Subgroups — C₃₁×#25888 #21482647

Order 7936.

1282 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁×#477	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2563	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#2036	C₂	1	4	yes	maximal, complemented
6	C₃₁×#1981	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1954	C₂	1	1	yes	maximal, characteristic
8	C₃₁×#1787	C₂	1	4	yes	maximal, complemented
9	C₄×C₃₁×#103	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₃₁	C₂²	1	2	yes	—
11	D₄×Q₈×C₃₁	—	2	4	no	—
12	D₄×Q₈×C₃₁	—	2	4	no	—
13	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
14	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₃₁×C₂²⋊Q₈	—	2	2	no	—
17	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₃₁	—	2	1	no	—
20	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
21	C₃₁×#487	—	2	4	no	—
22	C₃₁×#477	—	2	4	no	—
23	C₂×C₃₁×#107	C₂²	1	2	yes	—
24	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#103	C₂²	1	4	yes	—
26	C₂×C₃₁×#103	C₂²	1	2	yes	—
27	C₂×C₃₁×#103	C₂²	1	2	yes	—
28	C₂×C₃₁×#103	C₂²	1	4	yes	—
29	C₂×C₃₁×C₂²⋊C₈	C₂²	1	4	yes	—
30	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
31	C₃₁×#393	—	2	2	no	—
32	C₃₁×#390	—	2	1	no	—
33	C₃₁×#382	—	2	1	no	—
34	C₃₁×#380	C₂²	1	4	yes	—
35	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
36	C₃₁×#340	C₂²	1	2	yes	—
37	C₂²×Q₈×C₃₁	—	2	4	no	—
38	C₂²×Q₈×C₃₁	—	2	4	no	—
39	C₂²×Q₈×C₃₁	—	2	2	no	—
40	C₂²×Q₈×C₃₁	—	2	1	no	—
41	C₂²×Q₈×C₃₁	—	2	8	no	—
42	C₂²×Q₈×C₃₁	—	4	4	no	—
43	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
44	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₃₁	—	2	2	no	—
47	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
49	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
50	C₃₁×C₄⋊Q₈	—	2	8	no	—
51	C₃₁×C₄⋊Q₈	—	2	2	no	—
52	C₃₁×C₄⋊Q₈	—	2	2	no	—
53	C₃₁×C₄⋊Q₈	—	2	2	no	—
54	C₃₁×C₄⋊Q₈	D₄	1	4	yes	—
55	C₃₁×C₂²⋊Q₈	—	2	16	no	—
56	C₃₁×C₂²⋊Q₈	—	2	4	no	—
57	C₃₁×C₂²⋊Q₈	—	2	4	no	—
58	C₄×Q₈×C₃₁	—	2	2	no	—
59	C₄×Q₈×C₃₁	D₄	1	4	yes	—
60	C₄×D₄×C₃₁	—	2	8	no	—
61	C₄×D₄×C₃₁	—	2	2	no	—
62	C₄×D₄×C₃₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
67	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
74	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
75	C₂×C₄²×C₃₁	—	2	1	no	—
76	C₂×C₄²×C₃₁	—	2	1	no	—
77	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
78	C₃₁×#107	—	2	4	no	—
79	C₃₁×C₄⋊C₈	—	2	2	no	—
80	C₃₁×#103	—	2	4	no	—
81	C₃₁×#103	—	2	8	no	—
82	C₃₁×#103	—	2	4	no	—
