Subgroups — C₃₁×#7984 #21464743

Order 7936.

650 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#432	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2285	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2283	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1289	C₂	1	4	yes	maximal
5	C₂×C₃₁×#117	—	2	1	no	—
6	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
7	C₃₁×#432	—	2	1	no	—
8	C₃₁×#432	—	2	1	no	—
9	C₃₁×#432	—	2	1	no	—
10	C₃₁×#432	—	2	1	no	—
11	C₂×C₃₁×C₄⋊C₈	C₄	1	2	yes	complemented
12	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
13	C₂×C₃₁×#97	C₄	1	2	yes	complemented
14	C₃₁×#384	—	2	1	no	—
15	C₃₁×#383	C₄	1	2	yes	complemented
16	C₃₁×#382	—	2	1	no	—
17	C₃₁×#382	C₄	1	2	yes	complemented
18	C₃₁×#381	—	2	1	no	—
19	C₃₁×#380	—	2	1	no	—
20	C₃₁×#380	C₂²	1	2	yes	—
21	C₃₁×#380	C₂²	1	2	yes	—
22	C₄×C₄⋊C₄×C₃₁	—	2	1	no	—
23	C₄×C₄⋊C₄×C₃₁	—	2	1	no	—
24	C₄×C₄⋊C₄×C₃₁	C₄	1	2	yes	complemented
25	C₄×C₂²⋊C₄×C₃₁	—	2	1	no	—
26	C₃₁×#376	C₄	1	2	yes	complemented
27	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
30	C₂²×C₈×C₃₁	C₂×C₄	1	4	yes	—
31	C₃₁×#117	—	4	4	no	—
32	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
33	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
34	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
35	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
36	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
37	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
38	C₂×C₄²×C₃₁	—	2	2	no	—
39	C₂×C₄²×C₃₁	—	2	2	no	—
40	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₃₁	Q₈	1	1	yes	characteristic
51	C₂×C₄²×C₃₁	Q₈	1	1	yes	characteristic
52	C₃₁×C₄⋊C₈	—	2	2	no	—
53	C₃₁×C₄⋊C₈	—	2	2	no	—
54	C₃₁×C₂²⋊C₈	—	2	2	no	—
55	C₃₁×C₂²⋊C₈	—	2	2	no	—
56	C₃₁×#97	—	2	2	no	—
57	C₃₁×#97	—	2	2	no	—
58	C₃₁×#95	—	2	2	no	—
59	C₃₁×#95	—	2	2	no	—
60	C₃₁×#95	—	2	2	no	—
61	C₃₁×#95	—	2	2	no	—
62	C₃₁×#95	C₂×C₄	1	4	yes	—
63	C₃₁×#95	C₂×C₄	1	4	yes	—
64	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₃₁	—	2	2	no	—
66	C₂²×C₄×C₃₁	—	2	2	no	—
67	C₂²×C₄×C₃₁	—	2	4	no	—
68	C₂²×C₄×C₃₁	—	2	4	no	—
69	C₂²×C₄×C₃₁	—	4	2	no	—
70	C₂²×C₄×C₃₁	—	4	2	no	—
71	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
89	C₂×C₈×C₃₁	—	2	4	no	—
90	C₂×C₈×C₃₁	—	4	4	no	—
91	C₄⋊C₄×C₃₁	—	4	4	no	—
92	C₄⋊C₄×C₃₁	—	4	4	no	—
93	C₄⋊C₄×C₃₁	—	4	4	no	—
94	C₄⋊C₄×C₃₁	—	4	4	no	—
95	C₂²⋊C₄×C₃₁	—	4	2	no	—
96	C₂²⋊C₄×C₃₁	—	4	4	no	—
97	C₂²⋊C₄×C₃₁	—	4	2	no	—
98	C₄²×C₃₁	—	4	4	no	—
99	C₄²×C₃₁	—	4	4	no	—
100	C₄²×C₃₁	C₄²	1	1	yes	characteristic
101	C₄²×C₃₁	C₄²	1	1	yes	characteristic
102	C₄²×C₃₁	C₄²	1	1	yes	characteristic
103	C₄²×C₃₁	C₄²	1	1	yes	characteristic
104	C₄²×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
105	C₄²×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
106	C₄²×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
107	C₄²×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
108	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
111	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
112	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
