Subgroups — C₃₁×#7932 #21464691

Order 7936.

666 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#431	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#431	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1283	C₂	1	4	yes	maximal, complemented
5	C₂²×M₁₆×C₃₁	C₄	1	2	yes	—
6	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
7	C₃₁×#431	—	2	1	no	—
8	C₃₁×#431	—	2	1	no	—
9	C₃₁×#431	—	2	1	no	—
10	C₃₁×#431	—	2	1	no	—
11	C₃₁×#431	—	2	1	no	—
12	C₃₁×#431	—	2	1	no	—
13	C₃₁×#431	C₄	1	2	yes	—
14	C₃₁×#431	C₂²	1	2	yes	—
15	C₂×C₃₁×C₄⋊C₈	—	2	1	no	—
16	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₃₁×C₂²⋊C₈	C₄	1	2	yes	—
18	C₂×C₃₁×C₂²⋊C₈	C₄	1	2	yes	—
19	C₄×M₁₆×C₃₁	—	2	1	no	—
20	C₄×M₁₆×C₃₁	—	2	1	no	—
21	C₄×M₁₆×C₃₁	C₄	1	2	yes	—
22	C₄×M₁₆×C₃₁	C₂²	1	2	yes	—
23	C₂×C₃₁×#97	—	2	1	no	—
24	C₂×C₄×C₈×C₃₁	—	2	1	no	—
25	C₂×C₄×C₈×C₃₁	—	2	1	no	—
26	C₂×C₄×C₈×C₃₁	C₄	1	2	yes	—
27	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
30	C₂×M₁₆×C₃₁	—	2	2	no	—
31	C₂×M₁₆×C₃₁	—	2	4	no	—
32	C₂×M₁₆×C₃₁	C₈	1	8	yes	complemented
33	C₂×M₁₆×C₃₁	C₂×C₄	1	4	yes	—
34	C₂²×C₈×C₃₁	—	2	2	no	—
35	C₂²×C₈×C₃₁	—	2	2	no	—
36	C₂²×C₈×C₃₁	C₂×C₄	1	4	yes	—
37	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₃₁	Q₈	1	1	yes	characteristic
47	C₂×C₄²×C₃₁	Q₈	1	1	yes	characteristic
48	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
49	C₃₁×C₄⋊C₈	—	2	2	no	—
50	C₃₁×C₄⋊C₈	—	2	2	no	—
51	C₃₁×C₄⋊C₈	—	2	2	no	—
52	C₃₁×C₄⋊C₈	—	2	2	no	—
53	C₃₁×C₂²⋊C₈	—	2	2	no	—
54	C₃₁×C₂²⋊C₈	—	2	2	no	—
55	C₃₁×C₂²⋊C₈	—	2	2	no	—
56	C₃₁×C₂²⋊C₈	C₂×C₄	1	4	yes	—
57	C₃₁×#97	—	2	2	no	—
58	C₃₁×#97	—	2	2	no	—
59	C₄×C₈×C₃₁	—	2	2	no	—
60	C₄×C₈×C₃₁	—	2	2	no	—
61	C₄×C₈×C₃₁	—	2	2	no	—
62	C₄×C₈×C₃₁	—	2	2	no	—
63	C₄×C₈×C₃₁	—	2	2	no	—
64	C₄×C₈×C₃₁	—	2	2	no	—
65	C₂⁴×C₃₁	C₄²	1	1	yes	characteristic
66	C₂²×C₄×C₃₁	—	4	2	no	—
67	C₂²×C₄×C₃₁	—	4	2	no	—
68	C₂²×C₄×C₃₁	C₄²	1	1	yes	characteristic
69	C₂²×C₄×C₃₁	C₄²	1	1	yes	characteristic
70	C₂²×C₄×C₃₁	C₄²	1	1	yes	characteristic
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	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₃₁	C₄⋊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	C₂×C₈	1	4	yes	—
84	C₂²×C₄×C₃₁	M₁₆	1	4	yes	—
85	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
88	M₁₆×C₃₁	—	2	8	no	—
89	M₁₆×C₃₁	—	2	4	no	—
90	M₁₆×C₃₁	C₂×C₈	1	8	yes	complemented
91	C₂×C₈×C₃₁	—	2	8	no	—
92	C₂×C₈×C₃₁	—	2	4	no	—
93	C₂×C₈×C₃₁	—	2	4	no	—
94	C₂×C₈×C₃₁	—	2	4	no	—
95	C₂×C₈×C₃₁	—	4	4	no	—
96	C₂×C₈×C₃₁	—	4	4	no	—
97	C₄²×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
98	C₄²×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
101	C₄²×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
102	C₄²×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
103	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₃₁	C₂×Q₈	1	1	yes	characteristic
113	#7932	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
114	C₂³×C₃₁	—	4	1	no	—
115	C₂³×C₃₁	—	4	1	no	—
116	C₂³×C₃₁	#95	1	1	yes	characteristic
117	C₂³×C₃₁	#95	1	1	yes	characteristic
118	C₂³×C₃₁	C₄×C₈	1	2	yes	—
