Subgroups — C₂×C₃₁×#2504 #21491540

Order 7936.

3438 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×#121	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2504	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃₁×#397	C₂	1	4	yes	maximal, complemented
5	C₂×C₃₁×#390	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#386	C₂	1	4	yes	maximal, complemented
7	C₂×C₃₁×#382	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₃₁	C₂²	1	2	yes	—
10	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₃₁	C₂²	1	2	yes	—
13	C₂×C₃₁×#121	—	2	8	no	—
14	C₂×C₃₁×#121	C₂²	1	8	yes	—
15	C₂²×C₄⋊C₄×C₃₁	—	2	8	no	—
16	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₃₁	C₂²	1	8	yes	complemented
20	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
21	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
22	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	8	yes	—
23	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
24	C₃₁×#397	C₂²	1	32	yes	complemented
25	C₃₁×#390	C₂²	1	16	yes	complemented
26	C₃₁×#386	C₂²	1	32	yes	complemented
27	C₃₁×#382	C₂²	1	16	yes	complemented
28	C₄×C₂²⋊C₄×C₃₁	C₂²	1	8	yes	complemented
29	C₂×C₃₁×#95	C₂²	1	2	yes	—
30	C₂×C₃₁×#95	C₂²	1	8	yes	—
31	C₂⁵×C₃₁	C₂³	1	2	yes	—
32	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
33	C₂²×D₄×C₃₁	—	2	8	no	—
34	C₂²×D₄×C₃₁	—	2	16	no	—
35	C₂²×D₄×C₃₁	—	2	4	no	—
36	C₂²×D₄×C₃₁	—	2	8	no	—
37	C₂²×D₄×C₃₁	C₂³	1	8	yes	—
38	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
39	C₂³×C₄×C₃₁	—	2	8	no	—
40	C₂³×C₄×C₃₁	—	2	8	no	—
41	C₂³×C₄×C₃₁	—	4	8	no	—
42	C₂³×C₄×C₃₁	D₄	1	8	yes	—
43	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
44	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
45	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
46	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
47	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₃₁	C₂³	1	8	yes	—
49	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
50	C₃₁×#121	—	2	32	no	—
51	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
52	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
53	C₂×C₄⋊C₄×C₃₁	—	2	32	no	—
54	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
55	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
56	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
57	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
58	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
59	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
60	C₂×C₂²⋊C₄×C₃₁	—	4	16	no	—
61	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
62	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
63	C₂×C₂²⋊C₄×C₃₁	C₂³	1	32	yes	—
64	C₂×C₄²×C₃₁	—	2	8	no	—
65	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
66	C₃₁×#95	C₂³	1	8	yes	—
67	C₃₁×#95	C₂³	1	32	yes	—
68	C₂⁴×C₃₁	—	2	4	no	—
69	C₂⁴×C₃₁	—	2	4	no	—
70	C₂⁴×C₃₁	—	2	4	no	—
