Subgroups — C₂×C₃₁×#1286 #21464714

Order 7936.

702 conjugacy classes of subgroups.

The subgroup lattice has 418 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×#423	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₁×#382	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1286	C₂	1	4	yes	maximal, direct product factor
5	C₂²×M₁₆×C₃₁	—	2	1	no	—
6	C₂²×C₄⋊C₄×C₃₁	—	2	1	no	—
7	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
8	C₃₁×#431	—	2	1	no	—
9	C₃₁×#431	—	2	1	no	—
10	C₃₁×#431	C₄	1	2	yes	complemented
11	C₃₁×#431	C₂²	1	2	yes	—
12	C₃₁×#423	—	2	1	no	—
13	C₃₁×#423	—	2	1	no	—
14	C₃₁×#423	C₄	1	2	yes	complemented
15	C₃₁×#423	C₂²	1	2	yes	—
16	C₂×C₃₁×C₄⋊C₈	—	2	1	no	—
17	C₂×C₃₁×C₄⋊C₈	—	2	1	no	—
18	C₂×C₃₁×C₄⋊C₈	C₄	1	2	yes	complemented
19	C₂×C₃₁×C₂²⋊C₈	—	2	1	no	—
20	C₂×C₄×C₈×C₃₁	C₄	1	2	yes	complemented
21	C₃₁×#382	—	2	1	no	—
22	C₃₁×#382	—	2	1	no	—
23	C₃₁×#382	C₄	1	2	yes	—
24	C₃₁×#382	C₂²	1	2	yes	—
25	C₂×C₃₁×#95	—	2	1	no	—
26	C₂×C₃₁×#95	C₄	1	2	yes	—
27	C₂³×C₄×C₃₁	—	2	2	no	—
28	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
31	C₂×M₁₆×C₃₁	—	2	2	no	—
32	C₂×M₁₆×C₃₁	—	2	2	no	—
33	C₂×M₁₆×C₃₁	—	4	2	no	—
34	C₂×M₁₆×C₃₁	—	4	2	no	—
35	C₂²×C₈×C₃₁	—	2	2	no	—
36	C₂²×C₈×C₃₁	—	2	2	no	—
37	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
38	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
39	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
40	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
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	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
53	C₃₁×C₄⋊C₈	—	2	2	no	—
54	C₃₁×C₄⋊C₈	—	2	2	no	—
55	C₃₁×C₄⋊C₈	—	2	2	no	—
56	C₃₁×C₄⋊C₈	—	2	2	no	—
57	C₃₁×C₄⋊C₈	—	2	2	no	—
58	C₃₁×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
59	C₃₁×C₂²⋊C₈	—	2	2	no	—
60	C₃₁×C₂²⋊C₈	—	2	2	no	—
61	C₄×C₈×C₃₁	—	2	2	no	—
62	C₄×C₈×C₃₁	C₂×C₄	1	4	yes	complemented
63	C₃₁×#95	—	2	2	no	—
64	C₃₁×#95	—	2	2	no	—
65	C₃₁×#95	—	2	2	no	—
66	C₃₁×#95	C₂×C₄	1	4	yes	—
67	C₂⁴×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
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	—	4	4	no	—
72	C₂²×C₄×C₃₁	—	4	4	no	—
73	C₂²×C₄×C₃₁	—	4	4	no	—
74	C₂²×C₄×C₃₁	C₄²	1	1	yes	characteristic
75	C₂²×C₄×C₃₁	C₄²	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	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₃₁	D₈	1	2	yes	—
90	C₂²×C₄×C₃₁	SD₁₆	1	2	yes	—
91	C₂²×C₄×C₃₁	SD₁₆	1	2	yes	—
92	C₂²×C₄×C₃₁	Q₁₆	1	2	yes	—
93	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
96	M₁₆×C₃₁	—	4	4	no	—
97	M₁₆×C₃₁	—	4	2	no	—
98	M₁₆×C₃₁	—	4	2	no	—
99	C₂×C₈×C₃₁	—	2	4	no	—
100	C₂×C₈×C₃₁	—	2	4	no	—
101	C₂×C₈×C₃₁	—	4	4	no	—
102	C₂×C₈×C₃₁	—	4	4	no	—
103	C₄⋊C₄×C₃₁	—	4	4	no	—
104	C₄⋊C₄×C₃₁	—	4	2	no	—
105	C₄⋊C₄×C₃₁	—	4	2	no	—
106	C₄²×C₃₁	C₄²	1	1	yes	characteristic
107	C₄²×C₃₁	C₄²	1	1	yes	characteristic
108	C₄²×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
109	C₄²×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
110	C₄²×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
111	C₄²×C₃₁	C₂²⋊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	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
117	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
118	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₃₁	C₂×Q₈	1	1	yes	characteristic
122	C₂×#1286	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
123	C₂³×C₃₁	—	2	2	no	—
124	C₂³×C₃₁	—	2	2	no	—
