Subgroups — C₂×C₃₁×#3095 #21517269

Order 7936.

2326 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃₁×#117	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3095	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃₁×#484	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₁×#485	C₂	1	4	yes	maximal, complemented
6	C₂×C₃₁×#483	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₁×#428	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₁×#419	C₂	1	2	yes	maximal, complemented
9	C₂×C₃₁×#407	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
13	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
14	C₂×C₃₁×C₂²⋊Q₈	—	2	4	no	—
15	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
16	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	8	yes	—
19	C₂×C₃₁×#117	—	2	1	no	—
20	C₂×C₃₁×#117	—	2	4	no	—
21	C₂×C₃₁×#117	—	2	1	no	—
22	C₂×C₃₁×#117	C₂²	1	2	yes	—
23	C₂×C₃₁×#117	C₂²	1	8	yes	—
24	C₂×C₃₁×#117	C₂²	1	2	yes	—
25	C₂²×C₄⋊C₄×C₃₁	—	2	1	no	—
26	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₃₁	—	2	1	no	—
30	C₂²×C₂²⋊C₄×C₃₁	—	2	1	no	—
31	C₂²×C₄²×C₃₁	—	2	1	no	—
32	C₃₁×#485	C₂²	1	32	yes	complemented
33	C₃₁×#484	C₂²	1	16	yes	complemented
34	C₃₁×#483	C₂²	1	16	yes	complemented
35	C₃₁×#428	C₂²	1	16	yes	complemented
36	C₂×C₃₁×#107	C₂²	1	4	yes	complemented
37	C₂×C₃₁×#106	C₂²	1	4	yes	complemented
38	C₃₁×#419	C₂²	1	16	yes	complemented
39	C₂×C₃₁×#103	C₂²	1	4	yes	complemented
40	C₂×C₃₁×#103	C₂²	1	4	yes	complemented
41	C₃₁×#407	C₂²	1	8	yes	—
42	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
43	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
44	C₂⁵×C₃₁	D₄	1	1	yes	characteristic
45	C₂²×Q₈×C₃₁	—	2	2	no	—
46	C₂²×Q₈×C₃₁	—	2	1	no	—
47	C₂²×Q₈×C₃₁	—	2	8	no	—
48	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
49	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
50	C₂³×C₄×C₃₁	—	2	8	no	—
51	C₂³×C₄×C₃₁	—	2	1	no	—
52	C₂³×C₄×C₃₁	—	2	1	no	—
53	C₂³×C₄×C₃₁	—	2	1	no	—
54	C₂³×C₄×C₃₁	—	2	1	no	—
55	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₃₁	D₄	1	4	yes	—
58	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
62	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
63	C₂×M₁₆×C₃₁	—	2	8	no	—
64	C₂×M₁₆×C₃₁	C₂³	1	8	yes	—
65	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
66	C₃₁×C₂²⋊Q₈	—	2	8	no	—
67	C₃₁×C₂²⋊Q₈	—	2	4	no	—
68	C₃₁×C₂²⋊Q₈	—	2	4	no	—
69	C₃₁×C₂²⋊Q₈	—	2	8	no	—
70	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
71	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
72	C₃₁×#117	—	2	8	no	—
73	C₃₁×#117	—	2	4	no	—
74	C₃₁×#117	—	2	8	no	—
75	C₃₁×#117	—	2	4	no	—
76	C₃₁×#117	C₂³	1	8	yes	—
77	C₃₁×#117	C₂³	1	8	yes	—
78	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
79	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
80	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
81	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
82	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
83	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