71	C₂⁴×C₃₁	—	2	8	no	—
72	C₂⁴×C₃₁	—	2	8	no	—
73	C₂⁴×C₃₁	—	2	8	no	—
74	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
75	C₂⁴×C₃₁	#41	1	8	yes	—
76	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
77	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
78	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
79	C₂×D₄×C₃₁	—	2	16	no	—
80	C₂×D₄×C₃₁	—	2	32	no	—
81	C₂×D₄×C₃₁	—	2	8	no	—
82	C₂×D₄×C₃₁	—	2	16	no	—
83	C₂×D₄×C₃₁	—	4	32	no	—
84	C₂×D₄×C₃₁	—	4	16	no	—
85	C₂²×C₄×C₃₁	—	2	4	no	—
86	C₂²×C₄×C₃₁	—	2	32	no	—
87	C₂²×C₄×C₃₁	—	2	16	no	—
88	C₂²×C₄×C₃₁	—	2	4	no	—
89	C₂²×C₄×C₃₁	—	2	16	no	—
90	C₂²×C₄×C₃₁	—	2	8	no	—
91	C₂²×C₄×C₃₁	—	2	8	no	—
92	C₂²×C₄×C₃₁	—	2	8	no	—
93	C₂²×C₄×C₃₁	—	2	8	no	—
94	C₂²×C₄×C₃₁	—	2	8	no	—
95	C₂²×C₄×C₃₁	—	2	16	no	—
96	C₂²×C₄×C₃₁	—	4	16	no	—
97	C₂²×C₄×C₃₁	—	4	32	no	—
98	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
99	C₂²×C₄×C₃₁	C₂×D₄	1	16	yes	—
100	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₃₁	#41	1	8	yes	—
102	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
103	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
104	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
105	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
106	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
107	C₄⋊C₄×C₃₁	—	2	16	no	—
108	C₄⋊C₄×C₃₁	—	2	16	no	—
109	C₄⋊C₄×C₃₁	—	2	8	no	—
110	C₂²⋊C₄×C₃₁	—	2	16	no	—
111	C₂²⋊C₄×C₃₁	—	2	16	no	—
112	C₂²⋊C₄×C₃₁	—	4	32	no	—
113	C₄²×C₃₁	—	2	16	no	—
114	C₂×#2504	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂³×C₃₁	—	2	8	no	—
116	C₂³×C₃₁	—	2	8	no	—
117	C₂³×C₃₁	—	2	32	no	—
118	C₂³×C₃₁	—	2	4	no	—
119	C₂³×C₃₁	—	2	4	no	—
120	C₂³×C₃₁	—	2	4	no	—
121	C₂³×C₃₁	—	2	8	no	—
122	C₂³×C₃₁	—	2	8	no	—
123	C₂³×C₃₁	—	2	8	no	—
124	C₂³×C₃₁	—	4	8	no	—
125	C₂³×C₃₁	—	4	8	no	—
126	C₂³×C₃₁	—	4	8	no	—
127	C₂³×C₃₁	—	4	32	no	—
128	C₂³×C₃₁	#124	1	16	yes	—
129	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
130	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
131	C₂³×C₃₁	C₂×#41	1	8	yes	—
132	C₂³×C₃₁	C₂×#41	1	4	yes	—
133	C₂³×C₃₁	C₂×#41	1	4	yes	—
134	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
135	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
136	D₄×C₃₁	—	4	32	no	—
137	D₄×C₃₁	—	4	16	no	—
138	C₂×C₄×C₃₁	—	2	8	no	—
139	C₂×C₄×C₃₁	—	2	4	no	—
140	C₂×C₄×C₃₁	—	2	32	no	—
141	C₂×C₄×C₃₁	—	2	4	no	—
142	C₂×C₄×C₃₁	—	2	8	no	—
143	C₂×C₄×C₃₁	—	2	8	no	—
144	C₂×C₄×C₃₁	—	2	8	no	—
145	C₂×C₄×C₃₁	—	2	8	no	—
146	C₂×C₄×C₃₁	—	2	8	no	—
147	C₂×C₄×C₃₁	—	2	16	no	—
148	C₂×C₄×C₃₁	—	4	32	no	—
149	C₂×C₄×C₃₁	—	4	8	no	—
150	C₂×C₄×C₃₁	—	4	16	no	—
151	C₂×C₄×C₃₁	—	4	16	no	—
152	C₂×C₄×C₃₁	#123	1	16	yes	—
153	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
154	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
155	C₂×C₄×C₃₁	C₂×#41	1	8	yes	—
156	C₂²×#121	C₂×C₃₁	1	1	yes	characteristic
157	C₂³×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