113	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
114	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
115	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
116	#7984	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂³×C₃₁	—	4	1	no	—
118	C₂³×C₃₁	—	4	1	no	—
119	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂³×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂³×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
123	C₂³×C₃₁	#137	1	2	yes	—
124	C₂×C₄×C₃₁	—	2	2	no	—
125	C₂×C₄×C₃₁	—	2	2	no	—
126	C₂×C₄×C₃₁	—	2	1	no	—
127	C₂×C₄×C₃₁	—	2	1	no	—
128	C₂×C₄×C₃₁	—	2	1	no	—
129	C₂×C₄×C₃₁	—	2	1	no	—
130	C₂×C₄×C₃₁	—	2	2	no	—
131	C₂×C₄×C₃₁	—	2	2	no	—
132	C₂×C₄×C₃₁	—	2	2	no	—
133	C₂×C₄×C₃₁	—	2	2	no	—
134	C₂×C₄×C₃₁	—	2	2	no	—
135	C₂×C₄×C₃₁	—	2	2	no	—
136	C₂×C₄×C₃₁	—	2	2	no	—
137	C₂×C₄×C₃₁	—	2	2	no	—
138	C₂×C₄×C₃₁	—	4	1	no	—
139	C₂×C₄×C₃₁	—	4	1	no	—
140	C₂×C₄×C₃₁	—	4	1	no	—
141	C₂×C₄×C₃₁	—	4	1	no	—
142	C₂×C₄×C₃₁	—	4	1	no	—
143	C₂×C₄×C₃₁	—	4	1	no	—
144	C₂×C₄×C₃₁	—	4	4	no	—
145	C₂×C₄×C₃₁	—	4	4	no	—
146	C₂×C₄×C₃₁	—	4	4	no	—
147	C₂×C₄×C₃₁	—	4	4	no	—
148	C₂×C₄×C₃₁	—	4	4	no	—
149	C₂×C₄×C₃₁	—	4	4	no	—
150	C₂×C₄×C₃₁	#95	1	1	yes	characteristic
151	C₂×C₄×C₃₁	#95	1	1	yes	characteristic
152	C₂×C₄×C₃₁	#95	1	1	yes	characteristic
153	C₂×C₄×C₃₁	#95	1	1	yes	characteristic
154	C₂×C₄×C₃₁	#95	1	1	yes	characteristic
155	C₂×C₄×C₃₁	#95	1	1	yes	characteristic
156	C₂×C₄×C₃₁	#95	1	1	yes	characteristic
157	C₂×C₄×C₃₁	#95	1	1	yes	characteristic
158	C₂×C₄×C₃₁	C₂×C₄²	1	1	yes	characteristic
159	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₈×C₃₁	—	4	4	no	—
163	C₂×#432	C₂×C₃₁	1	1	yes	characteristic
164	#2285	C₂×C₃₁	1	1	yes	characteristic
165	#2283	C₂×C₃₁	1	1	yes	characteristic
166	#1289	C₂×C₃₁	1	4	yes	—
167	C₂²×C₃₁	—	2	1	no	—
168	C₂²×C₃₁	—	2	1	no	—
169	C₂²×C₃₁	—	2	1	no	—
170	C₂²×C₃₁	—	2	1	no	—
171	C₂²×C₃₁	—	2	1	no	—
172	C₂²×C₃₁	—	2	1	no	—
173	C₂²×C₃₁	—	4	2	no	—
174	C₂²×C₃₁	—	4	2	no	—
175	C₂²×C₃₁	C₂×#95	1	1	yes	characteristic
176	C₂²×C₃₁	#417	1	2	yes	—
177	C₂²×C₃₁	#418	1	1	yes	characteristic
178	C₂²×C₃₁	#419	1	1	yes	characteristic
179	C₂²×C₃₁	#428	1	2	yes	—
180	C₄×C₃₁	—	2	1	no	—
181	C₄×C₃₁	—	2	1	no	—
182	C₄×C₃₁	—	2	1	no	—
183	C₄×C₃₁	—	2	1	no	—
184	C₄×C₃₁	—	2	1	no	—
185	C₄×C₃₁	—	2	1	no	—
186	C₄×C₃₁	—	2	1	no	—
187	C₄×C₃₁	—	2	1	no	—
188	C₄×C₃₁	—	2	1	no	—
189	C₄×C₃₁	—	2	1	no	—
190	C₄×C₃₁	—	8	4	no	—
191	C₄×C₃₁	—	8	4	no	—
192	C₄×C₃₁	H(3,ℤ/4)	1	2	yes	—
193	C₄×C₃₁	#410	1	2	yes	—
194	C₂×#117	—	2	1	no	—
195	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
196	#432	—	2	1	no	—
197	#432	—	2	1	no	—
198	#432	—	2	1	no	—
199	#432	—	2	1	no	—
200	C₂×C₄⋊C₈	C₄×C₃₁	1	2	yes	complemented
201	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
202	C₂×#97	C₄×C₃₁	1	2	yes	complemented
203	#384	—	2	1	no	—
204	#383	C₄×C₃₁	1	2	yes	complemented
205	#382	—	2	1	no	—
206	#382	C₄×C₃₁	1	2	yes	complemented
207	#381	—	2	1	no	—
208	#380	—	2	1	no	—
209	#380	C₂²×C₃₁	1	2	yes	—
210	#380	C₂²×C₃₁	1	2	yes	—
211	C₄×C₄⋊C₄	—	2	1	no	—
212	C₄×C₄⋊C₄	—	2	1	no	—
213	C₄×C₄⋊C₄	C₄×C₃₁	1	2	yes	complemented
214	C₄×C₂²⋊C₄	—	2	1	no	—