84	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
85	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
86	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
87	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
91	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
92	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
93	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
94	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
97	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
98	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
99	C₂×C₄²×C₃₁	—	2	8	no	—
100	C₂×C₄²×C₃₁	—	2	2	no	—
101	C₂×C₄²×C₃₁	—	2	2	no	—
102	C₃₁×#107	C₂³	1	16	yes	complemented
103	C₃₁×#106	C₂³	1	16	yes	complemented
104	C₃₁×#103	C₂³	1	16	yes	complemented
105	C₃₁×#103	C₂³	1	16	yes	complemented
106	C₃₁×C₂²⋊C₈	C₂³	1	8	yes	—
107	C₃₁×C₂²⋊C₈	C₂³	1	8	yes	—
108	C₂⁴×C₃₁	—	2	4	no	—
109	C₂⁴×C₃₁	—	2	4	no	—
110	C₂⁴×C₃₁	—	4	2	no	—
111	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
112	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
113	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
114	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
115	C₂×Q₈×C₃₁	—	2	4	no	—
116	C₂×Q₈×C₃₁	—	2	2	no	—
117	C₂×Q₈×C₃₁	—	2	8	no	—
118	C₂×Q₈×C₃₁	—	2	16	no	—
119	C₂×Q₈×C₃₁	—	4	8	no	—
120	C₂×Q₈×C₃₁	—	4	4	no	—
121	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
122	C₂²×C₄×C₃₁	—	2	4	no	—
123	C₂²×C₄×C₃₁	—	2	4	no	—
124	C₂²×C₄×C₃₁	—	2	16	no	—
125	C₂²×C₄×C₃₁	—	2	4	no	—
126	C₂²×C₄×C₃₁	—	2	4	no	—
127	C₂²×C₄×C₃₁	—	2	4	no	—
128	C₂²×C₄×C₃₁	—	2	16	no	—
129	C₂²×C₄×C₃₁	—	2	4	no	—
130	C₂²×C₄×C₃₁	—	2	4	no	—
131	C₂²×C₄×C₃₁	—	2	4	no	—
132	C₂²×C₄×C₃₁	—	2	4	no	—
133	C₂²×C₄×C₃₁	—	2	2	no	—
134	C₂²×C₄×C₃₁	—	2	2	no	—
135	C₂²×C₄×C₃₁	—	2	2	no	—
136	C₂²×C₄×C₃₁	—	2	2	no	—
137	C₂²×C₄×C₃₁	—	4	4	no	—
138	C₂²×C₄×C₃₁	—	4	4	no	—
139	C₂²×C₄×C₃₁	—	4	4	no	—
140	C₂²×C₄×C₃₁	—	4	4	no	—
141	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
146	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₃₁	#41	1	8	yes	—
151	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
152	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
155	M₁₆×C₃₁	—	2	16	no	—
156	C₂×C₈×C₃₁	—	2	8	no	—
157	C₂×C₈×C₃₁	C₂⁴	1	8	yes	—
158	C₄⋊C₄×C₃₁	—	2	8	no	—
159	C₄⋊C₄×C₃₁	—	2	8	no	—
160	C₄⋊C₄×C₃₁	—	2	4	no	—
161	C₄⋊C₄×C₃₁	—	2	4	no	—
162	C₄⋊C₄×C₃₁	—	2	2	no	—
163	C₄⋊C₄×C₃₁	—	2	2	no	—
164	C₄⋊C₄×C₃₁	—	2	4	no	—
165	C₄⋊C₄×C₃₁	—	2	2	no	—
166	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
167	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
168	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
169	C₂²⋊C₄×C₃₁	—	2	8	no	—
170	C₂²⋊C₄×C₃₁	—	2	8	no	—
171	C₂²⋊C₄×C₃₁	—	2	8	no	—
172	C₂²⋊C₄×C₃₁	—	2	8	no	—
173	C₄²×C₃₁	—	2	8	no	—
174	C₄²×C₃₁	—	2	8	no	—
175	C₂×#3095	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂³×C₃₁	—	2	2	no	—
177	C₂³×C₃₁	—	2	2	no	—
178	C₂³×C₃₁	—	2	2	no	—
179	C₂³×C₃₁	—	2	2	no	—
180	C₂³×C₃₁	—	2	8	no	—
181	C₂³×C₃₁	—	2	2	no	—
182	C₂³×C₃₁	—	2	8	no	—
183	C₂³×C₃₁	—	2	2	no	—
