Subgroups — C₃₁×#35001 #21491760

Order 7936.

4298 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#534	C₂	1	4	yes	maximal, complemented
2	C₂²×C₃₁×#121	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2856	C₂	1	4	yes	maximal, complemented
4	C₃₁×#2656	C₂	1	4	yes	maximal, complemented
5	C₃₁×#2539	C₂	1	8	yes	maximal, complemented
6	C₃₁×#2501	C₂	1	4	yes	maximal, complemented
7	C₃₁×#2433	C₂	1	4	yes	maximal, complemented
8	C₂×C₄×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₃₁	C₂²	1	4	yes	—
10	C₂³×D₄×C₃₁	C₂²	1	2	yes	complemented
11	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
12	C₃₁×#534	—	2	32	no	—
13	C₂×C₃₁×#127	C₂²	1	4	yes	complemented
14	C₂×C₃₁×#123	C₂²	1	16	yes	complemented
15	C₂×C₃₁×#121	—	2	16	no	—
16	C₂×C₃₁×#121	C₂²	1	4	yes	—
17	C₂×C₃₁×#121	C₂²	1	4	yes	—
18	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
19	C₂×C₃₁×#121	C₂²	1	16	yes	complemented
20	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
21	C₂×C₃₁×#120	C₂²	1	16	yes	complemented
22	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
23	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
25	C₂²×C₄²×C₃₁	C₂²	1	2	yes	complemented
26	C₃₁×#399	C₂²	1	16	yes	complemented
27	C₃₁×#392	C₂²	1	16	yes	complemented
28	C₃₁×#390	C₂²	1	8	yes	complemented
29	C₃₁×#390	C₂²	1	16	yes	complemented
30	C₃₁×#384	C₂²	1	4	yes	complemented
31	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
32	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
33	C₂×C₃₁×#95	C₂²	1	2	yes	complemented
34	C₂⁵×C₃₁	C₂³	1	4	yes	—
35	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
36	C₂²×D₄×C₃₁	—	2	16	no	—
37	C₂²×D₄×C₃₁	—	2	32	no	—
38	C₂²×D₄×C₃₁	—	2	8	no	—
39	C₂²×D₄×C₃₁	—	4	8	no	—
40	C₂²×D₄×C₃₁	C₂³	1	8	yes	—
41	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
42	C₂²×D₄×C₃₁	C₂³	1	8	yes	—
43	C₂²×D₄×C₃₁	C₂³	1	16	yes	—
44	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
45	C₂³×C₄×C₃₁	—	4	4	no	—
46	C₂³×C₄×C₃₁	D₄	1	8	yes	complemented
47	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
48	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
50	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
51	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
53	C₃₁×#127	—	4	8	no	—
54	C₃₁×#123	—	2	64	no	—
55	C₃₁×#121	—	2	16	no	—
56	C₃₁×#121	—	2	16	no	—
57	C₃₁×#121	—	2	16	no	—
58	C₃₁×#121	—	2	16	no	—
59	C₃₁×#121	—	2	64	no	—
60	C₃₁×#120	—	2	64	no	—
61	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
62	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
63	C₂×C₄⋊C₄×C₃₁	C₂³	1	16	yes	—
64	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
65	C₂×C₂²⋊C₄×C₃₁	—	2	16	no	—
66	C₂×C₂²⋊C₄×C₃₁	D₄	1	16	yes	complemented
67	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
68	C₂×C₂²⋊C₄×C₃₁	C₂³	1	32	yes	—
69	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
70	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
71	C₂×C₄²×C₃₁	—	4	4	no	—
72	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
73	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
74	C₃₁×#95	C₂³	1	8	yes	—
75	C₂⁴×C₃₁	—	2	8	no	—
76	C₂⁴×C₃₁	—	2	16	no	—
77	C₂⁴×C₃₁	—	4	2	no	—
78	C₂⁴×C₃₁	—	4	2	no	—
79	C₂⁴×C₃₁	—	4	8	no	—
80	C₂⁴×C₃₁	—	4	8	no	—
81	C₂⁴×C₃₁	C₂×D₄	1	8	yes	—
82	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
