Subgroups — C₃₁×#10806 #21467565

Order 7936.

914 conjugacy classes of subgroups.

The subgroup lattice has 452 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	2	no	—
53	C₂×C₄²×C₃₁	—	4	2	no	—
54	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₃₁	D₄	1	2	yes	—
56	C₃₁×#95	—	2	4	no	—
57	C₃₁×#95	—	4	2	no	—
58	C₃₁×#95	—	4	2	no	—
59	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
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	2	no	—
64	C₂²×C₄×C₃₁	—	2	4	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	2	no	—
69	C₂²×C₄×C₃₁	—	2	1	no	—
70	C₂²×C₄×C₃₁	—	2	1	no	—
71	C₂²×C₄×C₃₁	—	2	4	no	—
72	C₂²×C₄×C₃₁	—	4	1	no	—
73	C₂²×C₄×C₃₁	—	4	1	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	1	no	—
78	C₂²×C₄×C₃₁	—	4	1	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	—	4	2	no	—
83	C₂²×C₄×C₃₁	—	4	2	no	—
84	C₂²×C₄×C₃₁	—	4	2	no	—
85	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
86	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
87	C₂²×C₄×C₃₁	D₈	1	2	yes	—
88	C₂²×C₄×C₃₁	SD₁₆	1	2	yes	—
89	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
94	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
95	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
96	C₂²×C₄×C₃₁	#41	1	2	yes	—
97	C₂²×C₄×C₃₁	#41	1	2	yes	—
98	C₂²×C₄×C₃₁	#41	1	2	yes	—
99	C₂×C₈×C₃₁	—	2	4	no	—
100	C₂×C₈×C₃₁	—	2	4	no	—
101	C₂×C₈×C₃₁	—	2	4	no	—
102	C₂×C₈×C₃₁	—	4	2	no	—
103	C₂×C₈×C₃₁	—	4	2	no	—
104	C₂×C₈×C₃₁	—	4	2	no	—
105	C₂×C₈×C₃₁	—	4	2	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	2	no	—
110	C₄⋊C₄×C₃₁	—	2	2	no	—
111	C₄⋊C₄×C₃₁	—	2	4	no	—
112	C₄⋊C₄×C₃₁	—	2	4	no	—
113	C₄⋊C₄×C₃₁	—	4	2	no	—
114	C₄⋊C₄×C₃₁	—	4	2	no	—
115	C₄⋊C₄×C₃₁	C₄²	1	4	yes	—
116	C₄⋊C₄×C₃₁	C₄⋊C₄	1	4	yes	—
117	C₄²×C₃₁	—	2	2	no	—
118	C₄²×C₃₁	—	2	2	no	—
119	C₄²×C₃₁	—	2	4	no	—
120	C₄²×C₃₁	—	4	8	no	—
121	#10806	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
122	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
123	C₂³×C₃₁	C₄×D₄	1	2	yes	—
124	C₂³×C₃₁	#121	1	1	yes	characteristic
125	C₂³×C₃₁	C₂²⋊Q₈	1	1	yes	characteristic
126	C₂³×C₃₁	#123	1	2	yes	—
127	C₂³×C₃₁	C₂×D₈	1	1	yes	characteristic
128	C₂³×C₃₁	C₂×SD₁₆	1	1	yes	characteristic
129	C₂³×C₃₁	#135	1	2	yes	—
130	C₂³×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
131	C₂³×C₃₁	#137	1	1	yes	characteristic
132	C₂³×C₃₁	#137	1	2	yes	—
133	C₂×C₄×C₃₁	—	2	2	no	—
134	C₂×C₄×C₃₁	—	2	2	no	—
135	C₂×C₄×C₃₁	—	2	4	no	—
136	C₂×C₄×C₃₁	—	2	4	no	—
137	C₂×C₄×C₃₁	—	2	4	no	—
138	C₂×C₄×C₃₁	—	2	4	no	—
139	C₂×C₄×C₃₁	—	2	2	no	—
140	C₂×C₄×C₃₁	—	2	2	no	—
141	C₂×C₄×C₃₁	—	2	2	no	—
142	C₂×C₄×C₃₁	—	4	2	no	—
143	C₂×C₄×C₃₁	—	4	2	no	—
144	C₂×C₄×C₃₁	—	4	2	no	—
145	C₂×C₄×C₃₁	—	4	2	no	—
146	C₂×C₄×C₃₁	—	4	4	no	—
147	C₂×C₄×C₃₁	—	4	4	no	—
148	C₂×C₄×C₃₁	—	4	2	no	—
149	C₂×C₄×C₃₁	—	4	2	no	—
150	C₂×C₄×C₃₁	—	4	2	no	—
151	C₂×C₄×C₃₁	—	4	2	no	—
152	C₂×C₄×C₃₁	—	4	2	no	—
153	C₂×C₄×C₃₁	—	4	2	no	—
154	C₂×C₄×C₃₁	—	4	4	no	—
155	C₂×C₄×C₃₁	—	4	4	no	—