125	C₂³×C₃₁	#95	1	1	yes	characteristic
126	C₂³×C₃₁	#95	1	1	yes	characteristic
127	C₂³×C₃₁	#102	1	2	yes	—
128	C₂³×C₃₁	#103	1	2	yes	—
129	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	—	4	1	no	—
135	C₂×C₄×C₃₁	—	4	1	no	—
136	C₂×C₄×C₃₁	—	4	1	no	—
137	C₂×C₄×C₃₁	—	4	1	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	4	no	—
143	C₂×C₄×C₃₁	—	4	4	no	—
144	C₂×C₄×C₃₁	—	4	4	no	—
145	C₂×C₄×C₃₁	—	8	8	no	—
146	C₂×C₄×C₃₁	#95	1	1	yes	characteristic
147	C₂×C₄×C₃₁	#95	1	1	yes	characteristic
148	C₂×C₄×C₃₁	#95	1	1	yes	characteristic
149	C₂×C₄×C₃₁	#95	1	1	yes	characteristic
150	C₂×C₄×C₃₁	#95	1	1	yes	characteristic
151	C₂×C₄×C₃₁	#95	1	1	yes	characteristic
152	C₂×C₄×C₃₁	#102	1	2	yes	—
153	C₂×C₄×C₃₁	#102	1	2	yes	—
154	C₂×C₄×C₃₁	#102	1	2	yes	—
155	C₂×C₄×C₃₁	#103	1	2	yes	—
156	C₂×C₄×C₃₁	#103	1	2	yes	—
157	C₂×C₄×C₃₁	#103	1	2	yes	—
158	C₂×C₄×C₃₁	#106	1	2	yes	—
159	C₂×C₄×C₃₁	#106	1	2	yes	—
160	C₂×C₄×C₃₁	#107	1	2	yes	—
161	C₂×C₄×C₃₁	#107	1	2	yes	—
162	C₂×C₄×C₃₁	C₂×C₄²	1	1	yes	characteristic
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×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₃₁	C₂×SD₁₆	1	1	yes	characteristic
170	C₂×C₄×C₃₁	C₂×SD₁₆	1	1	yes	characteristic
171	C₂×C₄×C₃₁	C₂×Q₁₆	1	1	yes	characteristic
172	C₈×C₃₁	—	4	4	no	—
173	C₈×C₃₁	—	4	4	no	—
174	C₂×#431	C₂×C₃₁	1	1	yes	characteristic
175	C₂×#423	C₂×C₃₁	1	1	yes	characteristic
176	C₂×#382	C₂×C₃₁	1	1	yes	characteristic
177	#1286	C₂×C₃₁	1	4	yes	direct product factor
178	C₂²×C₃₁	—	2	4	no	—
179	C₂²×C₃₁	—	2	4	no	—
180	C₂²×C₃₁	—	2	1	no	—
181	C₂²×C₃₁	—	2	1	no	—
182	C₂²×C₃₁	—	2	1	no	—
183	C₂²×C₃₁	—	2	1	no	—
184	C₂²×C₃₁	H(3,ℤ/4)	1	2	yes	—
185	C₂²×C₃₁	#340	1	2	yes	—
186	C₂²×C₃₁	#340	1	2	yes	—
187	C₂²×C₃₁	#344	1	2	yes	—
188	C₂²×C₃₁	C₂×#95	1	1	yes	characteristic
189	C₂²×C₃₁	C₂×#102	1	1	yes	characteristic
190	C₂²×C₃₁	C₂×#103	1	1	yes	characteristic
191	C₄×C₃₁	—	2	1	no	—
192	C₄×C₃₁	—	2	1	no	—
193	C₄×C₃₁	—	2	1	no	—
194	C₄×C₃₁	—	2	1	no	—
195	C₄×C₃₁	—	2	1	no	—
196	C₄×C₃₁	—	2	1	no	—
197	C₄×C₃₁	—	2	1	no	—
198	C₄×C₃₁	—	2	1	no	—
199	C₄×C₃₁	—	8	4	no	—
200	C₄×C₃₁	#340	1	2	yes	—
201	C₄×C₃₁	#340	1	2	yes	—
202	C₄×C₃₁	C₂×#102	1	1	yes	characteristic
203	C₄×C₃₁	C₂×#103	1	1	yes	characteristic
204	C₄×C₃₁	C₂×#106	1	1	yes	characteristic
205	C₄×C₃₁	C₂×#107	1	1	yes	characteristic
206	C₂²×M₁₆	—	2	1	no	—
207	C₂²×C₄⋊C₄	—	2	1	no	—
208	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
209	#431	—	2	1	no	—
210	#431	—	2	1	no	—
211	#431	C₄×C₃₁	1	2	yes	complemented
212	#431	C₂²×C₃₁	1	2	yes	—
213	#423	—	2	1	no	—
214	#423	—	2	1	no	—
215	#423	C₄×C₃₁	1	2	yes	complemented
216	#423	C₂²×C₃₁	1	2	yes	—
217	C₂×C₄⋊C₈	—	2	1	no	—
218	C₂×C₄⋊C₈	—	2	1	no	—
219	C₂×C₄⋊C₈	C₄×C₃₁	1	2	yes	complemented
220	C₂×C₂²⋊C₈	—	2	1	no	—
221	C₂×C₄×C₈	C₄×C₃₁	1	2	yes	complemented
222	#382	—	2	1	no	—
223	#382	—	2	1	no	—
224	#382	C₄×C₃₁	1	2	yes	—
225	#382	C₂²×C₃₁	1	2	yes	—
226	C₂×#95	—	2	1	no	—
227	C₂×#95	C₄×C₃₁	1	2	yes	—
228	C₂×C₃₁	—	2	1	no	—
229	C₂×C₃₁	—	2	2	no	—
230	C₂×C₃₁	—	2	1	no	—
231	C₂×C₃₁	#1286	1	4	yes	direct product factor
232	C₂×C₃₁	C₂×H(3,ℤ/4)	1	1	yes	characteristic
233	C₂×C₃₁	C₂×#340	1	1	yes	characteristic
234	C₂×C₃₁	C₂×#344	1	1	yes	characteristic
235	C₂³×C₄	—	2	2	no	—
236	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
237	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
238	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
239	C₂×M₁₆	—	2	2	no	—
240	C₂×M₁₆	—	2	2	no	—