83	C₂⁴×C₃₁	C₂⁴	1	8	yes	—
84	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
85	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
86	C₂×D₄×C₃₁	—	2	32	no	—
87	C₂×D₄×C₃₁	—	2	16	no	—
88	C₂×D₄×C₃₁	—	2	16	no	—
89	C₂×D₄×C₃₁	—	2	32	no	—
90	C₂×D₄×C₃₁	—	2	8	no	—
91	C₂×D₄×C₃₁	—	2	8	no	—
92	C₂×D₄×C₃₁	—	2	32	no	—
93	C₂×D₄×C₃₁	—	2	16	no	—
94	C₂×D₄×C₃₁	—	4	8	no	—
95	C₂×D₄×C₃₁	—	4	32	no	—
96	C₂×D₄×C₃₁	—	4	16	no	—
97	C₂×D₄×C₃₁	—	4	16	no	—
98	C₂×D₄×C₃₁	—	4	64	no	—
99	C₂²×C₄×C₃₁	—	2	4	no	—
100	C₂²×C₄×C₃₁	—	2	8	no	—
101	C₂²×C₄×C₃₁	—	2	8	no	—
102	C₂²×C₄×C₃₁	—	2	16	no	—
103	C₂²×C₄×C₃₁	—	4	16	no	—
104	C₂²×C₄×C₃₁	—	4	4	no	—
105	C₂²×C₄×C₃₁	—	4	4	no	—
106	C₂²×C₄×C₃₁	—	4	2	no	—
107	C₂²×C₄×C₃₁	—	4	4	no	—
108	C₂²×C₄×C₃₁	C₂×D₄	1	8	yes	—
109	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₃₁	C₂×D₄	1	8	yes	—
111	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
112	C₂²×C₄×C₃₁	C₂×D₄	1	16	yes	complemented
113	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
114	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
115	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
116	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
117	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
118	C₄⋊C₄×C₃₁	—	2	8	no	—
119	C₄⋊C₄×C₃₁	—	2	8	no	—
120	C₄⋊C₄×C₃₁	—	2	32	no	—
121	C₂²⋊C₄×C₃₁	—	2	16	no	—
122	C₂²⋊C₄×C₃₁	—	2	16	no	—
123	C₂²⋊C₄×C₃₁	—	2	64	no	—
124	C₂²⋊C₄×C₃₁	C₂×D₄	1	32	yes	complemented
125	C₄²×C₃₁	—	2	8	no	—
126	C₄²×C₃₁	—	4	4	no	—
127	#35001	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂³×C₃₁	—	2	2	no	—
129	C₂³×C₃₁	—	2	4	no	—
130	C₂³×C₃₁	—	2	2	no	—
131	C₂³×C₃₁	—	2	4	no	—
132	C₂³×C₃₁	—	2	8	no	—
133	C₂³×C₃₁	—	2	16	no	—
134	C₂³×C₃₁	—	2	16	no	—
135	C₂³×C₃₁	—	2	16	no	—
136	C₂³×C₃₁	—	4	4	no	—
137	C₂³×C₃₁	—	4	4	no	—
138	C₂³×C₃₁	—	4	16	no	—
139	C₂³×C₃₁	—	4	16	no	—
140	C₂³×C₃₁	—	4	16	no	—
141	C₂³×C₃₁	—	4	16	no	—
142	C₂³×C₃₁	—	8	32	no	—
143	C₂³×C₃₁	#127	1	16	yes	complemented
144	C₂³×C₃₁	C₂²×D₄	1	8	yes	—
145	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
146	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
147	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
148	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
149	D₄×C₃₁	—	4	16	no	—
150	D₄×C₃₁	—	4	32	no	—
151	D₄×C₃₁	—	4	32	no	—
152	D₄×C₃₁	—	4	16	no	—
153	D₄×C₃₁	—	8	32	no	—
154	C₂×C₄×C₃₁	—	2	8	no	—
155	C₂×C₄×C₃₁	—	2	2	no	—
156	C₂×C₄×C₃₁	—	2	4	no	—
157	C₂×C₄×C₃₁	—	2	8	no	—
158	C₂×C₄×C₃₁	—	2	8	no	—
159	C₂×C₄×C₃₁	—	2	16	no	—
160	C₂×C₄×C₃₁	—	2	8	no	—
161	C₂×C₄×C₃₁	—	2	16	no	—
162	C₂×C₄×C₃₁	—	4	8	no	—
163	C₂×C₄×C₃₁	—	4	4	no	—
164	C₂×C₄×C₃₁	—	4	16	no	—
165	C₂×C₄×C₃₁	—	4	16	no	—
166	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
167	C₂×C₄×C₃₁	C₂²×D₄	1	16	yes	—
168	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
169	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
170	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
171	C₂×#534	C₂×C₃₁	1	4	yes	complemented
172	C₂²×#121	C₂×C₃₁	1	2	yes	complemented
173	#2856	C₂×C₃₁	1	4	yes	complemented
174	#2656	C₂×C₃₁	1	4	yes	complemented
175	#2539	C₂×C₃₁	1	8	yes	complemented
176	#2501	C₂×C₃₁	1	4	yes	complemented
177	#2433	C₂×C₃₁	1	4	yes	complemented
178	C₂×C₄×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
179	C₂²×C₃₁	—	2	4	no	—