156	C₂×C₄×C₃₁	—	4	4	no	—
157	C₂×C₄×C₃₁	—	8	2	no	—
158	C₂×C₄×C₃₁	—	8	2	no	—
159	C₂×C₄×C₃₁	—	8	2	no	—
160	C₂×C₄×C₃₁	—	8	2	no	—
161	C₂×C₄×C₃₁	#102	1	4	yes	—
162	C₂×C₄×C₃₁	C₂×C₄²	1	1	yes	characteristic
163	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₃₁	#117	1	1	yes	characteristic
165	C₂×C₄×C₃₁	#117	1	1	yes	characteristic
166	C₂×C₄×C₃₁	#117	1	2	yes	—
167	C₂×C₄×C₃₁	#117	1	2	yes	—
168	C₂×C₄×C₃₁	#117	1	1	yes	characteristic
169	C₂×C₄×C₃₁	#117	1	1	yes	characteristic
170	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
171	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
172	C₂×C₄×C₃₁	C₄×Q₈	1	2	yes	—
173	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
174	C₂×C₄×C₃₁	C₂²⋊Q₈	1	1	yes	characteristic
175	C₂×C₄×C₃₁	#123	1	2	yes	—
176	C₂×C₄×C₃₁	#124	1	2	yes	—
177	C₂×C₄×C₃₁	#125	1	2	yes	—
178	C₂×C₄×C₃₁	#126	1	2	yes	—
179	C₂×C₄×C₃₁	#126	1	2	yes	—
180	C₈×C₃₁	—	4	4	no	—
181	C₂×C₄×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic
182	C₂×#340	C₂×C₃₁	1	2	yes	—
183	C₂×#340	C₂×C₃₁	1	2	yes	—
184	C₂×#336	C₂×C₃₁	1	1	yes	characteristic
185	C₄⋊#95	C₂×C₃₁	1	1	yes	characteristic
186	C₂²×C₃₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
187	C₂²×C₃₁	#380	1	1	yes	characteristic
188	C₂²×C₃₁	#381	1	1	yes	characteristic
189	C₂²×C₃₁	#387	1	2	yes	—
190	C₂²×C₃₁	#388	1	2	yes	—
191	C₂²×C₃₁	C₂×#102	1	1	yes	characteristic
192	C₂²×C₃₁	#416	1	1	yes	characteristic
193	C₂²×C₃₁	#417	1	1	yes	characteristic
194	C₂²×C₃₁	#419	1	1	yes	characteristic
195	C₂²×C₃₁	C₄×D₈	1	2	yes	—
196	C₂²×C₃₁	C₄×SD₁₆	1	2	yes	—
197	C₂²×C₃₁	#440	1	2	yes	—
198	C₂²×C₃₁	#441	1	2	yes	—
199	C₂²×C₃₁	#459	1	1	yes	characteristic
200	C₂²×C₃₁	#461	1	1	yes	characteristic
201	C₂²×C₃₁	#464	1	2	yes	—
202	C₂²×C₃₁	#474	1	1	yes	characteristic
203	C₂²×C₃₁	#476	1	1	yes	characteristic
204	C₂²×C₃₁	#479	1	2	yes	—
205	C₂²×C₃₁	#480	1	2	yes	—
206	C₂²×C₃₁	#482	1	2	yes	—
207	C₂²×C₃₁	#483	1	2	yes	—
208	C₂²×C₃₁	#485	1	2	yes	—
209	C₄×C₃₁	—	2	4	no	—
210	C₄×C₃₁	—	4	4	no	—
211	C₄×C₃₁	—	4	2	no	—
212	C₄×C₃₁	—	4	4	no	—
213	C₄×C₃₁	—	8	4	no	—
214	C₄×C₃₁	#376	1	1	yes	characteristic
215	C₄×C₃₁	C₄×C₄⋊C₄	1	1	yes	characteristic
216	C₄×C₃₁	#382	1	1	yes	characteristic
217	C₄×C₃₁	#383	1	1	yes	characteristic
218	C₄×C₃₁	#387	1	2	yes	—
219	C₄×C₃₁	#388	1	2	yes	—
220	C₂³×C₈	C₂²×C₃₁	1	2	yes	—
221	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
222	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
223	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
224	C₂²×C₄²	—	2	1	no	—
225	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
226	C₄×C₄⋊C₄	—	2	2	no	—
227	C₄×C₄⋊C₄	C₄×C₃₁	1	4	yes	complemented
228	C₂×#95	—	2	1	no	—
229	C₂×#95	—	2	1	no	—
230	C₂×#95	—	2	1	no	—
231	#340	—	2	4	no	—
232	#340	C₄×C₃₁	1	8	yes	complemented
233	#336	—	2	2	no	—
234	C₂×C₃₁	#1434	1	1	yes	characteristic
235	C₂×C₃₁	C₄×#102	1	1	yes	characteristic
236	C₂×C₃₁	#1763	1	1	yes	characteristic
