Subgroups — C₂×C₃₁×#1515 #21474316

Order 7936.

1022 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#432	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₁×#383	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1515	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃₁×#328	C₂	1	4	yes	maximal
6	C₃₁×#533	—	2	2	no	—
7	C₃₁×#533	—	2	2	no	—
8	C₃₁×#533	C₄	1	4	yes	complemented
9	C₃₁×#533	C₂²	1	4	yes	—
10	C₂×C₃₁×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
11	C₂×C₃₁×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
12	C₂×C₃₁×#125	—	2	1	no	—
13	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
14	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₃₁	—	2	1	no	—
16	C₂×C₄×Q₈×C₃₁	C₄	1	2	yes	complemented
17	C₂×C₃₁×#117	—	2	1	no	—
18	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
19	C₃₁×#432	—	2	2	no	—
20	C₃₁×#432	C₂²	1	4	yes	—
21	C₂×C₃₁×C₄⋊C₈	—	2	1	no	—
22	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₂×C₃₁×#97	—	2	1	no	—
24	C₃₁×#383	—	2	2	no	—
25	C₃₁×#383	C₂²	1	4	yes	—
26	C₂×C₃₁×#95	—	2	1	no	—
27	C₂×C₃₁×#95	—	2	1	no	—
28	C₂×C₃₁×#95	C₂²	1	2	yes	—
29	C₃₁×#328	C₂²	1	16	yes	—
30	C₂²×Q₈×C₃₁	—	2	1	no	—
31	C₂²×Q₈×C₃₁	C₂×C₄	1	2	yes	—
32	C₂³×C₄×C₃₁	—	2	2	no	—
33	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
36	C₂²×C₈×C₃₁	—	2	2	no	—
37	C₃₁×C₄⋊Q₈	—	2	2	no	—
38	C₃₁×C₄⋊Q₈	—	2	2	no	—
39	C₃₁×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
40	C₃₁×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
41	C₃₁×#125	—	2	4	no	—
42	C₃₁×#125	—	2	4	no	—
43	C₃₁×C₂²⋊Q₈	—	2	4	no	—
44	C₃₁×C₂²⋊Q₈	—	2	4	no	—
45	C₃₁×C₂²⋊Q₈	—	2	2	no	—
46	C₃₁×C₂²⋊Q₈	—	2	2	no	—
47	C₃₁×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
48	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
49	C₄×Q₈×C₃₁	—	2	4	no	—
50	C₄×Q₈×C₃₁	—	2	4	no	—
51	C₄×Q₈×C₃₁	—	2	4	no	—
52	C₄×Q₈×C₃₁	C₂×C₄	1	8	yes	complemented
53	C₃₁×#117	—	2	4	no	—
54	C₃₁×#117	—	2	4	no	—
55	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
56	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
57	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
61	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
62	C₂×C₄²×C₃₁	—	2	2	no	—
63	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₃₁	D₄	1	2	yes	—
67	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₃₁	D₄	1	2	yes	—
70	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
71	C₃₁×C₄⋊C₈	—	2	4	no	—
72	C₃₁×C₂²⋊C₈	—	2	2	no	—
73	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
74	C₃₁×#97	—	2	4	no	—
75	C₃₁×#95	—	2	4	no	—
76	C₃₁×#95	—	2	4	no	—
77	C₃₁×#95	—	2	2	no	—
78	C₃₁×#95	C₂³	1	4	yes	—
79	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
80	C₂×Q₈×C₃₁	—	2	2	no	—
81	C₂×Q₈×C₃₁	—	2	4	no	—
82	C₂×Q₈×C₃₁	—	4	4	no	—
83	C₂×Q₈×C₃₁	—	4	4	no	—
84	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
85	C₂²×C₄×C₃₁	—	2	4	no	—
86	C₂²×C₄×C₃₁	—	2	2	no	—
87	C₂²×C₄×C₃₁	—	2	2	no	—
88	C₂²×C₄×C₃₁	—	2	4	no	—
89	C₂²×C₄×C₃₁	—	4	2	no	—
90	C₂²×C₄×C₃₁	—	4	2	no	—
91	C₂²×C₄×C₃₁	—	4	4	no	—
92	C₂²×C₄×C₃₁	—	4	4	no	—