180	C₂²×C₃₁	—	2	2	no	—
181	C₂²×C₃₁	—	2	4	no	—
182	C₂²×C₃₁	—	2	2	no	—
183	C₂²×C₃₁	—	2	8	no	—
184	C₂²×C₃₁	—	2	16	no	—
185	C₂²×C₃₁	—	4	16	no	—
186	C₂²×C₃₁	—	4	8	no	—
187	C₂²×C₃₁	—	4	8	no	—
188	C₂²×C₃₁	—	4	8	no	—
189	C₂²×C₃₁	—	4	32	no	—
190	C₂²×C₃₁	—	8	32	no	—
191	C₂²×C₃₁	C₂×#127	1	8	yes	—
192	C₂²×C₃₁	C₂×#127	1	4	yes	—
193	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
194	C₂²×C₃₁	C₂³×D₄	1	2	yes	—
195	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
196	C₂²×C₃₁	#585	1	2	yes	—
197	C₄×C₃₁	—	2	2	no	—
198	C₄×C₃₁	—	2	4	no	—
199	C₄×C₃₁	—	2	16	no	—
200	C₄×C₃₁	—	4	8	no	—
201	C₄×C₃₁	#534	1	4	yes	complemented
202	C₂³×D₄	C₂²×C₃₁	1	4	yes	—
203	C₂³×D₄	C₂²×C₃₁	1	2	yes	complemented
204	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
205	#534	—	2	32	no	—
206	C₂×#127	C₂²×C₃₁	1	4	yes	complemented
207	C₂×#123	C₂²×C₃₁	1	16	yes	complemented
208	C₂×#121	—	2	16	no	—
209	C₂×#121	C₂²×C₃₁	1	4	yes	—
210	C₂×#121	C₂²×C₃₁	1	4	yes	—
211	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
212	C₂×#121	C₂²×C₃₁	1	16	yes	complemented
213	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
214	C₂×#120	C₂²×C₃₁	1	16	yes	complemented
215	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
216	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
217	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
218	C₂²×C₄²	C₂²×C₃₁	1	2	yes	complemented
219	#399	C₂²×C₃₁	1	16	yes	complemented
220	#392	C₂²×C₃₁	1	16	yes	complemented
221	#390	C₂²×C₃₁	1	8	yes	complemented
222	#390	C₂²×C₃₁	1	16	yes	complemented
223	#384	C₂²×C₃₁	1	4	yes	complemented
224	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
225	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
226	C₂×#95	C₂²×C₃₁	1	2	yes	complemented
227	C₂×C₃₁	—	2	8	no	—
228	C₂×C₃₁	—	2	4	no	—
229	C₂×C₃₁	—	8	8	no	—
230	C₂×C₃₁	C₂²×#127	1	1	yes	characteristic
231	C₂×C₃₁	C₂×#534	1	1	yes	characteristic
232	C₂×C₃₁	#3449	1	1	yes	characteristic
233	C₂×C₃₁	#3496	1	4	yes	—
234	C₂⁵	C₂³×C₃₁	1	4	yes	—
235	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
236	C₂²×D₄	—	2	16	no	—
237	C₂²×D₄	—	2	32	no	—
238	C₂²×D₄	—	2	8	no	—
239	C₂²×D₄	—	4	8	no	—
240	C₂²×D₄	C₂³×C₃₁	1	8	yes	—
241	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
242	C₂²×D₄	C₂³×C₃₁	1	8	yes	—
243	C₂²×D₄	C₂³×C₃₁	1	16	yes	—
244	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
245	C₂³×C₄	—	4	4	no	—
246	C₂³×C₄	D₄×C₃₁	1	8	yes	complemented
247	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
248	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
249	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
250	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
251	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
252	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
253	#127	—	4	8	no	—
254	#123	—	2	64	no	—
255	#121	—	2	16	no	—
256	#121	—	2	16	no	—
257	#121	—	2	16	no	—
258	#121	—	2	16	no	—
259	#121	—	2	64	no	—
260	#120	—	2	64	no	—
261	C₂×C₄⋊C₄	—	2	8	no	—
262	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
263	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
264	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	—
265	C₂×C₂²⋊C₄	—	2	16	no	—
266	C₂×C₂²⋊C₄	D₄×C₃₁	1	16	yes	complemented
267	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