158	#2504	C₂×C₃₁	1	16	yes	direct product factor
159	C₂×#397	C₂×C₃₁	1	4	yes	complemented
160	C₂×#390	C₂×C₃₁	1	2	yes	complemented
161	C₂×#386	C₂×C₃₁	1	4	yes	complemented
162	C₂×#382	C₂×C₃₁	1	2	yes	complemented
163	C₂×C₄×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
164	C₂²×C₃₁	—	2	4	no	—
165	C₂²×C₃₁	—	2	4	no	—
166	C₂²×C₃₁	—	2	16	no	—
167	C₂²×C₃₁	—	2	32	no	—
168	C₂²×C₃₁	—	4	4	no	—
169	C₂²×C₃₁	—	4	4	no	—
170	C₂²×C₃₁	—	4	4	no	—
171	C₂²×C₃₁	—	4	16	no	—
172	C₂²×C₃₁	—	8	16	no	—
173	C₂²×C₃₁	C₂×#123	1	4	yes	—
174	C₂²×C₃₁	C₂×#124	1	8	yes	—
175	C₂²×C₃₁	C₂×#124	1	4	yes	—
176	C₂²×C₃₁	#535	1	4	yes	—
177	C₂²×C₃₁	#553	1	16	yes	—
178	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
179	C₂²×C₃₁	C₂²×#41	1	2	yes	—
180	C₂²×C₃₁	C₂²×#41	1	2	yes	—
181	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
182	C₄×C₃₁	—	2	4	no	—
183	C₄×C₃₁	—	4	4	no	—
184	C₄×C₃₁	—	4	8	no	—
185	C₄×C₃₁	—	4	8	no	—
186	C₄×C₃₁	C₂×#123	1	8	yes	—
187	C₂³×D₄	C₂²×C₃₁	1	2	yes	—
188	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
189	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
190	C₂⁴×C₄	C₂²×C₃₁	1	2	yes	—
191	C₂×#121	—	2	8	no	—
192	C₂×#121	C₂²×C₃₁	1	8	yes	—
193	C₂²×C₄⋊C₄	—	2	8	no	—
194	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
195	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
196	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
197	C₂²×C₄⋊C₄	C₂²×C₃₁	1	8	yes	complemented
198	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
199	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
200	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	8	yes	—
201	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
202	#397	C₂²×C₃₁	1	32	yes	complemented
203	#390	C₂²×C₃₁	1	16	yes	complemented
204	#386	C₂²×C₃₁	1	32	yes	complemented
205	#382	C₂²×C₃₁	1	16	yes	complemented
206	C₄×C₂²⋊C₄	C₂²×C₃₁	1	8	yes	complemented
207	C₂×#95	C₂²×C₃₁	1	2	yes	—
208	C₂×#95	C₂²×C₃₁	1	8	yes	—
209	C₂×C₃₁	—	2	8	no	—
210	C₂×C₃₁	—	8	4	no	—
211	C₂×C₃₁	#2504	1	8	yes	direct product factor
212	C₂×C₃₁	C₂²×#123	1	1	yes	characteristic
213	C₂×C₃₁	C₂²×#124	1	1	yes	characteristic
214	C₂×C₃₁	C₂×#535	1	1	yes	characteristic
215	C₂×C₃₁	C₂×#553	1	4	yes	—
216	C₂⁵	C₂³×C₃₁	1	2	yes	—
217	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
218	C₂²×D₄	—	2	8	no	—
219	C₂²×D₄	—	2	16	no	—
220	C₂²×D₄	—	2	4	no	—
221	C₂²×D₄	—	2	8	no	—
222	C₂²×D₄	C₂³×C₃₁	1	8	yes	—
223	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
224	C₂³×C₄	—	2	8	no	—
225	C₂³×C₄	—	2	8	no	—
226	C₂³×C₄	—	4	8	no	—
227	C₂³×C₄	D₄×C₃₁	1	8	yes	—
228	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
229	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
230	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
231	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
232	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
