Subgroups — C₃₁×#10807 #21467566

Order 7936.

914 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#340	C₂	1	2	yes	maximal
3	C₂×C₃₁×#340	C₂	1	2	yes	maximal
4	C₂×C₃₁×#336	C₂	1	1	yes	maximal, characteristic
5	C₃₁×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₃₁	C₂²	1	2	yes	—
7	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
8	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
10	C₂²×C₄²×C₃₁	—	2	1	no	—
11	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
12	C₄×C₄⋊C₄×C₃₁	—	2	2	no	—
13	C₄×C₄⋊C₄×C₃₁	C₄	1	4	yes	complemented
14	C₂×C₃₁×#95	—	2	1	no	—
15	C₂×C₃₁×#95	—	2	1	no	—
16	C₂×C₃₁×#95	—	2	1	no	—
17	C₃₁×#340	—	2	4	no	—
18	C₃₁×#340	C₄	1	8	yes	complemented
19	C₃₁×#336	—	2	2	no	—
20	C₂³×C₄×C₃₁	—	2	1	no	—
21	C₂³×C₄×C₃₁	—	2	1	no	—
22	C₂³×C₄×C₃₁	—	2	2	no	—
23	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
24	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
26	C₂²×C₈×C₃₁	—	2	2	no	—
27	C₂²×C₈×C₃₁	—	2	2	no	—
28	C₂²×C₈×C₃₁	—	2	2	no	—
29	C₂²×C₈×C₃₁	—	2	2	no	—
30	C₂²×C₈×C₃₁	—	2	2	no	—
31	C₂²×C₈×C₃₁	—	2	2	no	—
32	C₂²×C₈×C₃₁	C₂×C₄	1	4	yes	—
33	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
34	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
35	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
36	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
37	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
38	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
39	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
40	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
41	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
42	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
43	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
44	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
45	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
46	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₃₁	Q₈	1	2	yes	—
49	C₂×C₄²×C₃₁	—	2	2	no	—
50	C₂×C₄²×C₃₁	—	2	2	no	—
51	C₂×C₄²×C₃₁	—	2	4	no	—
52	C₂×C₄²×C₃₁	—	4	4	no	—
53	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₃₁	D₄	1	2	yes	—
55	C₃₁×#95	—	2	4	no	—
56	C₃₁×#95	—	4	2	no	—
57	C₃₁×#95	—	4	2	no	—
58	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₃₁	—	2	2	no	—
60	C₂²×C₄×C₃₁	—	2	2	no	—
61	C₂²×C₄×C₃₁	—	2	2	no	—
62	C₂²×C₄×C₃₁	—	2	2	no	—
63	C₂²×C₄×C₃₁	—	2	4	no	—
64	C₂²×C₄×C₃₁	—	2	2	no	—
65	C₂²×C₄×C₃₁	—	2	2	no	—
66	C₂²×C₄×C₃₁	—	2	2	no	—
67	C₂²×C₄×C₃₁	—	2	2	no	—
68	C₂²×C₄×C₃₁	—	2	1	no	—
69	C₂²×C₄×C₃₁	—	2	1	no	—
70	C₂²×C₄×C₃₁	—	2	4	no	—
71	C₂²×C₄×C₃₁	—	4	2	no	—
72	C₂²×C₄×C₃₁	—	4	2	no	—
73	C₂²×C₄×C₃₁	—	4	2	no	—
74	C₂²×C₄×C₃₁	—	4	1	no	—
75	C₂²×C₄×C₃₁	—	4	1	no	—
76	C₂²×C₄×C₃₁	—	4	2	no	—
77	C₂²×C₄×C₃₁	—	4	2	no	—
78	C₂²×C₄×C₃₁	—	4	2	no	—