237	C₂×C₃₁	#1802	1	1	yes	characteristic
238	C₂×C₃₁	#1805	1	1	yes	characteristic
239	C₂×C₃₁	#1823	1	1	yes	characteristic
240	C₂×C₃₁	#1825	1	1	yes	characteristic
241	C₂×C₃₁	#1918	1	2	yes	—
242	C₂×C₃₁	#1920	1	2	yes	—
243	C₂×C₃₁	#1925	1	2	yes	—
244	C₂×C₃₁	#1927	1	2	yes	—
245	C₂³×C₄	—	2	1	no	—
246	C₂³×C₄	—	2	1	no	—
247	C₂³×C₄	—	2	2	no	—
248	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
249	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
250	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
251	C₂²×C₈	—	2	2	no	—
252	C₂²×C₈	—	2	2	no	—
253	C₂²×C₈	—	2	2	no	—
254	C₂²×C₈	—	2	2	no	—
255	C₂²×C₈	—	2	2	no	—
256	C₂²×C₈	—	2	2	no	—
257	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
269	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
270	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
271	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
272	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
273	C₂×C₄⋊C₄	Q₈×C₃₁	1	2	yes	—
274	C₂×C₄²	—	2	2	no	—
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	—	2	4	no	—
277	C₂×C₄²	—	4	2	no	—
278	C₂×C₄²	—	4	2	no	—
279	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
280	C₂×C₄²	D₄×C₃₁	1	2	yes	—
281	#95	—	2	4	no	—
282	#95	—	4	2	no	—
283	#95	—	4	2	no	—
284	C₃₁	#10806	1	1	yes	characteristic, direct product factor, Sylow
285	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	4	2	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	—	4	2	no	—
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	—	4	2	no	—
311	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
312	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
313	C₂²×C₄	D₈×C₃₁	1	2	yes	—
314	C₂²×C₄	SD₁₆×C₃₁	1	2	yes	—
315	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
316	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
317	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
319	C₂²×C₄	C₂×Q₈×C₃₁	1	1	yes	characteristic
320	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
321	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
322	C₂²×C₄	#41×C₃₁	1	2	yes	—
323	C₂²×C₄	#41×C₃₁	1	2	yes	—
324	C₂²×C₄	#41×C₃₁	1	2	yes	—
325	C₂×C₈	—	2	4	no	—
326	C₂×C₈	—	2	4	no	—
327	C₂×C₈	—	2	4	no	—
328	C₂×C₈	—	4	2	no	—
329	C₂×C₈	—	4	2	no	—
330	C₂×C₈	—	4	2	no	—
331	C₂×C₈	—	4	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	4	no	—
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	—	4	2	no	—
340	C₄⋊C₄	—	4	2	no	—
341	C₄⋊C₄	C₄²×C₃₁	1	4	yes	—
342	C₄⋊C₄	C₄⋊C₄×C₃₁	1	4	yes	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	2	4	no	—
346	C₄²	—	4	8	no	—
347	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
348	C₂³	C₄×D₄×C₃₁	1	2	yes	—
349	C₂³	C₃₁×#121	1	1	yes	characteristic
350	C₂³	C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
351	C₂³	C₃₁×#123	1	2	yes	—
352	C₂³	C₂×D₈×C₃₁	1	1	yes	characteristic
353	C₂³	C₂×SD₁₆×C₃₁	1	1	yes	characteristic
354	C₂³	C₃₁×#135	1	2	yes	—