83	C₃₁×#103	—	4	4	no	—
84	C₃₁×C₂²⋊C₈	—	4	4	no	—
85	C₄×C₈×C₃₁	—	2	2	no	—
86	C₃₁×#95	—	2	1	no	—
87	C₃₁×#95	—	2	4	no	—
88	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
89	C₂×Q₈×C₃₁	—	2	8	no	—
90	C₂×Q₈×C₃₁	—	2	1	no	—
91	C₂×Q₈×C₃₁	—	2	2	no	—
92	C₂×Q₈×C₃₁	—	2	2	no	—
93	C₂×Q₈×C₃₁	—	2	4	no	—
94	C₂×Q₈×C₃₁	—	2	4	no	—
95	C₂×Q₈×C₃₁	—	4	8	no	—
96	C₂×Q₈×C₃₁	—	4	16	no	—
97	C₂×Q₈×C₃₁	—	4	8	no	—
98	C₂×Q₈×C₃₁	—	4	8	no	—
99	C₂×Q₈×C₃₁	—	4	2	no	—
100	C₂×Q₈×C₃₁	—	8	2	no	—
101	C₂×Q₈×C₃₁	C₂×D₄	1	4	yes	—
102	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
103	C₂×Q₈×C₃₁	#41	1	4	yes	—
104	C₂×D₄×C₃₁	—	2	2	no	—
105	C₂×D₄×C₃₁	—	2	2	no	—
106	C₂×D₄×C₃₁	Q₁₆	1	4	yes	—
107	C₂²×C₄×C₃₁	—	2	1	no	—
108	C₂²×C₄×C₃₁	—	2	8	no	—
109	C₂²×C₄×C₃₁	—	2	1	no	—
110	C₂²×C₄×C₃₁	—	2	2	no	—
111	C₂²×C₄×C₃₁	—	2	2	no	—
112	C₂²×C₄×C₃₁	—	2	2	no	—
113	C₂²×C₄×C₃₁	—	2	4	no	—
114	C₂²×C₄×C₃₁	—	2	4	no	—
115	C₂²×C₄×C₃₁	—	2	2	no	—
116	C₂²×C₄×C₃₁	—	2	2	no	—
117	C₂²×C₄×C₃₁	—	4	8	no	—
118	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
122	C₂×C₈×C₃₁	—	2	2	no	—
123	C₂×C₈×C₃₁	—	2	2	no	—
124	C₂×C₈×C₃₁	—	2	2	no	—
125	C₂×C₈×C₃₁	—	2	2	no	—
126	C₂×C₈×C₃₁	—	2	4	no	—
127	C₄⋊C₄×C₃₁	—	2	8	no	—
128	C₄⋊C₄×C₃₁	—	2	4	no	—
129	C₄⋊C₄×C₃₁	—	2	4	no	—
130	C₄⋊C₄×C₃₁	—	2	4	no	—
131	C₄⋊C₄×C₃₁	—	2	2	no	—
132	C₄⋊C₄×C₃₁	—	2	1	no	—
133	C₄⋊C₄×C₃₁	—	2	2	no	—
134	C₄⋊C₄×C₃₁	—	2	2	no	—
135	C₄⋊C₄×C₃₁	—	2	2	no	—
136	C₄⋊C₄×C₃₁	—	2	2	no	—
137	C₄⋊C₄×C₃₁	—	4	2	no	—
138	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
139	C₂²⋊C₄×C₃₁	—	2	8	no	—
140	C₂²⋊C₄×C₃₁	—	2	4	no	—
141	C₂²⋊C₄×C₃₁	—	8	4	no	—
142	C₄²×C₃₁	—	2	4	no	—
143	C₄²×C₃₁	—	4	2	no	—
144	C₄²×C₃₁	C₂×D₄	1	2	yes	—
145	C₄²×C₃₁	C₂×D₄	1	2	yes	—
146	#25888	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
147	C₂³×C₃₁	—	2	2	no	—
148	C₂³×C₃₁	—	2	4	no	—
149	C₂³×C₃₁	—	2	2	no	—
150	C₂³×C₃₁	—	2	4	no	—
151	C₂³×C₃₁	C₂×Q₁₆	1	4	yes	—
152	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
153	Q₈×C₃₁	—	2	2	no	—
154	Q₈×C₃₁	—	2	4	no	—
155	Q₈×C₃₁	—	2	8	no	—
156	Q₈×C₃₁	—	4	16	no	—
157	Q₈×C₃₁	—	4	2	no	—
158	Q₈×C₃₁	—	4	2	no	—
159	Q₈×C₃₁	—	8	4	no	—
160	Q₈×C₃₁	#124	1	4	yes	—
161	D₄×C₃₁	—	2	8	no	—
162	C₂×C₄×C₃₁	—	2	2	no	—
163	C₂×C₄×C₃₁	—	2	4	no	—
164	C₂×C₄×C₃₁	—	2	2	no	—
165	C₂×C₄×C₃₁	—	2	2	no	—
166	C₂×C₄×C₃₁	—	2	4	no	—
167	C₂×C₄×C₃₁	—	2	2	no	—
168	C₂×C₄×C₃₁	—	2	4	no	—
169	C₂×C₄×C₃₁	—	4	16	no	—
170	C₂×C₄×C₃₁	—	4	4	no	—
171	C₂×C₄×C₃₁	—	4	2	no	—
172	C₂×C₄×C₃₁	—	4	2	no	—
173	C₂×C₄×C₃₁	—	4	2	no	—
174	C₂×C₄×C₃₁	—	4	4	no	—