215	#376	C₄×C₃₁	1	2	yes	complemented
216	C₂×C₃₁	—	2	1	no	—
217	C₂×C₃₁	—	2	2	no	—
218	C₂×C₃₁	—	2	1	no	—
219	C₂×C₃₁	—	2	2	no	—
220	C₂×C₃₁	C₂×H(3,ℤ/4)	1	1	yes	characteristic
221	C₂×C₃₁	#1736	1	1	yes	characteristic
222	C₂×C₃₁	#1740	1	1	yes	characteristic
223	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
224	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
225	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
226	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
227	#117	—	4	4	no	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	—	2	2	no	—
232	C₂×C₂²⋊C₄	—	2	2	no	—
233	C₂×C₂²⋊C₄	—	2	2	no	—
234	C₂×C₄²	—	2	2	no	—
235	C₂×C₄²	—	2	2	no	—
236	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
237	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
238	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
239	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
240	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
241	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
242	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
243	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
244	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
245	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
246	C₂×C₄²	Q₈×C₃₁	1	1	yes	characteristic
247	C₂×C₄²	Q₈×C₃₁	1	1	yes	characteristic
248	C₄⋊C₈	—	2	2	no	—
249	C₄⋊C₈	—	2	2	no	—
250	C₂²⋊C₈	—	2	2	no	—
251	C₂²⋊C₈	—	2	2	no	—
252	#97	—	2	2	no	—
253	#97	—	2	2	no	—
254	#95	—	2	2	no	—
255	#95	—	2	2	no	—
256	#95	—	2	2	no	—
257	#95	—	2	2	no	—
258	#95	C₂×C₄×C₃₁	1	4	yes	—
259	#95	C₂×C₄×C₃₁	1	4	yes	—
260	C₃₁	#7984	1	1	yes	characteristic, direct product factor, Sylow
261	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	4	2	no	—
267	C₂²×C₄	—	4	2	no	—
268	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
269	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
270	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
271	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
272	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
273	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
274	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
275	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
276	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
277	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
278	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
279	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
280	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
281	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
282	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
285	C₂²×C₄	C₂×Q₈×C₃₁	1	1	yes	characteristic
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	4	4	no	—
288	C₄⋊C₄	—	4	4	no	—
289	C₄⋊C₄	—	4	4	no	—
290	C₄⋊C₄	—	4	4	no	—
291	C₄⋊C₄	—	4	4	no	—
292	C₂²⋊C₄	—	4	2	no	—
293	C₂²⋊C₄	—	4	4	no	—
294	C₂²⋊C₄	—	4	2	no	—
295	C₄²	—	4	4	no	—
296	C₄²	—	4	4	no	—
297	C₄²	C₄²×C₃₁	1	1	yes	characteristic
298	C₄²	C₄²×C₃₁	1	1	yes	characteristic
299	C₄²	C₄²×C₃₁	1	1	yes	characteristic