233	C₂³×C₄	C₂³×C₃₁	1	8	yes	—
234	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
235	#121	—	2	32	no	—
236	C₂×C₄⋊C₄	—	2	8	no	—
237	C₂×C₄⋊C₄	—	2	8	no	—
238	C₂×C₄⋊C₄	—	2	32	no	—
239	C₂×C₄⋊C₄	—	2	4	no	—
240	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
241	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
242	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
243	C₂×C₂²⋊C₄	—	2	8	no	—
244	C₂×C₂²⋊C₄	—	2	8	no	—
245	C₂×C₂²⋊C₄	—	4	16	no	—
246	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
247	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
248	C₂×C₂²⋊C₄	C₂³×C₃₁	1	32	yes	—
249	C₂×C₄²	—	2	8	no	—
250	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
251	#95	C₂³×C₃₁	1	8	yes	—
252	#95	C₂³×C₃₁	1	32	yes	—
253	C₃₁	C₂×#2504	1	1	yes	characteristic, direct product factor, Sylow
254	C₂⁴	—	2	4	no	—
255	C₂⁴	—	2	4	no	—
256	C₂⁴	—	2	4	no	—
257	C₂⁴	—	2	8	no	—
258	C₂⁴	—	2	8	no	—
259	C₂⁴	—	2	8	no	—
260	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
261	C₂⁴	#41×C₃₁	1	8	yes	—
262	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
263	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
264	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
265	C₂×D₄	—	2	16	no	—
266	C₂×D₄	—	2	32	no	—
267	C₂×D₄	—	2	8	no	—
268	C₂×D₄	—	2	16	no	—
269	C₂×D₄	—	4	32	no	—
270	C₂×D₄	—	4	16	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	32	no	—
273	C₂²×C₄	—	2	16	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	16	no	—
276	C₂²×C₄	—	2	8	no	—
277	C₂²×C₄	—	2	8	no	—
278	C₂²×C₄	—	2	8	no	—
279	C₂²×C₄	—	2	8	no	—
280	C₂²×C₄	—	2	8	no	—
281	C₂²×C₄	—	2	16	no	—
282	C₂²×C₄	—	4	16	no	—
283	C₂²×C₄	—	4	32	no	—
284	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
285	C₂²×C₄	C₂×D₄×C₃₁	1	16	yes	—
286	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
287	C₂²×C₄	#41×C₃₁	1	8	yes	—
288	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
289	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
290	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
291	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
292	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
293	C₄⋊C₄	—	2	16	no	—
294	C₄⋊C₄	—	2	16	no	—
295	C₄⋊C₄	—	2	8	no	—
296	C₂²⋊C₄	—	2	16	no	—
297	C₂²⋊C₄	—	2	16	no	—
298	C₂²⋊C₄	—	4	32	no	—
299	C₄²	—	2	16	no	—
300	C₂³	—	2	8	no	—
301	C₂³	—	2	8	no	—
302	C₂³	—	2	32	no	—
303	C₂³	—	2	4	no	—
304	C₂³	—	2	4	no	—
305	C₂³	—	2	4	no	—
306	C₂³	—	2	8	no	—
307	C₂³	—	2	8	no	—
308	C₂³	—	2	8	no	—
309	C₂³	—	4	8	no	—
310	C₂³	—	4	8	no	—
311	C₂³	—	4	8	no	—
312	C₂³	—	4	32	no	—
313	C₂³	C₃₁×#124	1	16	yes	—
314	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
315	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
316	C₂³	C₂×#41×C₃₁	1	8	yes	—
317	C₂³	C₂×#41×C₃₁	1	4	yes	—
318	C₂³	C₂×#41×C₃₁	1	4	yes	—
319	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