79	C₂²×C₄×C₃₁	—	4	2	no	—
80	C₂²×C₄×C₃₁	—	4	2	no	—
81	C₂²×C₄×C₃₁	—	4	2	no	—
82	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
83	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
84	C₂²×C₄×C₃₁	SD₁₆	1	2	yes	—
85	C₂²×C₄×C₃₁	Q₁₆	1	2	yes	—
86	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
91	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
92	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
93	C₂²×C₄×C₃₁	#41	1	2	yes	—
94	C₂²×C₄×C₃₁	#41	1	2	yes	—
95	C₂²×C₄×C₃₁	#41	1	2	yes	—
96	C₂×C₈×C₃₁	—	2	4	no	—
97	C₂×C₈×C₃₁	—	2	4	no	—
98	C₂×C₈×C₃₁	—	2	4	no	—
99	C₂×C₈×C₃₁	—	4	2	no	—
100	C₂×C₈×C₃₁	—	4	2	no	—
101	C₂×C₈×C₃₁	—	4	2	no	—
102	C₂×C₈×C₃₁	—	4	2	no	—
103	C₄⋊C₄×C₃₁	—	2	2	no	—
104	C₄⋊C₄×C₃₁	—	2	2	no	—
105	C₄⋊C₄×C₃₁	—	2	4	no	—
106	C₄⋊C₄×C₃₁	—	2	2	no	—
107	C₄⋊C₄×C₃₁	—	2	2	no	—
108	C₄⋊C₄×C₃₁	—	2	4	no	—
109	C₄⋊C₄×C₃₁	—	2	4	no	—
110	C₄⋊C₄×C₃₁	—	4	2	no	—
111	C₄⋊C₄×C₃₁	—	4	2	no	—
112	C₄⋊C₄×C₃₁	C₄²	1	4	yes	—
113	C₄⋊C₄×C₃₁	C₄⋊C₄	1	4	yes	—
114	C₄²×C₃₁	—	2	2	no	—
115	C₄²×C₃₁	—	2	2	no	—
116	C₄²×C₃₁	—	2	4	no	—
117	C₄²×C₃₁	—	4	8	no	—
118	#10807	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂³×C₃₁	C₄×D₄	1	2	yes	—
121	C₂³×C₃₁	#121	1	1	yes	characteristic
122	C₂³×C₃₁	C₂²⋊Q₈	1	1	yes	characteristic
123	C₂³×C₃₁	#123	1	2	yes	—
124	C₂³×C₃₁	C₂×SD₁₆	1	1	yes	characteristic
125	C₂³×C₃₁	C₂×Q₁₆	1	1	yes	characteristic
126	C₂³×C₃₁	#135	1	2	yes	—
127	C₂³×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
128	C₂³×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
129	C₂³×C₃₁	#137	1	1	yes	characteristic
130	C₂×C₄×C₃₁	—	2	2	no	—
131	C₂×C₄×C₃₁	—	2	2	no	—
132	C₂×C₄×C₃₁	—	2	4	no	—
133	C₂×C₄×C₃₁	—	2	4	no	—
134	C₂×C₄×C₃₁	—	2	4	no	—
135	C₂×C₄×C₃₁	—	2	4	no	—
136	C₂×C₄×C₃₁	—	2	2	no	—
137	C₂×C₄×C₃₁	—	2	2	no	—
138	C₂×C₄×C₃₁	—	2	2	no	—
139	C₂×C₄×C₃₁	—	4	2	no	—
140	C₂×C₄×C₃₁	—	4	2	no	—
141	C₂×C₄×C₃₁	—	4	2	no	—
142	C₂×C₄×C₃₁	—	4	2	no	—
143	C₂×C₄×C₃₁	—	4	4	no	—
144	C₂×C₄×C₃₁	—	4	4	no	—
145	C₂×C₄×C₃₁	—	4	4	no	—
146	C₂×C₄×C₃₁	—	4	4	no	—
147	C₂×C₄×C₃₁	—	4	2	no	—
148	C₂×C₄×C₃₁	—	4	2	no	—
149	C₂×C₄×C₃₁	—	4	4	no	—
150	C₂×C₄×C₃₁	—	4	4	no	—
151	C₂×C₄×C₃₁	—	4	4	no	—
152	C₂×C₄×C₃₁	—	8	2	no	—
153	C₂×C₄×C₃₁	—	8	2	no	—
154	C₂×C₄×C₃₁	—	8	2	no	—
155	C₂×C₄×C₃₁	—	8	2	no	—
156	C₂×C₄×C₃₁	#103	1	4	yes	—
157	C₂×C₄×C₃₁	C₂×C₄²	1	1	yes	characteristic
158	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₃₁	#117	1	1	yes	characteristic
160	C₂×C₄×C₃₁	#117	1	1	yes	characteristic
161	C₂×C₄×C₃₁	#117	1	2	yes	—
162	C₂×C₄×C₃₁	#117	1	2	yes	—
163	C₂×C₄×C₃₁	#117	1	1	yes	characteristic
164	C₂×C₄×C₃₁	#117	1	1	yes	characteristic
165	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
166	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₃₁	C₄×Q₈	1	2	yes	—