355	C₂³	C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
356	C₂³	C₃₁×#137	1	1	yes	characteristic
357	C₂³	C₃₁×#137	1	2	yes	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	8	2	no	—
383	C₂×C₄	—	8	2	no	—
384	C₂×C₄	—	8	2	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	C₃₁×#102	1	4	yes	—
387	C₂×C₄	C₂×C₄²×C₃₁	1	1	yes	characteristic
388	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
389	C₂×C₄	C₃₁×#117	1	1	yes	characteristic
390	C₂×C₄	C₃₁×#117	1	1	yes	characteristic
391	C₂×C₄	C₃₁×#117	1	2	yes	—
392	C₂×C₄	C₃₁×#117	1	2	yes	—
393	C₂×C₄	C₃₁×#117	1	1	yes	characteristic
394	C₂×C₄	C₃₁×#117	1	1	yes	characteristic
395	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
396	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
397	C₂×C₄	C₄×Q₈×C₃₁	1	2	yes	—
398	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
399	C₂×C₄	C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
400	C₂×C₄	C₃₁×#123	1	2	yes	—
401	C₂×C₄	C₃₁×#124	1	2	yes	—
402	C₂×C₄	C₃₁×#125	1	2	yes	—
403	C₂×C₄	C₃₁×#126	1	2	yes	—
404	C₂×C₄	C₃₁×#126	1	2	yes	—
405	C₈	—	4	4	no	—
406	C₂²	C₄×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
407	C₂²	C₃₁×#380	1	1	yes	characteristic
408	C₂²	C₃₁×#381	1	1	yes	characteristic
409	C₂²	C₃₁×#387	1	2	yes	—
410	C₂²	C₃₁×#388	1	2	yes	—
411	C₂²	C₂×C₃₁×#102	1	1	yes	characteristic
412	C₂²	C₃₁×#416	1	1	yes	characteristic
413	C₂²	C₃₁×#417	1	1	yes	characteristic
414	C₂²	C₃₁×#419	1	1	yes	characteristic
415	C₂²	C₄×D₈×C₃₁	1	2	yes	—
416	C₂²	C₄×SD₁₆×C₃₁	1	2	yes	—
417	C₂²	C₃₁×#440	1	2	yes	—
418	C₂²	C₃₁×#441	1	2	yes	—
419	C₂²	C₃₁×#459	1	1	yes	characteristic
420	C₂²	C₃₁×#461	1	1	yes	characteristic
421	C₂²	C₃₁×#464	1	2	yes	—
422	C₂²	C₃₁×#474	1	1	yes	characteristic
423	C₂²	C₃₁×#476	1	1	yes	characteristic
424	C₂²	C₃₁×#479	1	2	yes	—
425	C₂²	C₃₁×#480	1	2	yes	—
426	C₂²	C₃₁×#482	1	2	yes	—
427	C₂²	C₃₁×#483	1	2	yes	—
428	C₂²	C₃₁×#485	1	2	yes	—
429	C₄	—	2	4	no	—
430	C₄	—	4	4	no	—
431	C₄	—	4	2	no	—
432	C₄	—	4	4	no	—
433	C₄	—	8	4	no	—
434	C₄	C₃₁×#376	1	1	yes	characteristic
435	C₄	C₄×C₄⋊C₄×C₃₁	1	1	yes	characteristic
436	C₄	C₃₁×#382	1	1	yes	characteristic
437	C₄	C₃₁×#383	1	1	yes	characteristic
438	C₄	C₃₁×#387	1	2	yes	—
439	C₄	C₃₁×#388	1	2	yes	—
440	C₂	C₃₁×#1434	1	1	yes	characteristic
441	C₂	C₄×C₃₁×#102	1	1	yes	characteristic
442	C₂	C₃₁×#1763	1	1	yes	characteristic
443	C₂	C₃₁×#1802	1	1	yes	characteristic
444	C₂	C₃₁×#1805	1	1	yes	characteristic
445	C₂	C₃₁×#1823	1	1	yes	characteristic
446	C₂	C₃₁×#1825	1	1	yes	characteristic
447	C₂	C₃₁×#1918	1	2	yes	—
448	C₂	C₃₁×#1920	1	2	yes	—
449	C₂	C₃₁×#1925	1	2	yes	—
450	C₂	C₃₁×#1927	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
121. #10806	C₃₁	direct (N × H)
227. C₄×C₄⋊C₄	C₄×C₃₁	semidirect
232. #340	C₄×C₃₁	semidirect
284. C₃₁	#10806	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
#10806	31

Subgroups — C31×#10806 #21467565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#10806 #21467565