175	C₂×C₄×C₃₁	—	4	2	no	—
176	C₂×C₄×C₃₁	—	4	2	no	—
177	C₂×C₄×C₃₁	—	4	2	no	—
178	C₂×C₄×C₃₁	—	4	2	no	—
179	C₂×C₄×C₃₁	—	4	4	no	—
180	C₂×C₄×C₃₁	#120	1	2	yes	—
181	C₂×C₄×C₃₁	#120	1	2	yes	—
182	C₂×C₄×C₃₁	C₂×Q₁₆	1	2	yes	—
183	C₂×C₄×C₃₁	#137	1	2	yes	—
184	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
187	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
188	C₈×C₃₁	—	4	2	no	—
189	C₈×C₃₁	—	4	2	no	—
190	C₂×D₄×Q₈	C₂×C₃₁	1	1	yes	characteristic
191	C₂×#487	C₂×C₃₁	1	1	yes	characteristic, complemented
192	C₂×#477	C₂×C₃₁	1	1	yes	characteristic, complemented
193	#2563	C₂×C₃₁	1	1	yes	characteristic
194	#2036	C₂×C₃₁	1	4	yes	complemented
195	#1981	C₂×C₃₁	1	1	yes	characteristic, complemented
196	#1954	C₂×C₃₁	1	1	yes	characteristic
197	#1787	C₂×C₃₁	1	4	yes	complemented
198	C₄×#103	C₂×C₃₁	1	1	yes	characteristic, complemented
199	C₂²×C₃₁	—	2	4	no	—
200	C₂²×C₃₁	—	2	8	no	—
201	C₂²×C₃₁	—	4	4	no	—
202	C₂²×C₃₁	—	4	2	no	—
203	C₂²×C₃₁	—	4	2	no	—
204	C₂²×C₃₁	C₂×#120	1	1	yes	characteristic
205	C₂²×C₃₁	#546	1	2	yes	—
206	C₂²×C₃₁	C₂²×Q₁₆	1	1	yes	characteristic
207	C₂²×C₃₁	C₂×#137	1	1	yes	characteristic
208	C₂²×C₃₁	#577	1	2	yes	—
209	C₄×C₃₁	—	2	4	no	—
210	C₄×C₃₁	—	2	2	no	—
211	C₄×C₃₁	—	4	2	no	—
212	C₄×C₃₁	—	4	4	no	—
213	C₄×C₃₁	—	4	2	no	—
214	C₄×C₃₁	—	8	2	no	—
215	C₄×C₃₁	—	8	2	no	—
216	C₄×C₃₁	#451	1	4	yes	—
217	C₄×C₃₁	C₂×#124	1	1	yes	characteristic
218	C₄×C₃₁	#535	1	1	yes	characteristic
219	C₄×C₃₁	#546	1	2	yes	—
220	C₂³×Q₈	C₂²×C₃₁	1	2	yes	—
221	D₄×Q₈	—	2	4	no	—
222	D₄×Q₈	—	2	4	no	—
223	C₂×C₄⋊Q₈	—	2	1	no	—
224	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
225	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
226	C₂×C₂²⋊Q₈	—	2	2	no	—
227	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
228	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
229	C₂×C₄×D₄	—	2	1	no	—
230	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
231	#487	—	2	4	no	—
232	#477	—	2	4	no	—
233	C₂×#107	C₂²×C₃₁	1	2	yes	—
234	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
235	C₂×#103	C₂²×C₃₁	1	2	yes	—
236	C₂×#103	C₂²×C₃₁	1	4	yes	—
237	C₂×#103	C₂²×C₃₁	1	2	yes	—
238	C₂×#103	C₂²×C₃₁	1	4	yes	—
239	C₂×C₂²⋊C₈	C₂²×C₃₁	1	4	yes	—
240	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
241	#393	—	2	2	no	—
242	#390	—	2	1	no	—
243	#382	—	2	1	no	—
244	#380	C₂²×C₃₁	1	4	yes	—
245	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
246	#340	C₂²×C₃₁	1	2	yes	—
247	C₂×C₃₁	—	4	4	no	—