168	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
169	C₂×C₄×C₃₁	C₂²⋊Q₈	1	1	yes	characteristic
170	C₂×C₄×C₃₁	#123	1	2	yes	—
171	C₂×C₄×C₃₁	#124	1	2	yes	—
172	C₂×C₄×C₃₁	#125	1	2	yes	—
173	C₂×C₄×C₃₁	#126	1	2	yes	—
174	C₂×C₄×C₃₁	#126	1	2	yes	—
175	C₈×C₃₁	—	4	4	no	—
176	C₂×C₄×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic
177	C₂×#340	C₂×C₃₁	1	2	yes	—
178	C₂×#340	C₂×C₃₁	1	2	yes	—
179	C₂×#336	C₂×C₃₁	1	1	yes	characteristic
180	C₄⋊#95	C₂×C₃₁	1	1	yes	characteristic
181	C₂²×C₃₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
182	C₂²×C₃₁	#380	1	1	yes	characteristic
183	C₂²×C₃₁	#381	1	1	yes	characteristic
184	C₂²×C₃₁	#387	1	2	yes	—
185	C₂²×C₃₁	#388	1	2	yes	—
186	C₂²×C₃₁	C₂×#103	1	1	yes	characteristic
187	C₂²×C₃₁	#416	1	1	yes	characteristic
188	C₂²×C₃₁	#417	1	1	yes	characteristic
189	C₂²×C₃₁	#418	1	1	yes	characteristic
190	C₂²×C₃₁	C₄×SD₁₆	1	2	yes	—
191	C₂²×C₃₁	C₄×Q₁₆	1	2	yes	—
192	C₂²×C₃₁	#440	1	2	yes	—
193	C₂²×C₃₁	#442	1	2	yes	—
194	C₂²×C₃₁	#460	1	1	yes	characteristic
195	C₂²×C₃₁	#462	1	1	yes	characteristic
196	C₂²×C₃₁	#463	1	2	yes	—
197	C₂²×C₃₁	#475	1	1	yes	characteristic
198	C₂²×C₃₁	#477	1	1	yes	characteristic
199	C₂²×C₃₁	#478	1	2	yes	—
200	C₂²×C₃₁	#481	1	2	yes	—
201	C₂²×C₃₁	#482	1	2	yes	—
202	C₂²×C₃₁	#484	1	2	yes	—
203	C₂²×C₃₁	#485	1	2	yes	—
204	C₄×C₃₁	—	2	4	no	—
205	C₄×C₃₁	—	4	4	no	—
206	C₄×C₃₁	—	4	2	no	—
207	C₄×C₃₁	—	4	4	no	—
208	C₄×C₃₁	—	8	4	no	—
209	C₄×C₃₁	#376	1	1	yes	characteristic
210	C₄×C₃₁	C₄×C₄⋊C₄	1	1	yes	characteristic
211	C₄×C₃₁	#382	1	1	yes	characteristic
212	C₄×C₃₁	#383	1	1	yes	characteristic
213	C₄×C₃₁	#387	1	2	yes	—
214	C₄×C₃₁	#388	1	2	yes	—
215	C₂³×C₈	C₂²×C₃₁	1	2	yes	—
216	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
217	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
218	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
219	C₂²×C₄²	—	2	1	no	—
220	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
221	C₄×C₄⋊C₄	—	2	2	no	—
222	C₄×C₄⋊C₄	C₄×C₃₁	1	4	yes	complemented
223	C₂×#95	—	2	1	no	—
224	C₂×#95	—	2	1	no	—
225	C₂×#95	—	2	1	no	—
226	#340	—	2	4	no	—
227	#340	C₄×C₃₁	1	8	yes	complemented
228	#336	—	2	2	no	—
229	C₂×C₃₁	#1434	1	1	yes	characteristic
230	C₂×C₃₁	C₄×#103	1	1	yes	characteristic
231	C₂×C₃₁	#1762	1	1	yes	characteristic
232	C₂×C₃₁	#1803	1	1	yes	characteristic
233	C₂×C₃₁	#1804	1	1	yes	characteristic
234	C₂×C₃₁	#1824	1	1	yes	characteristic
235	C₂×C₃₁	#1825	1	1	yes	characteristic
236	C₂×C₃₁	#1919	1	2	yes	—
237	C₂×C₃₁	#1921	1	2	yes	—
238	C₂×C₃₁	#1926	1	2	yes	—
239	C₂×C₃₁	#1928	1	2	yes	—
240	C₂³×C₄	—	2	1	no	—
241	C₂³×C₄	—	2	1	no	—
242	C₂³×C₄	—	2	2	no	—
243	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
244	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
