Subgroups — C₂×C₃₁×#1542 #21474456

Order 7936.

1050 conjugacy classes of subgroups.

The subgroup lattice has 400 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×#431	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1542	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃₁×#333	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#332	C₂	1	2	yes	maximal, complemented
7	C₂³×C₈×C₃₁	—	2	1	no	—
8	C₃₁×#533	—	2	2	no	—
9	C₃₁×#533	—	2	2	no	—
10	C₃₁×#533	C₄	1	4	yes	—
11	C₃₁×#533	C₂²	1	4	yes	—
12	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₃₁×#125	—	2	1	no	—
15	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
16	C₂×C₃₁×C₂²⋊Q₈	C₄	1	2	yes	—
17	C₂×C₄×Q₈×C₃₁	—	2	1	no	—
18	C₂×C₄×Q₈×C₃₁	C₄	1	2	yes	—
19	C₂×C₃₁×#117	—	2	1	no	—
20	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
21	C₃₁×#431	—	2	2	no	—
22	C₃₁×#431	C₂²	1	4	yes	—
23	C₂×C₃₁×C₄⋊C₈	—	2	1	no	—
24	C₂×C₃₁×C₄⋊C₈	—	2	2	no	—
25	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
26	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
27	C₂×C₃₁×C₄⋊C₈	C₂²	1	4	yes	—
28	C₂×C₃₁×C₂²⋊C₈	—	2	1	no	—
29	C₂×C₄×C₈×C₃₁	—	2	1	no	—
30	C₃₁×#333	C₂²	1	8	yes	complemented
31	C₃₁×#332	C₂²	1	8	yes	complemented
32	C₂²×Q₈×C₃₁	—	2	1	no	—
33	C₂²×Q₈×C₃₁	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
37	C₂²×C₈×C₃₁	—	2	2	no	—
38	C₂²×C₈×C₃₁	—	2	2	no	—
39	C₂²×C₈×C₃₁	—	2	4	no	—
40	C₂²×C₈×C₃₁	—	4	4	no	—
41	C₃₁×C₄⋊Q₈	—	2	1	no	—
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	C₃₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
47	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
48	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
49	C₃₁×#125	—	2	4	no	—
50	C₃₁×#125	—	2	4	no	—
51	C₃₁×C₂²⋊Q₈	—	2	4	no	—
52	C₃₁×C₂²⋊Q₈	—	2	4	no	—
53	C₃₁×C₂²⋊Q₈	—	2	4	no	—
54	C₃₁×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
55	C₄×Q₈×C₃₁	—	2	4	no	—
56	C₄×Q₈×C₃₁	—	2	4	no	—
57	C₄×Q₈×C₃₁	—	2	4	no	—
58	C₄×Q₈×C₃₁	C₂×C₄	1	8	yes	—
59	C₃₁×#117	—	2	4	no	—
60	C₃₁×#117	—	2	4	no	—
61	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
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	C₂×C₄	1	2	yes	—
67	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
68	C₂×C₄²×C₃₁	—	2	2	no	—
69	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
70	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₃₁	D₄	1	2	yes	—
73	C₂×C₄²×C₃₁	D₄	1	2	yes	—
74	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
77	C₃₁×C₄⋊C₈	—	2	4	no	—
78	C₃₁×C₄⋊C₈	—	2	2	no	—
79	C₃₁×C₄⋊C₈	—	2	2	no	—
80	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
81	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
82	C₃₁×C₂²⋊C₈	—	2	4	no	—
83	C₄×C₈×C₃₁	—	2	4	no	—
84	C₂⁴×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
85	C₂×Q₈×C₃₁	—	2	2	no	—
86	C₂×Q₈×C₃₁	—	2	2	no	—
87	C₂×Q₈×C₃₁	—	2	2	no	—
88	C₂×Q₈×C₃₁	—	4	4	no	—
89	C₂×Q₈×C₃₁	—	4	4	no	—
90	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
91	C₂²×C₄×C₃₁	—	2	4	no	—
92	C₂²×C₄×C₃₁	—	2	2	no	—
93	C₂²×C₄×C₃₁	—	2	2	no	—
94	C₂²×C₄×C₃₁	—	4	2	no	—
95	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
97	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