119	C₂³×C₃₁	#97	1	2	yes	—
120	C₂³×C₃₁	C₂×C₄²	1	1	yes	characteristic
121	C₂×C₄×C₃₁	—	2	2	no	—
122	C₂×C₄×C₃₁	—	2	2	no	—
123	C₂×C₄×C₃₁	—	2	2	no	—
124	C₂×C₄×C₃₁	—	2	2	no	—
125	C₂×C₄×C₃₁	—	2	2	no	—
126	C₂×C₄×C₃₁	—	2	2	no	—
127	C₂×C₄×C₃₁	—	4	1	no	—
128	C₂×C₄×C₃₁	—	4	1	no	—
129	C₂×C₄×C₃₁	—	4	1	no	—
130	C₂×C₄×C₃₁	—	4	1	no	—
131	C₂×C₄×C₃₁	—	4	1	no	—
132	C₂×C₄×C₃₁	—	4	1	no	—
133	C₂×C₄×C₃₁	#95	1	1	yes	characteristic
134	C₂×C₄×C₃₁	#95	1	1	yes	characteristic
135	C₂×C₄×C₃₁	#95	1	1	yes	characteristic
136	C₂×C₄×C₃₁	#95	1	1	yes	characteristic
137	C₂×C₄×C₃₁	#95	1	1	yes	characteristic
138	C₂×C₄×C₃₁	#95	1	1	yes	characteristic
139	C₂×C₄×C₃₁	C₄×C₈	1	2	yes	—
140	C₂×C₄×C₃₁	#97	1	2	yes	—
141	C₂×C₄×C₃₁	C₂²⋊C₈	1	4	yes	—
142	C₂×C₄×C₃₁	C₂²⋊C₈	1	4	yes	—
143	C₂×C₄×C₃₁	C₄⋊C₈	1	4	yes	—
144	C₂×C₄×C₃₁	C₄⋊C₈	1	4	yes	—
145	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₃₁	C₂²×C₈	1	2	yes	—
152	C₂×C₄×C₃₁	C₂×M₁₆	1	2	yes	—
153	C₈×C₃₁	—	2	8	no	—
154	C₈×C₃₁	—	4	4	no	—
155	C₈×C₃₁	—	4	4	no	—
156	C₂×#431	C₂×C₃₁	1	1	yes	characteristic
157	C₂×#431	C₂×C₃₁	1	1	yes	characteristic
158	C₂×C₄×M₁₆	C₂×C₃₁	1	1	yes	characteristic
159	#1283	C₂×C₃₁	1	4	yes	complemented
160	C₂²×C₃₁	—	2	1	no	—
161	C₂²×C₃₁	—	2	1	no	—
162	C₂²×C₃₁	—	2	1	no	—
163	C₂²×C₃₁	—	2	1	no	—
164	C₂²×C₃₁	—	2	1	no	—
165	C₂²×C₃₁	—	2	1	no	—
166	C₂²×C₃₁	—	4	2	no	—
167	C₂²×C₃₁	—	4	2	no	—
168	C₂²×C₃₁	#336	1	2	yes	—
169	C₂²×C₃₁	#336	1	2	yes	—
170	C₂²×C₃₁	C₂×#95	1	1	yes	characteristic
171	C₂²×C₃₁	C₂×C₄×C₈	1	1	yes	characteristic
172	C₂²×C₃₁	C₂×#97	1	1	yes	characteristic
173	C₄×C₃₁	—	2	1	no	—
174	C₄×C₃₁	—	2	1	no	—
175	C₄×C₃₁	—	2	1	no	—
176	C₄×C₃₁	—	2	1	no	—
177	C₄×C₃₁	—	2	1	no	—
178	C₄×C₃₁	—	2	1	no	—
179	C₄×C₃₁	#336	1	2	yes	—
180	C₄×C₃₁	#336	1	2	yes	—
181	C₄×C₃₁	#344	1	2	yes	—
182	C₄×C₃₁	C₂×C₂²⋊C₈	1	2	yes	—
183	C₄×C₃₁	#413	1	2	yes	—
184	C₄×C₃₁	C₂×C₄⋊C₈	1	2	yes	—
185	C₂²×M₁₆	C₄×C₃₁	1	2	yes	—
186	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
187	#431	—	2	1	no	—
188	#431	—	2	1	no	—
189	#431	—	2	1	no	—
190	#431	—	2	1	no	—
191	#431	—	2	1	no	—
192	#431	—	2	1	no	—
193	#431	C₄×C₃₁	1	2	yes	—
194	#431	C₂²×C₃₁	1	2	yes	—
195	C₂×C₄⋊C₈	—	2	1	no	—
196	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
197	C₂×C₂²⋊C₈	C₄×C₃₁	1	2	yes	—
198	C₂×C₂²⋊C₈	C₄×C₃₁	1	2	yes	—
199	C₄×M₁₆	—	2	1	no	—
200	C₄×M₁₆	—	2	1	no	—
201	C₄×M₁₆	C₄×C₃₁	1	2	yes	—
202	C₄×M₁₆	C₂²×C₃₁	1	2	yes	—
203	C₂×#97	—	2	1	no	—
204	C₂×C₄×C₈	—	2	1	no	—
205	C₂×C₄×C₈	—	2	1	no	—
206	C₂×C₄×C₈	C₄×C₃₁	1	2	yes	—
207	C₂×C₃₁	—	2	2	no	—
208	C₂×C₃₁	—	2	2	no	—
209	C₂×C₃₁	—	2	1	no	—
210	C₂×C₃₁	—	2	1	no	—
211	C₂×C₃₁	C₂×#336	1	1	yes	characteristic
212	C₂×C₃₁	#1742	1	1	yes	characteristic
213	C₂×C₃₁	C₂×#344	1	1	yes	characteristic
214	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
215	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
216	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
217	C₂×M₁₆	—	2	2	no	—
218	C₂×M₁₆	—	2	4	no	—
219	C₂×M₁₆	C₈×C₃₁	1	8	yes	complemented
220	C₂×M₁₆	C₂×C₄×C₃₁	1	4	yes	—
221	C₂²×C₈	—	2	2	no	—
222	C₂²×C₈	—	2	2	no	—