248	C₂×C₃₁	#2435	1	1	yes	characteristic
249	C₂×C₃₁	C₂×#451	1	1	yes	characteristic
250	C₂×C₃₁	#3010	1	1	yes	characteristic
251	C₂×C₃₁	#3299	1	2	yes	—
252	C₂×C₃₁	#3329	1	2	yes	—
253	C₂²×Q₈	—	2	4	no	—
254	C₂²×Q₈	—	2	4	no	—
255	C₂²×Q₈	—	2	2	no	—
256	C₂²×Q₈	—	2	1	no	—
257	C₂²×Q₈	—	2	8	no	—
258	C₂²×Q₈	—	4	4	no	—
259	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
260	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
261	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
262	C₂³×C₄	—	2	2	no	—
263	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
264	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
265	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
266	C₄⋊Q₈	—	2	8	no	—
267	C₄⋊Q₈	—	2	2	no	—
268	C₄⋊Q₈	—	2	2	no	—
269	C₄⋊Q₈	—	2	2	no	—
270	C₄⋊Q₈	D₄×C₃₁	1	4	yes	—
271	C₂²⋊Q₈	—	2	16	no	—
272	C₂²⋊Q₈	—	2	4	no	—
273	C₂²⋊Q₈	—	2	4	no	—
274	C₄×Q₈	—	2	2	no	—
275	C₄×Q₈	D₄×C₃₁	1	4	yes	—
276	C₄×D₄	—	2	8	no	—
277	C₄×D₄	—	2	2	no	—
278	C₄×D₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
286	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
288	C₂×C₂²⋊C₄	—	2	2	no	—
289	C₂×C₂²⋊C₄	—	2	4	no	—
290	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	—	2	1	no	—
293	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
294	#107	—	2	4	no	—
295	C₄⋊C₈	—	2	2	no	—
296	#103	—	2	4	no	—
297	#103	—	2	8	no	—
298	#103	—	2	4	no	—
299	#103	—	4	4	no	—
300	C₂²⋊C₈	—	4	4	no	—
301	C₄×C₈	—	2	2	no	—
302	#95	—	2	1	no	—
303	#95	—	2	4	no	—
304	C₃₁	#25888	1	1	yes	characteristic, direct product factor, Sylow
305	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
306	C₂×Q₈	—	2	8	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	4	no	—
311	C₂×Q₈	—	2	4	no	—
312	C₂×Q₈	—	4	8	no	—
313	C₂×Q₈	—	4	16	no	—
314	C₂×Q₈	—	4	8	no	—
315	C₂×Q₈	—	4	8	no	—
316	C₂×Q₈	—	4	2	no	—
317	C₂×Q₈	—	8	2	no	—
318	C₂×Q₈	C₂×D₄×C₃₁	1	4	yes	—
319	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
320	C₂×Q₈	#41×C₃₁	1	4	yes	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	Q₁₆×C₃₁	1	4	yes	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	8	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	4	8	no	—
335	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
338	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	4	no	—
344	C₄⋊C₄	—	2	8	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	2	4	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	4	2	no	—
355	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