99	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
100	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
101	C₂²×C₄×C₃₁	SD₁₆	1	4	yes	—
102	C₂²×C₄×C₃₁	Q₁₆	1	4	yes	—
103	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
109	C₂×C₈×C₃₁	—	2	4	no	—
110	C₂×C₈×C₃₁	—	2	4	no	—
111	C₂×C₈×C₃₁	—	4	8	no	—
112	C₂×C₈×C₃₁	—	4	4	no	—
113	C₂×C₈×C₃₁	—	4	4	no	—
114	C₄⋊C₄×C₃₁	—	2	2	no	—
115	C₄⋊C₄×C₃₁	—	2	2	no	—
116	C₄⋊C₄×C₃₁	—	2	2	no	—
117	C₄⋊C₄×C₃₁	—	2	8	no	—
118	C₄⋊C₄×C₃₁	—	2	8	no	—
119	C₄⋊C₄×C₃₁	—	2	2	no	—
120	C₄⋊C₄×C₃₁	—	2	2	no	—
121	C₄⋊C₄×C₃₁	—	2	2	no	—
122	C₄⋊C₄×C₃₁	—	2	2	no	—
123	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
124	C₂²⋊C₄×C₃₁	—	2	8	no	—
125	C₄²×C₃₁	—	2	8	no	—
126	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
127	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
128	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
129	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
130	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₃₁	C₂×D₄	1	2	yes	—
132	C₄²×C₃₁	C₂×D₄	1	2	yes	—
133	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
136	C₂×#1542	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₃₁	—	2	2	no	—
138	C₂³×C₃₁	—	2	2	no	—
139	C₂³×C₃₁	#103	1	4	yes	—
140	C₂³×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
141	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	Q₈×C₃₁	—	4	4	no	—
143	Q₈×C₃₁	—	4	4	no	—
144	Q₈×C₃₁	—	4	4	no	—
145	Q₈×C₃₁	—	4	4	no	—
146	C₂×C₄×C₃₁	—	2	2	no	—
147	C₂×C₄×C₃₁	—	2	2	no	—
148	C₂×C₄×C₃₁	—	2	2	no	—
149	C₂×C₄×C₃₁	—	2	4	no	—
150	C₂×C₄×C₃₁	—	2	4	no	—
151	C₂×C₄×C₃₁	—	2	4	no	—
152	C₂×C₄×C₃₁	—	2	4	no	—
153	C₂×C₄×C₃₁	—	4	2	no	—
154	C₂×C₄×C₃₁	—	4	2	no	—
155	C₂×C₄×C₃₁	—	4	4	no	—
156	C₂×C₄×C₃₁	—	4	4	no	—
157	C₂×C₄×C₃₁	#103	1	8	yes	—
158	C₂×C₄×C₃₁	#103	1	4	yes	—
159	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
160	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
163	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₃₁	C₂×SD₁₆	1	4	yes	—
166	C₂×C₄×C₃₁	C₂×SD₁₆	1	2	yes	—
167	C₂×C₄×C₃₁	C₂×Q₁₆	1	4	yes	—
168	C₂×C₄×C₃₁	C₂×Q₁₆	1	2	yes	—
169	C₂×C₄×C₃₁	#135	1	4	yes	—
170	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
173	C₈×C₃₁	—	4	4	no	—
174	C₈×C₃₁	—	4	4	no	—
175	C₂×#533	C₂×C₃₁	1	1	yes	characteristic
176	C₂×#431	C₂×C₃₁	1	1	yes	characteristic
177	C₂²×C₄⋊C₈	C₂×C₃₁	1	1	yes	characteristic
178	#1542	C₂×C₃₁	1	8	yes	direct product factor
179	C₂×#333	C₂×C₃₁	1	2	yes	complemented
180	C₂×#332	C₂×C₃₁	1	2	yes	complemented
181	C₂²×C₃₁	—	2	8	no	—
182	C₂²×C₃₁	—	2	2	no	—
183	C₂²×C₃₁	—	2	2	no	—
184	C₂²×C₃₁	#413	1	2	yes	—
185	C₂²×C₃₁	C₂×#103	1	4	yes	—
186	C₂²×C₃₁	C₂×#103	1	2	yes	—
187	C₂²×C₃₁	#416	1	2	yes	—
188	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
189	C₄×C₃₁	—	2	2	no	—
190	C₄×C₃₁	—	2	1	no	—
191	C₄×C₃₁	—	2	1	no	—
192	C₄×C₃₁	—	2	2	no	—
193	C₄×C₃₁	—	4	4	no	—
194	C₄×C₃₁	—	4	4	no	—
195	C₄×C₃₁	C₂×#103	1	2	yes	—
196	C₄×C₃₁	C₂×#103	1	4	yes	—
197	C₄×C₃₁	#416	1	2	yes	—
198	C₄×C₃₁	C₂²×SD₁₆	1	1	yes	characteristic
199	C₄×C₃₁	C₂²×Q₁₆	1	1	yes	characteristic
200	C₄×C₃₁	C₂×#135	1	2	yes	—
201	C₂³×C₈	—	2	1	no	—
202	#533	—	2	2	no	—
203	#533	—	2	2	no	—
204	#533	C₄×C₃₁	1	4	yes	—
205	#533	C₂²×C₃₁	1	4	yes	—