184	C₂³×C₃₁	—	2	2	no	—
185	C₂³×C₃₁	—	4	4	no	—
186	C₂³×C₃₁	—	4	16	no	—
187	C₂³×C₃₁	#123	1	4	yes	—
188	C₂³×C₃₁	#137	1	4	yes	—
189	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
190	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
191	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
192	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
193	Q₈×C₃₁	—	2	8	no	—
194	Q₈×C₃₁	—	4	8	no	—
195	Q₈×C₃₁	—	4	4	no	—
196	C₂×C₄×C₃₁	—	2	8	no	—
197	C₂×C₄×C₃₁	—	2	2	no	—
198	C₂×C₄×C₃₁	—	2	2	no	—
199	C₂×C₄×C₃₁	—	2	8	no	—
200	C₂×C₄×C₃₁	—	2	4	no	—
201	C₂×C₄×C₃₁	—	2	4	no	—
202	C₂×C₄×C₃₁	—	2	8	no	—
203	C₂×C₄×C₃₁	—	2	4	no	—
204	C₂×C₄×C₃₁	—	2	4	no	—
205	C₂×C₄×C₃₁	—	2	4	no	—
206	C₂×C₄×C₃₁	—	2	4	no	—
207	C₂×C₄×C₃₁	—	2	4	no	—
208	C₂×C₄×C₃₁	—	2	4	no	—
209	C₂×C₄×C₃₁	—	4	8	no	—
210	C₂×C₄×C₃₁	—	4	8	no	—
211	C₂×C₄×C₃₁	—	4	8	no	—
212	C₂×C₄×C₃₁	—	4	4	no	—
213	C₂×C₄×C₃₁	—	4	8	no	—
214	C₂×C₄×C₃₁	—	4	4	no	—
215	C₂×C₄×C₃₁	—	4	4	no	—
216	C₂×C₄×C₃₁	—	4	4	no	—
217	C₂×C₄×C₃₁	#123	1	8	yes	—
218	C₂×C₄×C₃₁	#123	1	4	yes	—
219	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
220	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
221	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
222	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
224	C₂×C₄×C₃₁	C₂×#41	1	8	yes	—
225	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
226	C₈×C₃₁	—	2	8	no	—
227	C₂²×C₂²⋊Q₈	C₂×C₃₁	1	1	yes	characteristic
228	C₂²×#117	C₂×C₃₁	1	1	yes	characteristic
229	#3095	C₂×C₃₁	1	16	yes	direct product factor
230	C₂×#484	C₂×C₃₁	1	2	yes	complemented
231	C₂×#485	C₂×C₃₁	1	4	yes	complemented
232	C₂×#483	C₂×C₃₁	1	2	yes	complemented
233	C₂×#428	C₂×C₃₁	1	2	yes	complemented
234	C₂×#419	C₂×C₃₁	1	2	yes	complemented
235	C₂×#407	C₂×C₃₁	1	1	yes	characteristic
236	C₂²×C₃₁	—	2	8	no	—
237	C₂²×C₃₁	—	2	8	no	—
238	C₂²×C₃₁	—	2	2	no	—
239	C₂²×C₃₁	—	2	2	no	—
240	C₂²×C₃₁	—	2	2	no	—
241	C₂²×C₃₁	—	2	2	no	—
242	C₂²×C₃₁	—	2	2	no	—
243	C₂²×C₃₁	—	2	2	no	—
244	C₂²×C₃₁	—	2	2	no	—
245	C₂²×C₃₁	—	4	16	no	—
246	C₂²×C₃₁	—	4	4	no	—
247	C₂²×C₃₁	C₂×#123	1	4	yes	—
248	C₂²×C₃₁	C₂×#123	1	2	yes	—
249	C₂²×C₃₁	C₂×#137	1	4	yes	—
250	C₂²×C₃₁	C₂×#137	1	2	yes	—
251	C₂²×C₃₁	#575	1	2	yes	—
252	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
253	C₄×C₃₁	—	2	2	no	—
254	C₄×C₃₁	—	2	2	no	—
255	C₄×C₃₁	—	4	4	no	—
256	C₄×C₃₁	—	4	4	no	—
257	C₄×C₃₁	—	4	4	no	—
258	C₄×C₃₁	—	4	4	no	—
259	C₄×C₃₁	C₂×#123	1	4	yes	—
260	C₄×C₃₁	C₂×#123	1	2	yes	—
261	C₄×C₃₁	C₂²×#41	1	2	yes	—
262	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic
263	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
264	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
265	C₂×C₂²⋊Q₈	—	2	1	no	—
266	C₂×C₂²⋊Q₈	—	2	4	no	—
267	C₂×C₂²⋊Q₈	—	2	1	no	—
268	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
269	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
270	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	8	yes	—
271	C₂×#117	—	2	1	no	—
272	C₂×#117	—	2	4	no	—
273	C₂×#117	—	2	1	no	—
274	C₂×#117	C₂²×C₃₁	1	2	yes	—
