—	2	2	no	—
355	D₄	—	2	2	no	—
356	D₄	—	4	1	no	—
357	D₄	—	4	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	8	1	no	—
369	C₂×C₄	—	8	1	no	—
370	C₂×C₄	—	8	1	no	—
371	C₂×C₄	—	8	1	no	—
372	C₂×C₄	—	8	1	no	—
373	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
374	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
375	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
376	C₂×C₄	C₃₁×#120	1	1	yes	characteristic
377	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
378	C₂×C₄	C₃₁×#123	1	1	yes	characteristic
379	C₂×C₄	C₂×SD₁₆×C₃₁	1	1	yes	characteristic
380	C₂×C₄	C₃₁×#135	1	1	yes	characteristic
381	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
382	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
383	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
384	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
385	C₂×C₄	C₃₁×#137	1	1	yes	characteristic
386	C₂×C₄	C₃₁×#137	1	1	yes	characteristic
387	C₈	—	2	2	no	—
388	C₈	—	4	2	no	—
389	C₈	—	4	2	no	—
390	C₈	—	4	1	no	—
391	C₈	—	8	1	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	8	1	no	—
396	C₂²	—	8	1	no	—
397	C₂²	—	8	1	no	—
398	C₂²	—	8	1	no	—
399	C₂²	C₃₁×#386	1	1	yes	characteristic
400	C₂²	C₃₁×#461	1	1	yes	characteristic
401	C₂²	C₃₁×#463	1	1	yes	characteristic
402	C₂²	C₃₁×#468	1	1	yes	characteristic
403	C₂²	C₃₁×#469	1	1	yes	characteristic
404	C₂²	C₃₁×#471	1	1	yes	characteristic
405	C₂²	C₃₁×#473	1	1	yes	characteristic
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	4	2	no	—
409	C₄	—	8	2	no	—
410	C₄	—	16	1	no	—
411	C₄	C₃₁×#417	1	1	yes	characteristic
412	C₄	C₃₁×#418	1	1	yes	characteristic
413	C₄	C₄×SD₁₆×C₃₁	1	1	yes	characteristic
414	C₄	C₃₁×#440	1	1	yes	characteristic
415	C₄	C₃₁×#450	1	1	yes	characteristic
416	C₄	C₃₁×#452	1	1	yes	characteristic
417	C₄	C₃₁×#468	1	1	yes	characteristic
418	C₄	C₃₁×#469	1	1	yes	characteristic
419	C₂	—	8	2	no	—
420	C₂	C₃₁×#1691	1	1	yes	characteristic
421	C₂	C₃₁×#1693	1	1	yes	characteristic
422	C₂	C₃₁×#1699	1	1	yes	characteristic
423	C₂	C₃₁×#1701	1	1	yes	characteristic
424	C₂	C₃₁×#1877	1	1	yes	characteristic
425	C₂	C₃₁×#1895	1	1	yes	characteristic
426	C₂	C₃₁×#1908	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	#121
commutator	C₄²	C₂²×C₄×C₃₁
Frattini, cosocle	C₂×C₄²	C₂³×C₃₁
prime radical	C₂²×D₄×C₃₁	D₄
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
3. C₃₁×#1990	C₂	semidirect
5. C₂×C₃₁×#332	C₂	semidirect
6. C₃₁×#1296	C₂	semidirect
7. C₃₁×#1277	C₂	semidirect
13. C₃₁×#461	C₄	semidirect
110. C₂×C₈×C₃₁	SD₁₆	semidirect
128. #9225	C₃₁	direct (N × H)
181. #1990	C₂×C₃₁	semidirect
183. C₂×#332	C₂×C₃₁	semidirect
184. #1296	C₂×C₃₁	semidirect
185. #1277	C₂×C₃₁	semidirect
218. #461	C₄×C₃₁	semidirect
282. C₃₁	#9225	direct (N × H)
324. C₂×C₈	SD₁₆×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#461	2
C₂×C₃₁×#436	2
C₃₁×#1990	2
C₃₁×#1802	2
C₂×C₃₁×#332	2
C₃₁×#1296	2
C₃₁×#1277	2
#9225	31

Subgroups — C31×#9225 #21465984

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#9225 #21465984