223	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
224	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
225	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
226	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
227	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
228	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
229	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
230	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
231	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
232	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
233	C₂×C₄²	Q₈×C₃₁	1	1	yes	characteristic
234	C₂×C₄²	Q₈×C₃₁	1	1	yes	characteristic
235	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
236	C₄⋊C₈	—	2	2	no	—
237	C₄⋊C₈	—	2	2	no	—
238	C₄⋊C₈	—	2	2	no	—
239	C₄⋊C₈	—	2	2	no	—
240	C₂²⋊C₈	—	2	2	no	—
241	C₂²⋊C₈	—	2	2	no	—
242	C₂²⋊C₈	—	2	2	no	—
243	C₂²⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
244	#97	—	2	2	no	—
245	#97	—	2	2	no	—
246	C₄×C₈	—	2	2	no	—
247	C₄×C₈	—	2	2	no	—
248	C₄×C₈	—	2	2	no	—
249	C₄×C₈	—	2	2	no	—
250	C₄×C₈	—	2	2	no	—
251	C₄×C₈	—	2	2	no	—
252	C₃₁	#7932	1	1	yes	characteristic, direct product factor, Sylow
253	C₂⁴	C₄²×C₃₁	1	1	yes	characteristic
254	C₂²×C₄	—	4	2	no	—
255	C₂²×C₄	—	4	2	no	—
256	C₂²×C₄	C₄²×C₃₁	1	1	yes	characteristic
257	C₂²×C₄	C₄²×C₃₁	1	1	yes	characteristic
258	C₂²×C₄	C₄²×C₃₁	1	1	yes	characteristic
259	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
260	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
261	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
262	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
263	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
264	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
265	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
266	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
267	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
268	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
269	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
270	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
271	C₂²×C₄	C₂×C₈×C₃₁	1	4	yes	—
272	C₂²×C₄	M₁₆×C₃₁	1	4	yes	—
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	M₁₆	—	2	8	no	—
277	M₁₆	—	2	4	no	—
278	M₁₆	C₂×C₈×C₃₁	1	8	yes	complemented
279	C₂×C₈	—	2	8	no	—
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	—	2	4	no	—
283	C₂×C₈	—	4	4	no	—
284	C₂×C₈	—	4	4	no	—
285	C₄²	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
286	C₄²	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
287	C₄²	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
288	C₄²	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
289	C₄²	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
290	C₄²	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
291	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
292	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
293	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