206	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
207	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
208	C₂×#125	—	2	1	no	—
209	C₂×C₂²⋊Q₈	—	2	1	no	—
210	C₂×C₂²⋊Q₈	C₄×C₃₁	1	2	yes	—
211	C₂×C₄×Q₈	—	2	1	no	—
212	C₂×C₄×Q₈	C₄×C₃₁	1	2	yes	—
213	C₂×#117	—	2	1	no	—
214	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
215	#431	—	2	2	no	—
216	#431	C₂²×C₃₁	1	4	yes	—
217	C₂×C₄⋊C₈	—	2	1	no	—
218	C₂×C₄⋊C₈	—	2	2	no	—
219	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
220	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
221	C₂×C₄⋊C₈	C₂²×C₃₁	1	4	yes	—
222	C₂×C₂²⋊C₈	—	2	1	no	—
223	C₂×C₄×C₈	—	2	1	no	—
224	#333	C₂²×C₃₁	1	8	yes	complemented
225	#332	C₂²×C₃₁	1	8	yes	complemented
226	C₂×C₃₁	—	2	4	no	—
227	C₂×C₃₁	#1542	1	4	yes	direct product factor
228	C₂×C₃₁	C₂×#413	1	1	yes	characteristic
229	C₂×C₃₁	C₂²×#103	1	1	yes	characteristic
230	C₂×C₃₁	C₂×#416	1	1	yes	characteristic
231	C₂²×Q₈	—	2	1	no	—
232	C₂²×Q₈	C₂×C₄×C₃₁	1	2	yes	—
233	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
234	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
235	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
236	C₂²×C₈	—	2	2	no	—
237	C₂²×C₈	—	2	4	no	—
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	—	4	4	no	—
240	C₄⋊Q₈	—	2	1	no	—
241	C₄⋊Q₈	—	2	1	no	—
242	C₄⋊Q₈	—	2	1	no	—
243	C₄⋊Q₈	—	2	1	no	—
244	C₄⋊Q₈	C₂×C₄×C₃₁	1	2	yes	—
245	C₄⋊Q₈	C₂×C₄×C₃₁	1	2	yes	—
246	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
247	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
248	#125	—	2	4	no	—
249	#125	—	2	4	no	—
250	C₂²⋊Q₈	—	2	4	no	—
251	C₂²⋊Q₈	—	2	4	no	—
252	C₂²⋊Q₈	—	2	4	no	—
253	C₂²⋊Q₈	C₂×C₄×C₃₁	1	8	yes	—
254	C₄×Q₈	—	2	4	no	—
255	C₄×Q₈	—	2	4	no	—
256	C₄×Q₈	—	2	4	no	—
257	C₄×Q₈	C₂×C₄×C₃₁	1	8	yes	—
258	#117	—	2	4	no	—
259	#117	—	2	4	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₄²	—	2	2	no	—
268	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
269	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
270	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
271	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
272	C₂×C₄²	D₄×C₃₁	1	2	yes	—
273	C₂×C₄²	D₄×C₃₁	1	2	yes	—
274	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
276	C₄⋊C₈	—	2	4	no	—
277	C₄⋊C₈	—	2	2	no	—
278	C₄⋊C₈	—	2	2	no	—
279	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
280	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
281	C₂²⋊C₈	—	2	4	no	—
282	C₄×C₈	—	2	4	no	—
283	C₃₁	C₂×#1542	1	1	yes	characteristic, direct product factor, Sylow
284	C₂⁴	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	4	4	no	—
289	C₂×Q₈	—	4	4	no	—
290	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	4	2	no	—
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	1	yes	characteristic
298	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
299	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
300	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
301	C₂²×C₄	SD₁₆×C₃₁	1	4	yes	—
302	C₂²×C₄	Q₁₆×C₃₁	1	4	yes	—
303	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
304	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	—	2	4	no	—
311	C₂×C₈	—	4	8	no	—
312	C₂×C₈	—	4	4	no	—