275	C₂×#117	C₂²×C₃₁	1	8	yes	—
276	C₂×#117	C₂²×C₃₁	1	2	yes	—
277	C₂²×C₄⋊C₄	—	2	1	no	—
278	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
279	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
280	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
281	C₂²×C₂²⋊C₄	—	2	1	no	—
282	C₂²×C₂²⋊C₄	—	2	1	no	—
283	C₂²×C₄²	—	2	1	no	—
284	#485	C₂²×C₃₁	1	32	yes	complemented
285	#484	C₂²×C₃₁	1	16	yes	complemented
286	#483	C₂²×C₃₁	1	16	yes	complemented
287	#428	C₂²×C₃₁	1	16	yes	complemented
288	C₂×#107	C₂²×C₃₁	1	4	yes	complemented
289	C₂×#106	C₂²×C₃₁	1	4	yes	complemented
290	#419	C₂²×C₃₁	1	16	yes	complemented
291	C₂×#103	C₂²×C₃₁	1	4	yes	complemented
292	C₂×#103	C₂²×C₃₁	1	4	yes	complemented
293	#407	C₂²×C₃₁	1	8	yes	—
294	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
295	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
296	C₂×C₃₁	—	2	4	no	—
297	C₂×C₃₁	—	2	4	no	—
298	C₂×C₃₁	—	4	2	no	—
299	C₂×C₃₁	#3095	1	4	yes	direct product factor
300	C₂×C₃₁	C₂²×#123	1	1	yes	characteristic
301	C₂×C₃₁	C₂²×#137	1	1	yes	characteristic
302	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
303	C₂⁵	D₄×C₃₁	1	1	yes	characteristic
304	C₂²×Q₈	—	2	1	no	—
305	C₂²×Q₈	—	2	2	no	—
306	C₂²×Q₈	—	2	8	no	—
307	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
308	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
309	C₂³×C₄	—	2	8	no	—
310	C₂³×C₄	—	2	1	no	—
311	C₂³×C₄	—	2	1	no	—
312	C₂³×C₄	—	2	1	no	—
313	C₂³×C₄	—	2	1	no	—
314	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
315	C₂³×C₄	D₄×C₃₁	1	4	yes	—
316	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
317	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
318	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
319	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
320	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
321	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
322	C₂×M₁₆	—	2	8	no	—
323	C₂×M₁₆	C₂³×C₃₁	1	8	yes	—
324	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
325	C₂²⋊Q₈	—	2	8	no	—
326	C₂²⋊Q₈	—	2	4	no	—
327	C₂²⋊Q₈	—	2	4	no	—
328	C₂²⋊Q₈	—	2	8	no	—
329	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
330	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
331	#117	—	2	8	no	—
332	#117	—	2	4	no	—
333	#117	—	2	8	no	—
334	#117	—	2	4	no	—
335	#117	C₂³×C₃₁	1	8	yes	—
336	#117	C₂³×C₃₁	1	8	yes	—
337	C₂×C₄⋊C₄	—	2	2	no	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	—	2	8	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	2	no	—
343	C₂×C₄⋊C₄	—	2	2	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	2	no	—
346	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
347	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
348	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
349	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
350	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
351	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₂²⋊C₄	—	2	8	no	—