320	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
321	D₄	—	4	32	no	—
322	D₄	—	4	16	no	—
323	C₂×C₄	—	2	8	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	32	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	2	8	no	—
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	2	16	no	—
333	C₂×C₄	—	4	32	no	—
334	C₂×C₄	—	4	8	no	—
335	C₂×C₄	—	4	16	no	—
336	C₂×C₄	—	4	16	no	—
337	C₂×C₄	C₃₁×#123	1	16	yes	—
338	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
339	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
340	C₂×C₄	C₂×#41×C₃₁	1	8	yes	—
341	C₂²	—	2	4	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	16	no	—
344	C₂²	—	2	32	no	—
345	C₂²	—	4	4	no	—
346	C₂²	—	4	4	no	—
347	C₂²	—	4	4	no	—
348	C₂²	—	4	16	no	—
349	C₂²	—	8	16	no	—
350	C₂²	C₂×C₃₁×#123	1	4	yes	—
351	C₂²	C₂×C₃₁×#124	1	8	yes	—
352	C₂²	C₂×C₃₁×#124	1	4	yes	—
353	C₂²	C₃₁×#535	1	4	yes	—
354	C₂²	C₃₁×#553	1	16	yes	—
355	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
356	C₂²	C₂²×#41×C₃₁	1	2	yes	—
357	C₂²	C₂²×#41×C₃₁	1	2	yes	—
358	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
359	C₄	—	2	4	no	—
360	C₄	—	4	4	no	—
361	C₄	—	4	8	no	—
362	C₄	—	4	8	no	—
363	C₄	C₂×C₃₁×#123	1	8	yes	—
364	C₂	—	2	8	no	—
365	C₂	—	8	4	no	—
366	C₂	C₃₁×#2504	1	8	yes	direct product factor
367	C₂	C₂²×C₃₁×#123	1	1	yes	characteristic
368	C₂	C₂²×C₃₁×#124	1	1	yes	characteristic
369	C₂	C₂×C₃₁×#535	1	1	yes	characteristic
370	C₂	C₂×C₃₁×#553	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂²×C₃₁×#121	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×C₄⋊C₄×C₃₁	C₂	semidirect
3. C₃₁×#2504	C₂	direct (N × H)
4. C₂×C₃₁×#397	C₂	semidirect
5. C₂×C₃₁×#390	C₂	semidirect
6. C₂×C₃₁×#386	C₂	semidirect
7. C₂×C₃₁×#382	C₂	semidirect
8. C₂×C₄×C₂²⋊C₄×C₃₁	C₂	semidirect
19. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
24. C₃₁×#397	C₂²	semidirect
25. C₃₁×#390	C₂²	semidirect
26. C₃₁×#386	C₂²	semidirect
27. C₃₁×#382	C₂²	semidirect
28. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
114. C₂×#2504	C₃₁	direct (N × H)
157. C₂³×C₄⋊C₄	C₂×C₃₁	semidirect
158. #2504	C₂×C₃₁	direct (N × H)
159. C₂×#397	C₂×C₃₁	semidirect
160. C₂×#390	C₂×C₃₁	semidirect
161. C₂×#386	C₂×C₃₁	semidirect
162. C₂×#382	C₂×C₃₁	semidirect
163. C₂×C₄×C₂²⋊C₄	C₂×C₃₁	semidirect
197. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
202. #397	C₂²×C₃₁	semidirect
203. #390	C₂²×C₃₁	semidirect
204. #386	C₂²×C₃₁	semidirect
205. #382	C₂²×C₃₁	semidirect
206. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
211. C₂×C₃₁	#2504	direct (N × H)
253. C₃₁	C₂×#2504	direct (N × H)
366. C₂	C₃₁×#2504	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×#121	2
C₂³×C₄⋊C₄×C₃₁	2
C₃₁×#2504	2
C₂×C₃₁×#397	2
C₂×C₃₁×#390	2
C₂×C₃₁×#386	2
C₂×C₃₁×#382	2
C₂×C₄×C₂²⋊C₄×C₃₁	2
C₂×#2504	31

Subgroups — C2×C31×#2504 #21491540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#2504 #21491540