93	C₂²×C₄×C₃₁	—	4	4	no	—
94	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
95	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
99	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
100	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
108	C₂×C₈×C₃₁	—	2	4	no	—
109	C₂×C₈×C₃₁	—	4	4	no	—
110	C₄⋊C₄×C₃₁	—	2	4	no	—
111	C₄⋊C₄×C₃₁	—	2	4	no	—
112	C₄⋊C₄×C₃₁	—	2	4	no	—
113	C₄⋊C₄×C₃₁	—	2	4	no	—
114	C₄⋊C₄×C₃₁	—	2	8	no	—
115	C₄⋊C₄×C₃₁	—	2	2	no	—
116	C₄⋊C₄×C₃₁	—	2	4	no	—
117	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
118	C₂²⋊C₄×C₃₁	—	2	4	no	—
119	C₂²⋊C₄×C₃₁	—	2	4	no	—
120	C₄²×C₃₁	—	2	8	no	—
121	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
122	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
123	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
124	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
125	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
126	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
127	C₄²×C₃₁	C₂×D₄	1	2	yes	—
128	C₄²×C₃₁	C₂×D₄	1	2	yes	—
129	C₂×#1515	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂³×C₃₁	—	2	2	no	—
131	C₂³×C₃₁	—	2	2	no	—
132	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂³×C₃₁	#137	1	4	yes	—
135	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
136	Q₈×C₃₁	—	4	4	no	—
137	Q₈×C₃₁	—	4	4	no	—
138	Q₈×C₃₁	—	4	8	no	—
139	C₂×C₄×C₃₁	—	2	4	no	—
140	C₂×C₄×C₃₁	—	2	2	no	—
141	C₂×C₄×C₃₁	—	2	2	no	—
142	C₂×C₄×C₃₁	—	2	4	no	—
143	C₂×C₄×C₃₁	—	2	2	no	—
144	C₂×C₄×C₃₁	—	2	2	no	—
145	C₂×C₄×C₃₁	—	2	2	no	—
146	C₂×C₄×C₃₁	—	2	2	no	—
147	C₂×C₄×C₃₁	—	2	4	no	—
148	C₂×C₄×C₃₁	—	2	4	no	—
149	C₂×C₄×C₃₁	—	4	2	no	—
150	C₂×C₄×C₃₁	—	4	1	no	—
151	C₂×C₄×C₃₁	—	4	1	no	—
152	C₂×C₄×C₃₁	—	4	1	no	—
153	C₂×C₄×C₃₁	—	4	2	no	—
154	C₂×C₄×C₃₁	—	4	1	no	—
155	C₂×C₄×C₃₁	—	4	4	no	—
156	C₂×C₄×C₃₁	—	4	4	no	—
157	C₂×C₄×C₃₁	—	4	4	no	—
158	C₂×C₄×C₃₁	—	4	4	no	—
159	C₂×C₄×C₃₁	—	4	4	no	—
160	C₂×C₄×C₃₁	—	8	8	no	—
161	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
169	C₈×C₃₁	—	4	4	no	—
170	C₂×#533	C₂×C₃₁	1	1	yes	characteristic
171	C₂×#432	C₂×C₃₁	1	1	yes	characteristic
172	C₂×#383	C₂×C₃₁	1	1	yes	characteristic
173	#1515	C₂×C₃₁	1	8	yes	direct product factor
174	C₂×#328	C₂×C₃₁	1	4	yes	—
175	C₂²×C₃₁	—	2	1	no	—
176	C₂²×C₃₁	—	2	1	no	—
177	C₂²×C₃₁	—	2	1	no	—
178	C₂²×C₃₁	—	2	1	no	—
179	C₂²×C₃₁	—	2	8	no	—
180	C₂²×C₃₁	#410	1	2	yes	—
181	C₂²×C₃₁	#419	1	2	yes	—
182	C₂²×C₃₁	#419	1	2	yes	—
183	C₂²×C₃₁	#421	1	2	yes	—
184	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
185	C₂²×C₃₁	C₂×#137	1	2	yes	—
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	—	2	2	no	—
191	C₄×C₃₁	—	2	2	no	—
192	C₄×C₃₁	—	2	2	no	—
193	C₄×C₃₁	—	2	2	no	—
194	C₄×C₃₁	—	4	4	no	—
195	C₄×C₃₁	—	4	4	no	—
196	C₄×C₃₁	—	8	4	no	—
197	#533	—	2	2	no	—
198	#533	—	2	2	no	—
199	#533	C₄×C₃₁	1	4	yes	complemented
200	#533	C₂²×C₃₁	1	4	yes	—
201	C₂×C₄⋊Q₈	C₄×C₃₁	1	1	yes	characteristic, complemented
202	C₂×C₄⋊Q₈	C₄×C₃₁	1	1	yes	characteristic, complemented
203	C₂×#125	—	2	1	no	—
204	C₂×C₂²⋊Q₈	—	2	1	no	—
205	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