294	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
295	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
296	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
297	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
298	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
299	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
300	C₄²	C₂×Q₈×C₃₁	1	1	yes	characteristic
301	C₂³	—	4	1	no	—
302	C₂³	—	4	1	no	—
303	C₂³	C₃₁×#95	1	1	yes	characteristic
304	C₂³	C₃₁×#95	1	1	yes	characteristic
305	C₂³	C₄×C₈×C₃₁	1	2	yes	—
306	C₂³	C₃₁×#97	1	2	yes	—
307	C₂³	C₂×C₄²×C₃₁	1	1	yes	characteristic
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	4	1	no	—
315	C₂×C₄	—	4	1	no	—
316	C₂×C₄	—	4	1	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	1	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	C₃₁×#95	1	1	yes	characteristic
321	C₂×C₄	C₃₁×#95	1	1	yes	characteristic
322	C₂×C₄	C₃₁×#95	1	1	yes	characteristic
323	C₂×C₄	C₃₁×#95	1	1	yes	characteristic
324	C₂×C₄	C₃₁×#95	1	1	yes	characteristic
325	C₂×C₄	C₃₁×#95	1	1	yes	characteristic
326	C₂×C₄	C₄×C₈×C₃₁	1	2	yes	—
327	C₂×C₄	C₃₁×#97	1	2	yes	—
328	C₂×C₄	C₃₁×C₂²⋊C₈	1	4	yes	—
329	C₂×C₄	C₃₁×C₂²⋊C₈	1	4	yes	—
330	C₂×C₄	C₃₁×C₄⋊C₈	1	4	yes	—
331	C₂×C₄	C₃₁×C₄⋊C₈	1	4	yes	—
332	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
333	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
334	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
335	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
336	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
337	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
338	C₂×C₄	C₂²×C₈×C₃₁	1	2	yes	—
339	C₂×C₄	C₂×M₁₆×C₃₁	1	2	yes	—
340	C₈	—	2	8	no	—
341	C₈	—	4	4	no	—
342	C₈	—	4	4	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	4	2	no	—
350	C₂²	—	4	2	no	—
351	C₂²	C₃₁×#336	1	2	yes	—
352	C₂²	C₃₁×#336	1	2	yes	—
353	C₂²	C₂×C₃₁×#95	1	1	yes	characteristic
354	C₂²	C₂×C₄×C₈×C₃₁	1	1	yes	characteristic
355	C₂²	C₂×C₃₁×#97	1	1	yes	characteristic
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	C₃₁×#336	1	2	yes	—
363	C₄	C₃₁×#336	1	2	yes	—
364	C₄	C₃₁×#344	1	2	yes	—
365	C₄	C₂×C₃₁×C₂²⋊C₈	1	2	yes	—
366	C₄	C₃₁×#413	1	2	yes	—
367	C₄	C₂×C₃₁×C₄⋊C₈	1	2	yes	—
368	C₂	—	2	1	no	—
369	C₂	—	2	1	no	—
370	C₂	—	2	2	no	—
371	C₂	—	2	2	no	—
372	C₂	C₂×C₃₁×#336	1	1	yes	characteristic
373	C₂	C₃₁×#1742	1	1	yes	characteristic
374	C₂	C₂×C₃₁×#344	1	1	yes	characteristic

	subgroup	G/H
center	C₄²×C₃₁	C₂²⋊C₄
commutator	C₂²	C₂×C₄×C₈×C₃₁
Frattini, cosocle	C₂×C₄²	C₂³×C₃₁
socle	C₂²×C₃₁	C₂×#95
prime radical	C₂⁴×C₃₁	C₄²
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₃₁×#1283	C₂	semidirect
32. C₂×M₁₆×C₃₁	C₈	semidirect
90. M₁₆×C₃₁	C₂×C₈	semidirect
113. #7932	C₃₁	direct (N × H)
159. #1283	C₂×C₃₁	semidirect
219. C₂×M₁₆	C₈×C₃₁	semidirect
252. C₃₁	#7932	direct (N × H)
278. M₁₆	C₂×C₈×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×#431	2
C₂×C₄×M₁₆×C₃₁	2
C₃₁×#1283	2
#7932	31

Subgroups — C31×#7932 #21464691

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#7932 #21464691