241	C₂×M₁₆	—	4	2	no	—
242	C₂×M₁₆	—	4	2	no	—
243	C₂²×C₈	—	2	2	no	—
244	C₂²×C₈	—	2	2	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	4	2	no	—
248	C₂×C₄⋊C₄	—	4	2	no	—
249	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
250	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
251	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
252	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
253	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
254	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
255	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
256	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
257	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
258	C₂×C₄²	Q₈×C₃₁	1	1	yes	characteristic
259	C₂×C₄²	Q₈×C₃₁	1	1	yes	characteristic
260	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
261	C₄⋊C₈	—	2	2	no	—
262	C₄⋊C₈	—	2	2	no	—
263	C₄⋊C₈	—	2	2	no	—
264	C₄⋊C₈	—	2	2	no	—
265	C₄⋊C₈	—	2	2	no	—
266	C₄⋊C₈	C₂×C₄×C₃₁	1	4	yes	complemented
267	C₂²⋊C₈	—	2	2	no	—
268	C₂²⋊C₈	—	2	2	no	—
269	C₄×C₈	—	2	2	no	—
270	C₄×C₈	C₂×C₄×C₃₁	1	4	yes	complemented
271	#95	—	2	2	no	—
272	#95	—	2	2	no	—
273	#95	—	2	2	no	—
274	#95	C₂×C₄×C₃₁	1	4	yes	—
275	C₃₁	C₂×#1286	1	1	yes	characteristic, direct product factor, Sylow
276	C₂⁴	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	—	4	4	no	—
281	C₂²×C₄	—	4	4	no	—
282	C₂²×C₄	—	4	4	no	—
283	C₂²×C₄	C₄²×C₃₁	1	1	yes	characteristic
284	C₂²×C₄	C₄²×C₃₁	1	1	yes	characteristic
285	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
286	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
287	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
288	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
289	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
290	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
291	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
292	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
293	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
294	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
295	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
296	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
297	C₂²×C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
298	C₂²×C₄	D₈×C₃₁	1	2	yes	—
299	C₂²×C₄	SD₁₆×C₃₁	1	2	yes	—
300	C₂²×C₄	SD₁₆×C₃₁	1	2	yes	—
301	C₂²×C₄	Q₁₆×C₃₁	1	2	yes	—
302	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
305	M₁₆	—	4	4	no	—
306	M₁₆	—	4	2	no	—
307	M₁₆	—	4	2	no	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	—	4	4	no	—
311	C₂×C₈	—	4	4	no	—
312	C₄⋊C₄	—	4	4	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄²	C₄²×C₃₁	1	1	yes	characteristic
316	C₄²	C₄²×C₃₁	1	1	yes	characteristic
317	C₄²	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
318	C₄²	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
319	C₄²	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
320	C₄²	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
321	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
322	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
323	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
324	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
325	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
326	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
327	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