206	C₂×C₄×Q₈	—	2	1	no	—
207	C₂×C₄×Q₈	C₄×C₃₁	1	2	yes	complemented
208	C₂×#117	—	2	1	no	—
209	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
210	#432	—	2	2	no	—
211	#432	C₂²×C₃₁	1	4	yes	—
212	C₂×C₄⋊C₈	—	2	1	no	—
213	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
214	C₂×#97	—	2	1	no	—
215	#383	—	2	2	no	—
216	#383	C₂²×C₃₁	1	4	yes	—
217	C₂×#95	—	2	1	no	—
218	C₂×#95	—	2	1	no	—
219	C₂×#95	C₂²×C₃₁	1	2	yes	—
220	#328	C₂²×C₃₁	1	16	yes	—
221	C₂×C₃₁	—	2	2	no	—
222	C₂×C₃₁	—	2	2	no	—
223	C₂×C₃₁	#1515	1	4	yes	direct product factor
224	C₂×C₃₁	C₂×#410	1	1	yes	characteristic
225	C₂×C₃₁	C₂×#419	1	1	yes	characteristic
226	C₂×C₃₁	C₂×#421	1	1	yes	characteristic
227	C₂²×Q₈	—	2	1	no	—
228	C₂²×Q₈	C₂×C₄×C₃₁	1	2	yes	—
229	C₂³×C₄	—	2	2	no	—
230	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
231	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
232	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
233	C₂²×C₈	—	2	2	no	—
234	C₄⋊Q₈	—	2	2	no	—
235	C₄⋊Q₈	—	2	2	no	—
236	C₄⋊Q₈	C₂×C₄×C₃₁	1	4	yes	complemented
237	C₄⋊Q₈	C₂×C₄×C₃₁	1	4	yes	complemented
238	#125	—	2	4	no	—
239	#125	—	2	4	no	—
240	C₂²⋊Q₈	—	2	4	no	—
241	C₂²⋊Q₈	—	2	4	no	—
242	C₂²⋊Q₈	—	2	2	no	—
243	C₂²⋊Q₈	—	2	2	no	—
244	C₂²⋊Q₈	C₂×C₄×C₃₁	1	4	yes	—
245	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
246	C₄×Q₈	—	2	4	no	—
247	C₄×Q₈	—	2	4	no	—
248	C₄×Q₈	—	2	4	no	—
249	C₄×Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
250	#117	—	2	4	no	—
251	#117	—	2	4	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₄²	—	2	2	no	—
260	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
261	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
262	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
263	C₂×C₄²	D₄×C₃₁	1	2	yes	—
264	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
265	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
266	C₂×C₄²	D₄×C₃₁	1	2	yes	—
267	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
268	C₄⋊C₈	—	2	4	no	—
269	C₂²⋊C₈	—	2	2	no	—
270	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
271	#97	—	2	4	no	—
272	#95	—	2	4	no	—
273	#95	—	2	4	no	—
274	#95	—	2	2	no	—
275	#95	C₂³×C₃₁	1	4	yes	—
276	C₃₁	C₂×#1515	1	1	yes	characteristic, direct product factor, Sylow
277	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	4	no	—
280	C₂×Q₈	—	4	4	no	—
281	C₂×Q₈	—	4	4	no	—
282	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	—	4	4	no	—
290	C₂²×C₄	—	4	4	no	—
291	C₂²×C₄	—	4	4	no	—
292	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
293	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
294	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
295	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
296	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
297	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
298	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
299	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
305	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
306	C₂×C₈	—	2	4	no	—
