Subgroups — C₂×C₃₁×#3080 #21517242

Order 7936.

2142 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3080	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃₁×#479	C₂	1	4	yes	maximal, complemented
5	C₂×C₃₁×#478	C₂	1	4	yes	maximal, complemented
6	C₂×C₃₁×#428	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₁×#423	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#417	C₂	1	2	yes	maximal
9	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
11	C₂×C₃₁×#125	—	2	1	no	—
12	C₂×C₃₁×#125	—	2	1	no	—
13	C₂×C₃₁×#125	—	2	4	no	—
14	C₂×C₃₁×#125	C₂²	1	4	yes	—
15	C₂×C₃₁×#125	C₂²	1	8	yes	complemented
16	C₄×#41×C₃₁	—	2	4	no	—
17	C₄×#41×C₃₁	C₂²	1	8	yes	—
18	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₃₁	—	2	2	no	—
20	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
21	C₂×C₃₁×#117	—	2	1	no	—
22	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₃₁	—	2	2	no	—
24	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
25	C₂²×C₄²×C₃₁	—	2	1	no	—
26	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
27	C₃₁×#479	C₂²	1	32	yes	complemented
28	C₃₁×#478	C₂²	1	32	yes	complemented
29	C₃₁×#428	C₂²	1	16	yes	complemented
30	C₂×C₃₁×#107	C₂²	1	4	yes	—
31	C₂×C₃₁×#106	C₂²	1	4	yes	—
32	C₃₁×#423	C₂²	1	8	yes	complemented
33	C₂×C₃₁×C₄⋊C₈	C₂²	1	4	yes	—
34	C₃₁×#417	C₂²	1	16	yes	—
35	C₂×C₃₁×#103	C₂²	1	4	yes	—
36	C₂×C₃₁×#102	C₂²	1	4	yes	—
37	C₂×#41×C₃₁	—	2	2	no	—
38	C₂×#41×C₃₁	—	2	4	no	—
39	C₂×#41×C₃₁	Q₈	1	8	yes	—
40	C₂×#41×C₃₁	C₂³	1	4	yes	—
41	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
42	C₂²×D₄×C₃₁	—	2	1	no	—
43	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₃₁	—	2	1	no	—
45	C₂³×C₄×C₃₁	—	2	2	no	—
46	C₂³×C₄×C₃₁	—	2	2	no	—
47	C₂³×C₄×C₃₁	D₄	1	2	yes	—
48	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
49	C₂×M₁₆×C₃₁	—	2	8	no	—
50	C₂×M₁₆×C₃₁	C₂³	1	8	yes	—
51	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
52	C₃₁×#125	—	2	8	no	—
53	C₃₁×#125	—	2	8	no	—
54	C₃₁×#125	—	2	8	no	—
55	C₃₁×#125	C₂³	1	16	yes	—
56	C₄×Q₈×C₃₁	—	2	4	no	—
57	C₄×Q₈×C₃₁	C₂³	1	8	yes	—
58	C₄×D₄×C₃₁	—	2	16	no	—
59	C₄×D₄×C₃₁	—	2	4	no	—
60	C₄×D₄×C₃₁	C₂³	1	8	yes	—
61	C₃₁×#117	—	2	2	no	—
62	C₃₁×#117	—	2	8	no	—
63	C₃₁×#117	C₂³	1	4	yes	—
64	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
65	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
66	C₂×C₄⋊C₄×C₃₁	—	2	16	no	—
67	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
68	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
69	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
70	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
71	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
72	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
73	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
75	C₂×C₄²×C₃₁	—	2	1	no	—
76	C₂×C₄²×C₃₁	—	2	2	no	—
77	C₂×C₄²×C₃₁	—	2	8	no	—
78	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₃₁	D₄	1	4	yes	—