328	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
329	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
330	C₄²	C₂×Q₈×C₃₁	1	1	yes	characteristic
331	C₂³	—	2	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	C₃₁×#95	1	1	yes	characteristic
334	C₂³	C₃₁×#95	1	1	yes	characteristic
335	C₂³	C₃₁×#102	1	2	yes	—
336	C₂³	C₃₁×#103	1	2	yes	—
337	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	8	8	no	—
354	C₂×C₄	C₃₁×#95	1	1	yes	characteristic
355	C₂×C₄	C₃₁×#95	1	1	yes	characteristic
356	C₂×C₄	C₃₁×#95	1	1	yes	characteristic
357	C₂×C₄	C₃₁×#95	1	1	yes	characteristic
358	C₂×C₄	C₃₁×#95	1	1	yes	characteristic
359	C₂×C₄	C₃₁×#95	1	1	yes	characteristic
360	C₂×C₄	C₃₁×#102	1	2	yes	—
361	C₂×C₄	C₃₁×#102	1	2	yes	—
362	C₂×C₄	C₃₁×#102	1	2	yes	—
363	C₂×C₄	C₃₁×#103	1	2	yes	—
364	C₂×C₄	C₃₁×#103	1	2	yes	—
365	C₂×C₄	C₃₁×#103	1	2	yes	—
366	C₂×C₄	C₃₁×#106	1	2	yes	—
367	C₂×C₄	C₃₁×#106	1	2	yes	—
368	C₂×C₄	C₃₁×#107	1	2	yes	—
369	C₂×C₄	C₃₁×#107	1	2	yes	—
370	C₂×C₄	C₂×C₄²×C₃₁	1	1	yes	characteristic
371	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
372	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
373	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
374	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
375	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
376	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
377	C₂×C₄	C₂×SD₁₆×C₃₁	1	1	yes	characteristic
378	C₂×C₄	C₂×SD₁₆×C₃₁	1	1	yes	characteristic
379	C₂×C₄	C₂×Q₁₆×C₃₁	1	1	yes	characteristic
380	C₈	—	4	4	no	—
381	C₈	—	4	4	no	—
382	C₂²	—	2	4	no	—
383	C₂²	—	2	4	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	C₃₁×H(3,ℤ/4)	1	2	yes	—
389	C₂²	C₃₁×#340	1	2	yes	—
390	C₂²	C₃₁×#340	1	2	yes	—
391	C₂²	C₃₁×#344	1	2	yes	—
392	C₂²	C₂×C₃₁×#95	1	1	yes	characteristic
393	C₂²	C₂×C₃₁×#102	1	1	yes	characteristic
394	C₂²	C₂×C₃₁×#103	1	1	yes	characteristic
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	8	4	no	—
404	C₄	C₃₁×#340	1	2	yes	—
405	C₄	C₃₁×#340	1	2	yes	—
406	C₄	C₂×C₃₁×#102	1	1	yes	characteristic
407	C₄	C₂×C₃₁×#103	1	1	yes	characteristic
408	C₄	C₂×C₃₁×#106	1	1	yes	characteristic
409	C₄	C₂×C₃₁×#107	1	1	yes	characteristic
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	2	2	no	—
413	C₂	C₃₁×#1286	1	4	yes	direct product factor
414	C₂	C₂×C₃₁×H(3,ℤ/4)	1	1	yes	characteristic
415	C₂	C₂×C₃₁×#340	1	1	yes	characteristic
416	C₂	C₂×C₃₁×#344	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	#95
commutator	C₂×C₄	C₂×C₄²×C₃₁
Frattini, cosocle	C₂×C₄²	C₂³×C₃₁
prime radical	C₂⁴×C₃₁	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ 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×#1286	C₂	direct (N × H)
10. C₃₁×#431	C₄	semidirect
14. C₃₁×#423	C₄	semidirect
18. C₂×C₃₁×C₄⋊C₈	C₄	semidirect
20. C₂×C₄×C₈×C₃₁	C₄	semidirect
58. C₃₁×C₄⋊C₈	C₂×C₄	semidirect
62. C₄×C₈×C₃₁	C₂×C₄	semidirect
122. C₂×#1286	C₃₁	direct (N × H)
177. #1286	C₂×C₃₁	direct (N × H)
211. #431	C₄×C₃₁	semidirect
215. #423	C₄×C₃₁	semidirect
219. C₂×C₄⋊C₈	C₄×C₃₁	semidirect
221. C₂×C₄×C₈	C₄×C₃₁	semidirect
231. C₂×C₃₁	#1286	direct (N × H)
266. C₄⋊C₈	C₂×C₄×C₃₁	semidirect
270. C₄×C₈	C₂×C₄×C₃₁	semidirect
275. C₃₁	C₂×#1286	direct (N × H)
413. C₂	C₃₁×#1286	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×#431	2
C₂×C₃₁×#423	2
C₂×C₃₁×#382	2
C₃₁×#1286	2
C₂×#1286	31

Subgroups — C2×C31×#1286 #21464714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#1286 #21464714