300	C₄²	C₄²×C₃₁	1	1	yes	characteristic
301	C₄²	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
302	C₄²	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
303	C₄²	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
304	C₄²	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
305	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
306	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
307	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
308	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
309	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
310	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
311	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
312	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
313	C₂³	—	4	1	no	—
314	C₂³	—	4	1	no	—
315	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
316	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
317	C₂³	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
318	C₂³	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
319	C₂³	C₃₁×#137	1	2	yes	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	C₃₁×#95	1	1	yes	characteristic
347	C₂×C₄	C₃₁×#95	1	1	yes	characteristic
348	C₂×C₄	C₃₁×#95	1	1	yes	characteristic
349	C₂×C₄	C₃₁×#95	1	1	yes	characteristic
350	C₂×C₄	C₃₁×#95	1	1	yes	characteristic
351	C₂×C₄	C₃₁×#95	1	1	yes	characteristic
352	C₂×C₄	C₃₁×#95	1	1	yes	characteristic
353	C₂×C₄	C₃₁×#95	1	1	yes	characteristic
354	C₂×C₄	C₂×C₄²×C₃₁	1	1	yes	characteristic
355	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
356	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
357	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
358	C₈	—	4	4	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	4	2	no	—
366	C₂²	—	4	2	no	—
367	C₂²	C₂×C₃₁×#95	1	1	yes	characteristic
368	C₂²	C₃₁×#417	1	2	yes	—
369	C₂²	C₃₁×#418	1	1	yes	characteristic
370	C₂²	C₃₁×#419	1	1	yes	characteristic
371	C₂²	C₃₁×#428	1	2	yes	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	8	4	no	—
383	C₄	—	8	4	no	—
384	C₄	C₃₁×H(3,ℤ/4)	1	2	yes	—
385	C₄	C₃₁×#410	1	2	yes	—
386	C₂	—	2	1	no	—
387	C₂	—	2	2	no	—
388	C₂	—	2	1	no	—
389	C₂	—	2	2	no	—
390	C₂	C₂×C₃₁×H(3,ℤ/4)	1	1	yes	characteristic
391	C₂	C₃₁×#1736	1	1	yes	characteristic
392	C₂	C₃₁×#1740	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂×#95
commutator	C₂×C₄	C₂×C₄²×C₃₁
Frattini, cosocle	C₂³×C₄	C₂³×C₃₁
prime radical	C₂⁴×C₃₁	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
11. C₂×C₃₁×C₄⋊C₈	C₄	semidirect
13. C₂×C₃₁×#97	C₄	semidirect
15. C₃₁×#383	C₄	semidirect
17. C₃₁×#382	C₄	semidirect
24. C₄×C₄⋊C₄×C₃₁	C₄	semidirect
26. C₃₁×#376	C₄	semidirect
116. #7984	C₃₁	direct (N × H)
200. C₂×C₄⋊C₈	C₄×C₃₁	semidirect
202. C₂×#97	C₄×C₃₁	semidirect
204. #383	C₄×C₃₁	semidirect
206. #382	C₄×C₃₁	semidirect
213. C₄×C₄⋊C₄	C₄×C₃₁	semidirect
215. #376	C₄×C₃₁	semidirect
260. C₃₁	#7984	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×#432	2
C₃₁×#2285	2
C₃₁×#2283	2
C₃₁×#1289	2
#7984	31

Subgroups — C31×#7984 #21464743

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#7984 #21464743