81	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
82	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
83	C₃₁×#107	C₂³	1	16	yes	—
84	C₃₁×#106	C₂³	1	16	yes	—
85	C₃₁×C₄⋊C₈	C₂³	1	16	yes	—
86	C₃₁×#103	C₂³	1	16	yes	—
87	C₃₁×#102	C₂³	1	16	yes	—
88	C₂⁴×C₃₁	—	2	1	no	—
89	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
90	#41×C₃₁	—	2	16	no	—
91	#41×C₃₁	—	2	8	no	—
92	#41×C₃₁	C₂×Q₈	1	16	yes	—
93	C₂×Q₈×C₃₁	—	2	1	no	—
94	C₂×Q₈×C₃₁	—	2	2	no	—
95	C₂×Q₈×C₃₁	C₂×Q₈	1	4	yes	—
96	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
97	C₂×D₄×C₃₁	—	2	8	no	—
98	C₂×D₄×C₃₁	—	2	4	no	—
99	C₂×D₄×C₃₁	—	2	1	no	—
100	C₂×D₄×C₃₁	—	2	2	no	—
101	C₂×D₄×C₃₁	C₂×Q₈	1	4	yes	—
102	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
103	C₂²×C₄×C₃₁	—	2	1	no	—
104	C₂²×C₄×C₃₁	—	2	8	no	—
105	C₂²×C₄×C₃₁	—	2	4	no	—
106	C₂²×C₄×C₃₁	—	2	8	no	—
107	C₂²×C₄×C₃₁	—	2	2	no	—
108	C₂²×C₄×C₃₁	—	2	4	no	—
109	C₂²×C₄×C₃₁	—	2	8	no	—
110	C₂²×C₄×C₃₁	—	4	4	no	—
111	C₂²×C₄×C₃₁	—	4	8	no	—
112	C₂²×C₄×C₃₁	—	4	8	no	—
113	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₃₁	C₂×D₄	1	8	yes	—
116	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₃₁	C₂×Q₈	1	4	yes	—
119	C₂²×C₄×C₃₁	#41	1	4	yes	—
120	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
121	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
122	M₁₆×C₃₁	—	2	16	no	—
123	C₂×C₈×C₃₁	—	2	8	no	—
124	C₂×C₈×C₃₁	C₂⁴	1	8	yes	—
125	C₄⋊C₄×C₃₁	—	2	16	no	—
126	C₄⋊C₄×C₃₁	—	2	16	no	—
127	C₄⋊C₄×C₃₁	—	2	8	no	—
128	C₄⋊C₄×C₃₁	—	2	4	no	—
129	C₄⋊C₄×C₃₁	—	2	8	no	—
130	C₄⋊C₄×C₃₁	—	2	2	no	—
131	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
132	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
133	C₂²⋊C₄×C₃₁	—	2	4	no	—
134	C₂²⋊C₄×C₃₁	—	2	8	no	—
135	C₄²×C₃₁	—	2	4	no	—
136	C₄²×C₃₁	—	2	8	no	—
137	C₄²×C₃₁	C₂×D₄	1	4	yes	—
138	C₄²×C₃₁	C₂×D₄	1	4	yes	—
139	C₄²×C₃₁	C₂×D₄	1	4	yes	—
140	C₄²×C₃₁	C₂⁴	1	4	yes	—
141	C₂×#3080	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂³×C₃₁	—	2	4	no	—
143	C₂³×C₃₁	—	2	4	no	—
144	C₂³×C₃₁	—	2	2	no	—
145	C₂³×C₃₁	—	4	4	no	—
146	C₂³×C₃₁	C₂²⋊Q₈	1	4	yes	—
147	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
148	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
149	Q₈×C₃₁	—	2	4	no	—
150	Q₈×C₃₁	—	2	2	no	—
151	Q₈×C₃₁	C₂²×Q₈	1	4	yes	—
152	D₄×C₃₁	—	2	16	no	—
153	D₄×C₃₁	—	2	4	no	—
154	D₄×C₃₁	—	2	2	no	—
155	D₄×C₃₁	C₂²×Q₈	1	4	yes	—
156	C₂×C₄×C₃₁	—	2	4	no	—
157	C₂×C₄×C₃₁	—	2	4	no	—
158	C₂×C₄×C₃₁	—	2	4	no	—
159	C₂×C₄×C₃₁	—	2	2	no	—
160	C₂×C₄×C₃₁	—	2	16	no	—
161	C₂×C₄×C₃₁	—	2	4	no	—
162	C₂×C₄×C₃₁	—	2	8	no	—
163	C₂×C₄×C₃₁	—	4	8	no	—
164	C₂×C₄×C₃₁	—	4	16	no	—
165	C₂×C₄×C₃₁	—	4	16	no	—
166	C₂×C₄×C₃₁	—	4	4	no	—
167	C₂×C₄×C₃₁	—	4	8	no	—
168	C₂×C₄×C₃₁	C₂²⋊Q₈	1	4	yes	—
169	C₂×C₄×C₃₁	C₂²⋊Q₈	1	8	yes	—
170	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
171	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
172	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
173	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