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	—	2	8	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₄²	—	2	2	no	—
359	C₂×C₄²	—	2	8	no	—
360	C₂×C₄²	—	2	2	no	—
361	#107	C₂³×C₃₁	1	16	yes	complemented
362	#106	C₂³×C₃₁	1	16	yes	complemented
363	#103	C₂³×C₃₁	1	16	yes	complemented
364	#103	C₂³×C₃₁	1	16	yes	complemented
365	C₂²⋊C₈	C₂³×C₃₁	1	8	yes	—
366	C₂²⋊C₈	C₂³×C₃₁	1	8	yes	—
367	C₃₁	C₂×#3095	1	1	yes	characteristic, direct product factor, Sylow
368	C₂⁴	—	2	4	no	—
369	C₂⁴	—	2	4	no	—
370	C₂⁴	—	4	2	no	—
371	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
372	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
373	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
374	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
375	C₂×Q₈	—	2	4	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	8	no	—
378	C₂×Q₈	—	2	16	no	—
379	C₂×Q₈	—	4	8	no	—
380	C₂×Q₈	—	4	4	no	—
381	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	16	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	16	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	4	4	no	—
398	C₂²×C₄	—	4	4	no	—
399	C₂²×C₄	—	4	4	no	—
400	C₂²×C₄	—	4	4	no	—
401	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
403	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
405	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
406	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
407	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
408	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
409	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
410	C₂²×C₄	#41×C₃₁	1	8	yes	—
411	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
412	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
413	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
414	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
415	M₁₆	—	2	16	no	—
416	C₂×C₈	—	2	8	no	—
417	C₂×C₈	C₂⁴×C₃₁	1	8	yes	—
418	C₄⋊C₄	—	2	8	no	—
419	C₄⋊C₄	—	2	8	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
427	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
428	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
429	C₂²⋊C₄	—	2	8	no	—
430	C₂²⋊C₄	—	2	8	no	—
431	C₂²⋊C₄	—	2	8	no	—
432	C₂²⋊C₄	—	2	8	no	—
433	C₄²	—	2	8	no	—
434	C₄²	—	2	8	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	8	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	2	8	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	4	4	no	—
445	C₂³	—	4	16	no	—
446	C₂³	C₃₁×#123	1	4	yes	—
447	C₂³	C₃₁×#137	1	4	yes	—
448	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
449	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
450	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
451	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
452	Q₈	—	2	8	no	—
453	Q₈	—	4	8	no	—
454	Q₈	—	4	4	no	—
455	C₂×C₄	—	2	8	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	8	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	8	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	4	8	no	—
469	C₂×C₄	—	4	8	no	—
470	C₂×C₄	—	4	8	no	—
471	C₂×C₄	—	4	4	no	—
472	C₂×C₄	—	4	8	no	—