313	C₂×C₈	—	4	4	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	8	no	—
318	C₄⋊C₄	—	2	8	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
324	C₂²⋊C₄	—	2	8	no	—
325	C₄²	—	2	8	no	—
326	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
327	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
328	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
329	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
330	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
331	C₄²	C₂×D₄×C₃₁	1	2	yes	—
332	C₄²	C₂×D₄×C₃₁	1	2	yes	—
333	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
334	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
335	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
336	C₂³	—	2	2	no	—
337	C₂³	—	2	2	no	—
338	C₂³	C₃₁×#103	1	4	yes	—
339	C₂³	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
340	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
341	Q₈	—	4	4	no	—
342	Q₈	—	4	4	no	—
343	Q₈	—	4	4	no	—
344	Q₈	—	4	4	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	C₃₁×#103	1	8	yes	—
357	C₂×C₄	C₃₁×#103	1	4	yes	—
358	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
359	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
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	1	yes	characteristic
363	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
364	C₂×C₄	C₂×SD₁₆×C₃₁	1	4	yes	—
365	C₂×C₄	C₂×SD₁₆×C₃₁	1	2	yes	—
366	C₂×C₄	C₂×Q₁₆×C₃₁	1	4	yes	—
367	C₂×C₄	C₂×Q₁₆×C₃₁	1	2	yes	—
368	C₂×C₄	C₃₁×#135	1	4	yes	—
369	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
370	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
371	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
372	C₈	—	4	4	no	—
373	C₈	—	4	4	no	—
374	C₂²	—	2	8	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	C₃₁×#413	1	2	yes	—
378	C₂²	C₂×C₃₁×#103	1	4	yes	—
379	C₂²	C₂×C₃₁×#103	1	2	yes	—
380	C₂²	C₃₁×#416	1	2	yes	—
381	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
382	C₄	—	2	1	no	—
383	C₄	—	2	2	no	—
384	C₄	—	2	1	no	—
385	C₄	—	2	2	no	—
386	C₄	—	4	4	no	—
387	C₄	—	4	4	no	—
388	C₄	C₂×C₃₁×#103	1	4	yes	—
389	C₄	C₂×C₃₁×#103	1	2	yes	—
390	C₄	C₃₁×#416	1	2	yes	—
391	C₄	C₂²×SD₁₆×C₃₁	1	1	yes	characteristic
392	C₄	C₂²×Q₁₆×C₃₁	1	1	yes	characteristic
393	C₄	C₂×C₃₁×#135	1	2	yes	—
394	C₂	—	2	4	no	—
395	C₂	C₃₁×#1542	1	4	yes	direct product factor
396	C₂	C₂×C₃₁×#413	1	1	yes	characteristic
397	C₂	C₂²×C₃₁×#103	1	1	yes	characteristic
398	C₂	C₂×C₃₁×#416	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₃₁×#1542	C₂	direct (N × H)
5. C₂×C₃₁×#333	C₂	semidirect
6. C₂×C₃₁×#332	C₂	semidirect
30. C₃₁×#333	C₂²	semidirect
31. C₃₁×#332	C₂²	semidirect
136. C₂×#1542	C₃₁	direct (N × H)
178. #1542	C₂×C₃₁	direct (N × H)
179. C₂×#333	C₂×C₃₁	semidirect
180. C₂×#332	C₂×C₃₁	semidirect
224. #333	C₂²×C₃₁	semidirect
225. #332	C₂²×C₃₁	semidirect
227. C₂×C₃₁	#1542	direct (N × H)
283. C₃₁	C₂×#1542	direct (N × H)
395. C₂	C₃₁×#1542	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×#431	2
C₂²×C₃₁×C₄⋊C₈	2
C₃₁×#1542	2
C₂×C₃₁×#333	2
C₂×C₃₁×#332	2
C₂×#1542	31

Subgroups — C2×C31×#1542 #21474456

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#1542 #21474456