245	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
246	C₂²×C₈	—	2	2	no	—
247	C₂²×C₈	—	2	2	no	—
248	C₂²×C₈	—	2	2	no	—
249	C₂²×C₈	—	2	2	no	—
250	C₂²×C₈	—	2	2	no	—
251	C₂²×C₈	—	2	2	no	—
252	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
264	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
265	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
266	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
267	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
268	C₂×C₄⋊C₄	Q₈×C₃₁	1	2	yes	—
269	C₂×C₄²	—	2	2	no	—
270	C₂×C₄²	—	2	2	no	—
271	C₂×C₄²	—	2	4	no	—
272	C₂×C₄²	—	4	4	no	—
273	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
274	C₂×C₄²	D₄×C₃₁	1	2	yes	—
275	#95	—	2	4	no	—
276	#95	—	4	2	no	—
277	#95	—	4	2	no	—
278	C₃₁	#10807	1	1	yes	characteristic, direct product factor, Sylow
279	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	—	4	2	no	—
300	C₂²×C₄	—	4	2	no	—
301	C₂²×C₄	—	4	2	no	—
302	C₂²×C₄	—	4	2	no	—
303	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
304	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
305	C₂²×C₄	SD₁₆×C₃₁	1	2	yes	—
306	C₂²×C₄	Q₁₆×C₃₁	1	2	yes	—
307	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
308	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
311	C₂²×C₄	C₂×Q₈×C₃₁	1	1	yes	characteristic
312	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
313	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
314	C₂²×C₄	#41×C₃₁	1	2	yes	—
315	C₂²×C₄	#41×C₃₁	1	2	yes	—
316	C₂²×C₄	#41×C₃₁	1	2	yes	—
317	C₂×C₈	—	2	4	no	—
318	C₂×C₈	—	2	4	no	—
319	C₂×C₈	—	2	4	no	—
320	C₂×C₈	—	4	2	no	—
321	C₂×C₈	—	4	2	no	—
322	C₂×C₈	—	4	2	no	—
323	C₂×C₈	—	4	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	4	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₄⋊C₄	C₄²×C₃₁	1	4	yes	—
334	C₄⋊C₄	C₄⋊C₄×C₃₁	1	4	yes	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	4	no	—
338	C₄²	—	4	8	no	—
339	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
340	C₂³	C₄×D₄×C₃₁	1	2	yes	—
341	C₂³	C₃₁×#121	1	1	yes	characteristic
342	C₂³	C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
343	C₂³	C₃₁×#123	1	2	yes	—
344	C₂³	C₂×SD₁₆×C₃₁	1	1	yes	characteristic
345	C₂³	C₂×Q₁₆×C₃₁	1	1	yes	characteristic
346	C₂³	C₃₁×#135	1	2	yes	—
347	C₂³	C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
348	C₂³	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
349	C₂³	C₃₁×#137	1	1	yes	characteristic
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	8	2	no	—
373	C₂×C₄	—	8	2	no	—
374	C₂×C₄	—	8	2	no	—
375	C₂×C₄	—	8	2	no	—
376	C₂×C₄	C₃₁×#103	1	4	yes	—
377	C₂×C₄	C₂×C₄²×C₃₁	1	1	yes	characteristic
378	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
379	C₂×C₄	C₃₁×#117	1	1	yes	characteristic