473	C₂×C₄	—	4	4	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	C₃₁×#123	1	8	yes	—
477	C₂×C₄	C₃₁×#123	1	4	yes	—
478	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
479	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
480	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
481	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
482	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
483	C₂×C₄	C₂×#41×C₃₁	1	8	yes	—
484	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
485	C₈	—	2	8	no	—
486	C₂²	—	2	8	no	—
487	C₂²	—	2	8	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	4	16	no	—
496	C₂²	—	4	4	no	—
497	C₂²	C₂×C₃₁×#123	1	4	yes	—
498	C₂²	C₂×C₃₁×#123	1	2	yes	—
499	C₂²	C₂×C₃₁×#137	1	4	yes	—
500	C₂²	C₂×C₃₁×#137	1	2	yes	—
501	C₂²	C₃₁×#575	1	2	yes	—
502	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
503	C₄	—	2	2	no	—
504	C₄	—	2	2	no	—
505	C₄	—	4	4	no	—
506	C₄	—	4	4	no	—
507	C₄	—	4	4	no	—
508	C₄	—	4	4	no	—
509	C₄	C₂×C₃₁×#123	1	4	yes	—
510	C₄	C₂×C₃₁×#123	1	2	yes	—
511	C₄	C₂²×#41×C₃₁	1	2	yes	—
512	C₂	—	2	4	no	—
513	C₂	—	2	4	no	—
514	C₂	—	4	2	no	—
515	C₂	C₃₁×#3095	1	4	yes	direct product factor
516	C₂	C₂²×C₃₁×#123	1	1	yes	characteristic
517	C₂	C₂²×C₃₁×#137	1	1	yes	characteristic
518	C₂	C₂×C₃₁×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₂⁵×C₃₁	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂⁴×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃₁×#3095	C₂	direct (N × H)
4. C₂×C₃₁×#484	C₂	semidirect
5. C₂×C₃₁×#485	C₂	semidirect
6. C₂×C₃₁×#483	C₂	semidirect
7. C₂×C₃₁×#428	C₂	semidirect
8. C₂×C₃₁×#419	C₂	semidirect
32. C₃₁×#485	C₂²	semidirect
33. C₃₁×#484	C₂²	semidirect
34. C₃₁×#483	C₂²	semidirect
35. C₃₁×#428	C₂²	semidirect
36. C₂×C₃₁×#107	C₂²	semidirect
37. C₂×C₃₁×#106	C₂²	semidirect
38. C₃₁×#419	C₂²	semidirect
39. C₂×C₃₁×#103	C₂²	semidirect
40. C₂×C₃₁×#103	C₂²	semidirect
102. C₃₁×#107	C₂³	semidirect
103. C₃₁×#106	C₂³	semidirect
104. C₃₁×#103	C₂³	semidirect
105. C₃₁×#103	C₂³	semidirect
175. C₂×#3095	C₃₁	direct (N × H)
229. #3095	C₂×C₃₁	direct (N × H)
230. C₂×#484	C₂×C₃₁	semidirect
231. C₂×#485	C₂×C₃₁	semidirect
232. C₂×#483	C₂×C₃₁	semidirect
233. C₂×#428	C₂×C₃₁	semidirect
234. C₂×#419	C₂×C₃₁	semidirect
284. #485	C₂²×C₃₁	semidirect
285. #484	C₂²×C₃₁	semidirect
286. #483	C₂²×C₃₁	semidirect
287. #428	C₂²×C₃₁	semidirect
288. C₂×#107	C₂²×C₃₁	semidirect
289. C₂×#106	C₂²×C₃₁	semidirect
290. #419	C₂²×C₃₁	semidirect
291. C₂×#103	C₂²×C₃₁	semidirect
292. C₂×#103	C₂²×C₃₁	semidirect
299. C₂×C₃₁	#3095	direct (N × H)
361. #107	C₂³×C₃₁	semidirect
362. #106	C₂³×C₃₁	semidirect
363. #103	C₂³×C₃₁	semidirect
364. #103	C₂³×C₃₁	semidirect
367. C₃₁	C₂×#3095	direct (N × H)
515. C₂	C₃₁×#3095	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃₁×C₂²⋊Q₈	2
C₂²×C₃₁×#117	2
C₃₁×#3095	2
C₂×C₃₁×#484	2
C₂×C₃₁×#485	2
C₂×C₃₁×#483	2
C₂×C₃₁×#428	2
C₂×C₃₁×#419	2
C₂×C₃₁×#407	2
C₂×#3095	31

Subgroups — C2×C31×#3095 #21517269

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3095 #21517269