175	C₂×C₄×C₃₁	C₂²×Q₈	1	4	yes	—
176	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
177	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
178	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
179	C₈×C₃₁	—	2	8	no	—
180	C₂²×#125	C₂×C₃₁	1	1	yes	characteristic, complemented
181	C₂×C₄×#41	C₂×C₃₁	1	1	yes	characteristic
182	#3080	C₂×C₃₁	1	16	yes	direct product factor
183	C₂×#479	C₂×C₃₁	1	4	yes	complemented
184	C₂×#478	C₂×C₃₁	1	4	yes	complemented
185	C₂×#428	C₂×C₃₁	1	2	yes	complemented
186	C₂×#423	C₂×C₃₁	1	1	yes	characteristic, complemented
187	C₂×#417	C₂×C₃₁	1	2	yes	—
188	C₂²×C₃₁	—	2	8	no	—
189	C₂²×C₃₁	—	2	4	no	—
190	C₂²×C₃₁	—	2	4	no	—
191	C₂²×C₃₁	—	4	8	no	—
192	C₂²×C₃₁	—	4	4	no	—
193	C₂²×C₃₁	C₂×C₂²⋊Q₈	1	4	yes	—
194	C₂²×C₃₁	C₂×C₂²⋊Q₈	1	2	yes	—
195	C₂²×C₃₁	#575	1	4	yes	—
196	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
197	C₄×C₃₁	—	2	4	no	—
198	C₄×C₃₁	—	2	4	no	—
199	C₄×C₃₁	—	2	4	no	—
200	C₄×C₃₁	—	4	4	no	—
201	C₄×C₃₁	—	4	8	no	—
202	C₄×C₃₁	C₂×C₂²⋊Q₈	1	4	yes	—
203	C₄×C₃₁	C₂×C₂²⋊Q₈	1	2	yes	—
204	C₄×C₃₁	C₂³×Q₈	1	1	yes	characteristic
205	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
206	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
207	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
208	C₂×#125	—	2	1	no	—
209	C₂×#125	—	2	4	no	—
210	C₂×#125	—	2	1	no	—
211	C₂×#125	C₂²×C₃₁	1	4	yes	—
212	C₂×#125	C₂²×C₃₁	1	8	yes	complemented
213	C₄×#41	—	2	4	no	—
214	C₄×#41	C₂²×C₃₁	1	8	yes	—
215	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
216	C₂×C₄×D₄	—	2	2	no	—
217	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
218	C₂×#117	—	2	1	no	—
219	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
220	C₂²×C₄⋊C₄	—	2	2	no	—
221	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
222	C₂²×C₄²	—	2	1	no	—
223	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
224	#479	C₂²×C₃₁	1	32	yes	complemented
225	#478	C₂²×C₃₁	1	32	yes	complemented
226	#428	C₂²×C₃₁	1	16	yes	complemented
227	C₂×#107	C₂²×C₃₁	1	4	yes	—
228	C₂×#106	C₂²×C₃₁	1	4	yes	—
229	#423	C₂²×C₃₁	1	8	yes	complemented
230	C₂×C₄⋊C₈	C₂²×C₃₁	1	4	yes	—
231	#417	C₂²×C₃₁	1	16	yes	—
232	C₂×#103	C₂²×C₃₁	1	4	yes	—
233	C₂×#102	C₂²×C₃₁	1	4	yes	—
234	C₂×C₃₁	—	2	4	no	—
235	C₂×C₃₁	—	4	4	no	—
236	C₂×C₃₁	#3080	1	4	yes	direct product factor
237	C₂×C₃₁	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
238	C₂×C₃₁	C₂×#575	1	2	yes	—
239	C₂×#41	—	2	2	no	—
240	C₂×#41	—	2	4	no	—
241	C₂×#41	Q₈×C₃₁	1	8	yes	—
242	C₂×#41	C₂³×C₃₁	1	4	yes	—
243	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
244	C₂²×D₄	—	2	1	no	—
245	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
246	C₂³×C₄	—	2	1	no	—
247	C₂³×C₄	—	2	2	no	—
248	C₂³×C₄	—	2	2	no	—
249	C₂³×C₄	D₄×C₃₁	1	2	yes	—
250	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
251	C₂×M₁₆	—	2	8	no	—
252	C₂×M₁₆	C₂³×C₃₁	1	8	yes	—
253	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