380	C₂×C₄	C₃₁×#117	1	1	yes	characteristic
381	C₂×C₄	C₃₁×#117	1	2	yes	—
382	C₂×C₄	C₃₁×#117	1	2	yes	—
383	C₂×C₄	C₃₁×#117	1	1	yes	characteristic
384	C₂×C₄	C₃₁×#117	1	1	yes	characteristic
385	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
386	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
387	C₂×C₄	C₄×Q₈×C₃₁	1	2	yes	—
388	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
389	C₂×C₄	C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
390	C₂×C₄	C₃₁×#123	1	2	yes	—
391	C₂×C₄	C₃₁×#124	1	2	yes	—
392	C₂×C₄	C₃₁×#125	1	2	yes	—
393	C₂×C₄	C₃₁×#126	1	2	yes	—
394	C₂×C₄	C₃₁×#126	1	2	yes	—
395	C₈	—	4	4	no	—
396	C₂²	C₄×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
397	C₂²	C₃₁×#380	1	1	yes	characteristic
398	C₂²	C₃₁×#381	1	1	yes	characteristic
399	C₂²	C₃₁×#387	1	2	yes	—
400	C₂²	C₃₁×#388	1	2	yes	—
401	C₂²	C₂×C₃₁×#103	1	1	yes	characteristic
402	C₂²	C₃₁×#416	1	1	yes	characteristic
403	C₂²	C₃₁×#417	1	1	yes	characteristic
404	C₂²	C₃₁×#418	1	1	yes	characteristic
405	C₂²	C₄×SD₁₆×C₃₁	1	2	yes	—
406	C₂²	C₄×Q₁₆×C₃₁	1	2	yes	—
407	C₂²	C₃₁×#440	1	2	yes	—
408	C₂²	C₃₁×#442	1	2	yes	—
409	C₂²	C₃₁×#460	1	1	yes	characteristic
410	C₂²	C₃₁×#462	1	1	yes	characteristic
411	C₂²	C₃₁×#463	1	2	yes	—
412	C₂²	C₃₁×#475	1	1	yes	characteristic
413	C₂²	C₃₁×#477	1	1	yes	characteristic
414	C₂²	C₃₁×#478	1	2	yes	—
415	C₂²	C₃₁×#481	1	2	yes	—
416	C₂²	C₃₁×#482	1	2	yes	—
417	C₂²	C₃₁×#484	1	2	yes	—
418	C₂²	C₃₁×#485	1	2	yes	—
419	C₄	—	2	4	no	—
420	C₄	—	4	4	no	—
421	C₄	—	4	2	no	—
422	C₄	—	4	4	no	—
423	C₄	—	8	4	no	—
424	C₄	C₃₁×#376	1	1	yes	characteristic
425	C₄	C₄×C₄⋊C₄×C₃₁	1	1	yes	characteristic
426	C₄	C₃₁×#382	1	1	yes	characteristic
427	C₄	C₃₁×#383	1	1	yes	characteristic
428	C₄	C₃₁×#387	1	2	yes	—
429	C₄	C₃₁×#388	1	2	yes	—
430	C₂	C₃₁×#1434	1	1	yes	characteristic
431	C₂	C₄×C₃₁×#103	1	1	yes	characteristic
432	C₂	C₃₁×#1762	1	1	yes	characteristic
433	C₂	C₃₁×#1803	1	1	yes	characteristic
434	C₂	C₃₁×#1804	1	1	yes	characteristic
435	C₂	C₃₁×#1824	1	1	yes	characteristic
436	C₂	C₃₁×#1825	1	1	yes	characteristic
437	C₂	C₃₁×#1919	1	2	yes	—
438	C₂	C₃₁×#1921	1	2	yes	—
439	C₂	C₃₁×#1926	1	2	yes	—
440	C₂	C₃₁×#1928	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₃₁	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₃₁
Frattini, cosocle	C₂³×C₄	C₂³×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
13. C₄×C₄⋊C₄×C₃₁	C₄	semidirect
18. C₃₁×#340	C₄	semidirect
118. #10807	C₃₁	direct (N × H)
222. C₄×C₄⋊C₄	C₄×C₃₁	semidirect
227. #340	C₄×C₃₁	semidirect
278. C₃₁	#10807	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×C₄×C₄⋊C₄×C₃₁	2
C₂×C₃₁×#340	2
C₂×C₃₁×#336	2
C₃₁×C₄⋊#95	2
#10807	31

Subgroups — C31×#10807 #21467566

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#10807 #21467566