307	C₂×C₈	—	4	4	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	2	4	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	8	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
316	C₂²⋊C₄	—	2	4	no	—
317	C₂²⋊C₄	—	2	4	no	—
318	C₄²	—	2	8	no	—
319	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
320	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
321	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
322	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
323	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
324	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
325	C₄²	C₂×D₄×C₃₁	1	2	yes	—
326	C₄²	C₂×D₄×C₃₁	1	2	yes	—
327	C₂³	—	2	2	no	—
328	C₂³	—	2	2	no	—
329	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
330	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
331	C₂³	C₃₁×#137	1	4	yes	—
332	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
333	Q₈	—	4	4	no	—
334	Q₈	—	4	4	no	—
335	Q₈	—	4	8	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	8	8	no	—
358	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
359	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
360	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
361	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
362	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
363	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
364	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
365	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
366	C₈	—	4	4	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	8	no	—
372	C₂²	C₃₁×#410	1	2	yes	—
373	C₂²	C₃₁×#419	1	2	yes	—
374	C₂²	C₃₁×#419	1	2	yes	—
375	C₂²	C₃₁×#421	1	2	yes	—
376	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
377	C₂²	C₂×C₃₁×#137	1	2	yes	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	2	no	—
383	C₄	—	2	2	no	—
384	C₄	—	2	2	no	—
385	C₄	—	2	2	no	—
386	C₄	—	4	4	no	—
387	C₄	—	4	4	no	—
388	C₄	—	8	4	no	—
389	C₂	—	2	2	no	—
390	C₂	—	2	2	no	—
391	C₂	C₃₁×#1515	1	4	yes	direct product factor
392	C₂	C₂×C₃₁×#410	1	1	yes	characteristic
393	C₂	C₂×C₃₁×#419	1	1	yes	characteristic
394	C₂	C₂×C₃₁×#421	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₃₁×#1515	C₂	direct (N × H)
8. C₃₁×#533	C₄	semidirect
10. C₂×C₃₁×C₄⋊Q₈	C₄	semidirect
11. C₂×C₃₁×C₄⋊Q₈	C₄	semidirect
16. C₂×C₄×Q₈×C₃₁	C₄	semidirect
39. C₃₁×C₄⋊Q₈	C₂×C₄	semidirect
40. C₃₁×C₄⋊Q₈	C₂×C₄	semidirect
52. C₄×Q₈×C₃₁	C₂×C₄	semidirect
129. C₂×#1515	C₃₁	direct (N × H)
173. #1515	C₂×C₃₁	direct (N × H)
199. #533	C₄×C₃₁	semidirect
201. C₂×C₄⋊Q₈	C₄×C₃₁	semidirect
202. C₂×C₄⋊Q₈	C₄×C₃₁	semidirect
207. C₂×C₄×Q₈	C₄×C₃₁	semidirect
223. C₂×C₃₁	#1515	direct (N × H)
236. C₄⋊Q₈	C₂×C₄×C₃₁	semidirect
237. C₄⋊Q₈	C₂×C₄×C₃₁	semidirect
249. C₄×Q₈	C₂×C₄×C₃₁	semidirect
276. C₃₁	C₂×#1515	direct (N × H)
391. C₂	C₃₁×#1515	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×#533	2
C₂×C₃₁×#432	2
C₂×C₃₁×#383	2
C₃₁×#1515	2
C₂×C₃₁×#328	2
C₂×#1515	31

Subgroups — C2×C31×#1515 #21474316

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#1515 #21474316