268	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
269	C₂×C₂²⋊C₄	C₂³×C₃₁	1	32	yes	—
270	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
271	C₂×C₄²	—	4	4	no	—
272	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
273	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
274	#95	C₂³×C₃₁	1	8	yes	—
275	C₃₁	#35001	1	1	yes	characteristic, direct product factor, Sylow
276	C₂⁴	—	2	8	no	—
277	C₂⁴	—	2	16	no	—
278	C₂⁴	—	4	2	no	—
279	C₂⁴	—	4	2	no	—
280	C₂⁴	—	4	8	no	—
281	C₂⁴	—	4	8	no	—
282	C₂⁴	C₂×D₄×C₃₁	1	8	yes	—
283	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
284	C₂⁴	C₂⁴×C₃₁	1	8	yes	—
285	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
286	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
287	C₂×D₄	—	2	32	no	—
288	C₂×D₄	—	2	16	no	—
289	C₂×D₄	—	2	16	no	—
290	C₂×D₄	—	2	32	no	—
291	C₂×D₄	—	2	8	no	—
292	C₂×D₄	—	2	8	no	—
293	C₂×D₄	—	2	32	no	—
294	C₂×D₄	—	2	16	no	—
295	C₂×D₄	—	4	8	no	—
296	C₂×D₄	—	4	32	no	—
297	C₂×D₄	—	4	16	no	—
298	C₂×D₄	—	4	16	no	—
299	C₂×D₄	—	4	64	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	8	no	—
302	C₂²×C₄	—	2	8	no	—
303	C₂²×C₄	—	2	16	no	—
304	C₂²×C₄	—	4	16	no	—
305	C₂²×C₄	—	4	4	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	4	4	no	—
309	C₂²×C₄	C₂×D₄×C₃₁	1	8	yes	—
310	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
311	C₂²×C₄	C₂×D₄×C₃₁	1	8	yes	—
312	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
313	C₂²×C₄	C₂×D₄×C₃₁	1	16	yes	complemented
314	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
315	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
316	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
317	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
318	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
319	C₄⋊C₄	—	2	8	no	—
320	C₄⋊C₄	—	2	8	no	—
321	C₄⋊C₄	—	2	32	no	—
322	C₂²⋊C₄	—	2	16	no	—
323	C₂²⋊C₄	—	2	16	no	—
324	C₂²⋊C₄	—	2	64	no	—
325	C₂²⋊C₄	C₂×D₄×C₃₁	1	32	yes	complemented
326	C₄²	—	2	8	no	—
327	C₄²	—	4	4	no	—
328	C₂³	—	2	2	no	—
329	C₂³	—	2	4	no	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	4	no	—
332	C₂³	—	2	8	no	—
333	C₂³	—	2	16	no	—
334	C₂³	—	2	16	no	—
335	C₂³	—	2	16	no	—
336	C₂³	—	4	4	no	—
337	C₂³	—	4	4	no	—
338	C₂³	—	4	16	no	—
339	C₂³	—	4	16	no	—
340	C₂³	—	4	16	no	—
341	C₂³	—	4	16	no	—
342	C₂³	—	8	32	no	—
343	C₂³	C₃₁×#127	1	16	yes	complemented
344	C₂³	C₂²×D₄×C₃₁	1	8	yes	—
345	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
346	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
347	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
348	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
349	D₄	—	4	16	no	—
350	D₄	—	4	32	no	—
351	D₄	—	4	32	no	—
352	D₄	—	4	16	no	—
353	D₄	—	8	32	no	—
354	C₂×C₄	—	2	8	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	2	8	no	—
359	C₂×C₄	—	2	16	no	—
360	C₂×C₄	—	2	8	no	—
361	C₂×C₄	—	2	16	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	8	no	—
364	C₂×C₄	—	4	16	no	—
365	C₂×C₄	—	4	16	no	—
366	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
367	C₂×C₄	C₂²×D₄×C₃₁	1	16	yes	—
368	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
369	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
370	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
371	C₂²	—	2	4	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	8	no	—