356	C₂²⋊C₄	—	2	8	no	—
357	C₂²⋊C₄	—	2	4	no	—
358	C₂²⋊C₄	—	8	4	no	—
359	C₄²	—	2	4	no	—
360	C₄²	—	4	2	no	—
361	C₄²	C₂×D₄×C₃₁	1	2	yes	—
362	C₄²	C₂×D₄×C₃₁	1	2	yes	—
363	C₂³	—	2	2	no	—
364	C₂³	—	2	4	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	2	4	no	—
367	C₂³	C₂×Q₁₆×C₃₁	1	4	yes	—
368	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
369	Q₈	—	2	2	no	—
370	Q₈	—	2	4	no	—
371	Q₈	—	2	8	no	—
372	Q₈	—	4	16	no	—
373	Q₈	—	4	2	no	—
374	Q₈	—	4	2	no	—
375	Q₈	—	8	4	no	—
376	Q₈	C₃₁×#124	1	4	yes	—
377	D₄	—	2	8	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	4	16	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	C₃₁×#120	1	2	yes	—
397	C₂×C₄	C₃₁×#120	1	2	yes	—
398	C₂×C₄	C₂×Q₁₆×C₃₁	1	2	yes	—
399	C₂×C₄	C₃₁×#137	1	2	yes	—
400	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
402	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
403	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
404	C₈	—	4	2	no	—
405	C₈	—	4	2	no	—
406	C₂²	—	2	4	no	—
407	C₂²	—	2	8	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	4	no	—
411	C₂²	C₂×C₃₁×#120	1	1	yes	characteristic
412	C₂²	C₃₁×#546	1	2	yes	—
413	C₂²	C₂²×Q₁₆×C₃₁	1	1	yes	characteristic
414	C₂²	C₂×C₃₁×#137	1	1	yes	characteristic
415	C₂²	C₃₁×#577	1	2	yes	—
416	C₄	—	2	4	no	—
417	C₄	—	2	2	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	4	no	—
420	C₄	—	4	2	no	—
421	C₄	—	8	2	no	—
422	C₄	—	8	2	no	—
423	C₄	C₃₁×#451	1	4	yes	—
424	C₄	C₂×C₃₁×#124	1	1	yes	characteristic
425	C₄	C₃₁×#535	1	1	yes	characteristic
426	C₄	C₃₁×#546	1	2	yes	—
427	C₂	—	4	4	no	—
428	C₂	C₃₁×#2435	1	1	yes	characteristic
429	C₂	C₂×C₃₁×#451	1	1	yes	characteristic
430	C₂	C₃₁×#3010	1	1	yes	characteristic
431	C₂	C₃₁×#3299	1	2	yes	—
432	C₂	C₃₁×#3329	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₁×#487	C₂	semidirect
3. C₂×C₃₁×#477	C₂	semidirect
5. C₃₁×#2036	C₂	semidirect
6. C₃₁×#1981	C₂	semidirect
8. C₃₁×#1787	C₂	semidirect
9. C₄×C₃₁×#103	C₂	semidirect
146. #25888	C₃₁	direct (N × H)
191. C₂×#487	C₂×C₃₁	semidirect
192. C₂×#477	C₂×C₃₁	semidirect
194. #2036	C₂×C₃₁	semidirect
195. #1981	C₂×C₃₁	semidirect
197. #1787	C₂×C₃₁	semidirect
198. C₄×#103	C₂×C₃₁	semidirect
304. C₃₁	#25888	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×D₄×Q₈×C₃₁	2
C₂×C₃₁×#487	2
C₂×C₃₁×#477	2
C₃₁×#2563	2
C₃₁×#2036	2
C₃₁×#1981	2
C₃₁×#1954	2
C₃₁×#1787	2
C₄×C₃₁×#103	2
#25888	31

Subgroups — C31×#25888 #21482647

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#25888 #21482647