254	#125	—	2	8	no	—
255	#125	—	2	8	no	—
256	#125	—	2	8	no	—
257	#125	C₂³×C₃₁	1	16	yes	—
258	C₄×Q₈	—	2	4	no	—
259	C₄×Q₈	C₂³×C₃₁	1	8	yes	—
260	C₄×D₄	—	2	16	no	—
261	C₄×D₄	—	2	4	no	—
262	C₄×D₄	C₂³×C₃₁	1	8	yes	—
263	#117	—	2	2	no	—
264	#117	—	2	8	no	—
265	#117	C₂³×C₃₁	1	4	yes	—
266	C₂×C₄⋊C₄	—	2	4	no	—
267	C₂×C₄⋊C₄	—	2	4	no	—
268	C₂×C₄⋊C₄	—	2	16	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	4	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
273	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
274	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
275	C₂×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₄²	—	2	1	no	—
278	C₂×C₄²	—	2	2	no	—
279	C₂×C₄²	—	2	8	no	—
280	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
281	C₂×C₄²	D₄×C₃₁	1	4	yes	—
282	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
283	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
284	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
285	#107	C₂³×C₃₁	1	16	yes	—
286	#106	C₂³×C₃₁	1	16	yes	—
287	C₄⋊C₈	C₂³×C₃₁	1	16	yes	—
288	#103	C₂³×C₃₁	1	16	yes	—
289	#102	C₂³×C₃₁	1	16	yes	—
290	C₃₁	C₂×#3080	1	1	yes	characteristic, direct product factor, Sylow
291	C₂⁴	—	2	1	no	—
292	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
293	#41	—	2	16	no	—
294	#41	—	2	8	no	—
295	#41	C₂×Q₈×C₃₁	1	16	yes	—
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	C₂×Q₈×C₃₁	1	4	yes	—
299	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
300	C₂×D₄	—	2	8	no	—
301	C₂×D₄	—	2	4	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	C₂×Q₈×C₃₁	1	4	yes	—
305	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	8	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	8	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	8	no	—
313	C₂²×C₄	—	4	4	no	—
314	C₂²×C₄	—	4	8	no	—
315	C₂²×C₄	—	4	8	no	—
316	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
317	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
318	C₂²×C₄	C₂×D₄×C₃₁	1	8	yes	—
319	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
321	C₂²×C₄	C₂×Q₈×C₃₁	1	4	yes	—
322	C₂²×C₄	#41×C₃₁	1	4	yes	—
323	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
324	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
325	M₁₆	—	2	16	no	—
326	C₂×C₈	—	2	8	no	—
327	C₂×C₈	C₂⁴×C₃₁	1	8	yes	—
328	C₄⋊C₄	—	2	16	no	—
329	C₄⋊C₄	—	2	16	no	—
330	C₄⋊C₄	—	2	8	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	8	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
335	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
336	C₂²⋊C₄	—	2	4	no	—
337	C₂²⋊C₄	—	2	8	no	—
338	C₄²	—	2	4	no	—
339	C₄²	—	2	8	no	—
340	C₄²	C₂×D₄×C₃₁	1	4	yes	—
341	C₄²	C₂×D₄×C₃₁	1	4	yes	—
342	C₄²	C₂×D₄×C₃₁	1	4	yes	—
343	C₄²	C₂⁴×C₃₁	1	4	yes	—
344	C₂³	—	2	4	no	—
345	C₂³	—	2	4	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	4	4	no	—
348	C₂³	C₃₁×C₂²⋊Q₈	1	4	yes	—
349	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