376	C₂²	—	2	16	no	—
377	C₂²	—	4	16	no	—
378	C₂²	—	4	8	no	—
379	C₂²	—	4	8	no	—
380	C₂²	—	4	8	no	—
381	C₂²	—	4	32	no	—
382	C₂²	—	8	32	no	—
383	C₂²	C₂×C₃₁×#127	1	8	yes	—
384	C₂²	C₂×C₃₁×#127	1	4	yes	—
385	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
386	C₂²	C₂³×D₄×C₃₁	1	2	yes	—
387	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
388	C₂²	C₃₁×#585	1	2	yes	—
389	C₄	—	2	4	no	—
390	C₄	—	2	2	no	—
391	C₄	—	2	16	no	—
392	C₄	—	4	8	no	—
393	C₄	C₃₁×#534	1	4	yes	complemented
394	C₂	—	2	8	no	—
395	C₂	—	2	4	no	—
396	C₂	—	8	8	no	—
397	C₂	C₂²×C₃₁×#127	1	1	yes	characteristic
398	C₂	C₂×C₃₁×#534	1	1	yes	characteristic
399	C₂	C₃₁×#3449	1	1	yes	characteristic
400	C₂	C₃₁×#3496	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#534	C₂	semidirect
2. C₂²×C₃₁×#121	C₂	semidirect
3. C₃₁×#2856	C₂	semidirect
4. C₃₁×#2656	C₂	semidirect
5. C₃₁×#2539	C₂	semidirect
6. C₃₁×#2501	C₂	semidirect
7. C₃₁×#2433	C₂	semidirect
8. C₂×C₄×C₂²⋊C₄×C₃₁	C₂	semidirect
10. C₂³×D₄×C₃₁	C₂²	semidirect
13. C₂×C₃₁×#127	C₂²	semidirect
14. C₂×C₃₁×#123	C₂²	semidirect
18. C₂×C₃₁×#121	C₂²	semidirect
19. C₂×C₃₁×#121	C₂²	semidirect
20. C₂×C₃₁×#121	C₂²	semidirect
21. C₂×C₃₁×#120	C₂²	semidirect
22. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
24. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
25. C₂²×C₄²×C₃₁	C₂²	semidirect
26. C₃₁×#399	C₂²	semidirect
27. C₃₁×#392	C₂²	semidirect
28. C₃₁×#390	C₂²	semidirect
29. C₃₁×#390	C₂²	semidirect
30. C₃₁×#384	C₂²	semidirect
31. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
32. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
33. C₂×C₃₁×#95	C₂²	semidirect
46. C₂³×C₄×C₃₁	D₄	semidirect
66. C₂×C₂²⋊C₄×C₃₁	D₄	semidirect
112. C₂²×C₄×C₃₁	C₂×D₄	semidirect
124. C₂²⋊C₄×C₃₁	C₂×D₄	semidirect
127. #35001	C₃₁	direct (N × H)
143. C₂³×C₃₁	#127	semidirect
171. C₂×#534	C₂×C₃₁	semidirect
172. C₂²×#121	C₂×C₃₁	semidirect
173. #2856	C₂×C₃₁	semidirect
174. #2656	C₂×C₃₁	semidirect
175. #2539	C₂×C₃₁	semidirect
176. #2501	C₂×C₃₁	semidirect
177. #2433	C₂×C₃₁	semidirect
178. C₂×C₄×C₂²⋊C₄	C₂×C₃₁	semidirect
201. C₄×C₃₁	#534	semidirect
203. C₂³×D₄	C₂²×C₃₁	semidirect
206. C₂×#127	C₂²×C₃₁	semidirect
207. C₂×#123	C₂²×C₃₁	semidirect
211. C₂×#121	C₂²×C₃₁	semidirect
212. C₂×#121	C₂²×C₃₁	semidirect
213. C₂×#121	C₂²×C₃₁	semidirect
214. C₂×#120	C₂²×C₃₁	semidirect
215. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
217. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
218. C₂²×C₄²	C₂²×C₃₁	semidirect
219. #399	C₂²×C₃₁	semidirect
220. #392	C₂²×C₃₁	semidirect
221. #390	C₂²×C₃₁	semidirect
222. #390	C₂²×C₃₁	semidirect
223. #384	C₂²×C₃₁	semidirect
224. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
225. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
226. C₂×#95	C₂²×C₃₁	semidirect
246. C₂³×C₄	D₄×C₃₁	semidirect
266. C₂×C₂²⋊C₄	D₄×C₃₁	semidirect
275. C₃₁	#35001	direct (N × H)
313. C₂²×C₄	C₂×D₄×C₃₁	semidirect
325. C₂²⋊C₄	C₂×D₄×C₃₁	semidirect
343. C₂³	C₃₁×#127	semidirect
393. C₄	C₃₁×#534	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#534	2
C₂²×C₃₁×#121	2
C₃₁×#2856	2
C₃₁×#2656	2
C₃₁×#2539	2
C₃₁×#2501	2
C₃₁×#2433	2
C₂×C₄×C₂²⋊C₄×C₃₁	2
#35001	31

Subgroups — C31×#35001 #21491760

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#35001 #21491760