350	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
351	Q₈	—	2	4	no	—
352	Q₈	—	2	2	no	—
353	Q₈	C₂²×Q₈×C₃₁	1	4	yes	—
354	D₄	—	2	16	no	—
355	D₄	—	2	4	no	—
356	D₄	—	2	2	no	—
357	D₄	C₂²×Q₈×C₃₁	1	4	yes	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	16	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	8	no	—
365	C₂×C₄	—	4	8	no	—
366	C₂×C₄	—	4	16	no	—
367	C₂×C₄	—	4	16	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	8	no	—
370	C₂×C₄	C₃₁×C₂²⋊Q₈	1	4	yes	—
371	C₂×C₄	C₃₁×C₂²⋊Q₈	1	8	yes	—
372	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
373	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
374	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
375	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
376	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
377	C₂×C₄	C₂²×Q₈×C₃₁	1	4	yes	—
378	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
379	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
380	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
381	C₈	—	2	8	no	—
382	C₂²	—	2	8	no	—
383	C₂²	—	2	4	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	4	8	no	—
386	C₂²	—	4	4	no	—
387	C₂²	C₂×C₃₁×C₂²⋊Q₈	1	4	yes	—
388	C₂²	C₂×C₃₁×C₂²⋊Q₈	1	2	yes	—
389	C₂²	C₃₁×#575	1	4	yes	—
390	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
391	C₄	—	2	4	no	—
392	C₄	—	2	4	no	—
393	C₄	—	2	4	no	—
394	C₄	—	4	4	no	—
395	C₄	—	4	8	no	—
396	C₄	C₂×C₃₁×C₂²⋊Q₈	1	4	yes	—
397	C₄	C₂×C₃₁×C₂²⋊Q₈	1	2	yes	—
398	C₄	C₂³×Q₈×C₃₁	1	1	yes	characteristic
399	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
400	C₂	—	2	4	no	—
401	C₂	—	4	4	no	—
402	C₂	C₃₁×#3080	1	4	yes	direct product factor
403	C₂	C₂²×C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
404	C₂	C₂×C₃₁×#575	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₂²×#41×C₃₁	C₂²
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
1. C₂²×C₃₁×#125	C₂	semidirect
3. C₃₁×#3080	C₂	direct (N × H)
4. C₂×C₃₁×#479	C₂	semidirect
5. C₂×C₃₁×#478	C₂	semidirect
6. C₂×C₃₁×#428	C₂	semidirect
7. C₂×C₃₁×#423	C₂	semidirect
15. C₂×C₃₁×#125	C₂²	semidirect
27. C₃₁×#479	C₂²	semidirect
28. C₃₁×#478	C₂²	semidirect
29. C₃₁×#428	C₂²	semidirect
32. C₃₁×#423	C₂²	semidirect
141. C₂×#3080	C₃₁	direct (N × H)
180. C₂²×#125	C₂×C₃₁	semidirect
182. #3080	C₂×C₃₁	direct (N × H)
183. C₂×#479	C₂×C₃₁	semidirect
184. C₂×#478	C₂×C₃₁	semidirect
185. C₂×#428	C₂×C₃₁	semidirect
186. C₂×#423	C₂×C₃₁	semidirect
212. C₂×#125	C₂²×C₃₁	semidirect
224. #479	C₂²×C₃₁	semidirect
225. #478	C₂²×C₃₁	semidirect
226. #428	C₂²×C₃₁	semidirect
229. #423	C₂²×C₃₁	semidirect
236. C₂×C₃₁	#3080	direct (N × H)
290. C₃₁	C₂×#3080	direct (N × H)
402. C₂	C₃₁×#3080	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×#125	2
C₂×C₄×#41×C₃₁	2
C₃₁×#3080	2
C₂×C₃₁×#479	2
C₂×C₃₁×#478	2
C₂×C₃₁×#428	2
C₂×C₃₁×#423	2
C₂×C₃₁×#417	2
C₂×#3080	31

Subgroups — C2×C31×#3080 #21517242

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3080 #21517242