Subgroups — C₃₁×#34487 #21491246

Order 7936.

2244 conjugacy classes of subgroups.

The subgroup lattice has 682 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	C₃₁×#2378	C₂	1	4	yes	maximal, complemented
3	C₃₁×#2369	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2365	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2362	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2357	C₂	1	2	yes	maximal
7	C₃₁×#2355	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2354	C₂	1	1	yes	maximal, characteristic
9	Q₈×C₂²⋊C₄×C₃₁	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2332	C₂	1	4	yes	maximal, complemented
11	C₃₁×#2331	C₂	1	2	yes	maximal, complemented
12	C₃₁×#2323	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2319	C₂	1	2	yes	maximal
14	C₃₁×#2310	C₂	1	2	yes	maximal, complemented
15	C₄×C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2295	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2293	C₂	1	1	yes	maximal, characteristic
18	C₂³×Q₈×C₃₁	C₂²	1	2	yes	—
19	D₄×Q₈×C₃₁	C₄	1	16	yes	complemented
20	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	—
24	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×#117	C₂²	1	2	yes	—
30	C₂×C₃₁×#117	C₂²	1	2	yes	—
31	C₃₁×#391	C₂²	1	2	yes	—
32	C₃₁×#391	C₂²	1	1	yes	characteristic
33	C₃₁×#391	C₂²	1	4	yes	—
34	C₃₁×#391	C₂²	1	2	yes	—
35	C₃₁×#391	C₂²	1	2	yes	—
36	C₃₁×#391	C₂²	1	4	yes	—
37	C₃₁×#391	C₂²	1	4	yes	—
38	C₃₁×#391	C₂²	1	4	yes	—
39	C₃₁×#391	C₂²	1	1	yes	characteristic
40	C₃₁×#390	C₂²	1	1	yes	characteristic
41	C₃₁×#390	C₂²	1	2	yes	—
42	C₃₁×#390	C₂²	1	1	yes	characteristic
43	C₃₁×#389	C₂²	1	2	yes	—
44	C₃₁×#389	C₂²	1	2	yes	—
45	C₃₁×#389	C₂²	1	2	yes	—
46	C₃₁×#389	C₂²	1	1	yes	characteristic
47	C₃₁×#389	C₂²	1	4	yes	—
48	C₃₁×#389	C₂²	1	1	yes	characteristic
49	C₃₁×#389	C₂²	1	1	yes	characteristic
50	C₃₁×#389	C₂²	1	1	yes	characteristic
51	C₃₁×#388	C₂²	1	4	yes	—
52	C₃₁×#388	C₂²	1	4	yes	—
53	C₃₁×#388	C₂²	1	4	yes	—
54	C₃₁×#388	C₂²	1	2	yes	—
55	C₃₁×#388	C₂²	1	4	yes	—
56	C₃₁×#388	C₂²	1	4	yes	—
57	C₃₁×#388	C₂²	1	2	yes	—
58	C₃₁×#387	C₂²	1	4	yes	—
59	C₃₁×#387	C₂²	1	4	yes	—
60	C₃₁×#387	C₂²	1	2	yes	—
61	C₃₁×#387	C₂²	1	4	yes	—
62	C₃₁×#387	C₂²	1	4	yes	—
63	C₃₁×#387	C₂²	1	2	yes	—
64	C₃₁×#384	C₂²	1	1	yes	characteristic
65	C₃₁×#382	C₂²	1	2	yes	—
66	C₃₁×#381	C₂²	1	4	yes	—
67	C₃₁×#381	C₂²	1	4	yes	—
68	C₃₁×#380	C₂²	1	4	yes	—
69	C₃₁×#380	C₂²	1	2	yes	—
70	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
72	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
73	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
74	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
75	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
76	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
77	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
78	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
79	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
81	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
82	C₃₁×#376	C₂²	1	2	yes	—
83	C₄³×C₃₁	C₂²	1	1	yes	characteristic
84	C₂²×Q₈×C₃₁	—	4	4	no	—
85	C₂²×Q₈×C₃₁	—	4	4	no	—
86	C₂²×Q₈×C₃₁	C₂×C₄	1	16	yes	—
87	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
88	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
90	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
92	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
93	C₃₁×C₄⋊Q₈	C₂×C₄	1	8	yes	—
94	C₃₁×C₄⋊Q₈	C₂×C₄	1	16	yes	—
95	C₃₁×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
96	C₃₁×C₂²⋊Q₈	C₂×C₄	1	32	yes	—
97	C₄×Q₈×C₃₁	—	4	4	no	—
98	C₄×Q₈×C₃₁	—	4	4	no	—
99	C₄×Q₈×C₃₁	C₂×C₄	1	8	yes	—
100	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	—
101	C₄×D₄×C₃₁	C₂×C₄	1	16	yes	—
102	C₃₁×#117	—	4	4	no	—
103	C₃₁×#117	—	4	4	no	—
104	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
131	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
133	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
138	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
139	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
140	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
141	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
143	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
145	C₃₁×#95	C₂³	1	2	yes	—
146	C₃₁×#95	C₂³	1	2	yes	—
147	C₃₁×#95	C₂³	1	2	yes	—
148	C₃₁×#95	C₂³	1	2	yes	—
149	C₃₁×#95	C₂³	1	2	yes	—
150	C₃₁×#95	C₂³	1	2	yes	—
151	C₃₁×#95	C₂³	1	4	yes	—
152	C₃₁×#95	C₂³	1	2	yes	—
153	C₃₁×#95	C₂³	1	4	yes	—
154	C₃₁×#95	C₂³	1	4	yes	—
155	C₃₁×#95	C₂³	1	2	yes	—
156	C₃₁×#95	C₂³	1	4	yes	—
157	C₃₁×#95	C₂³	1	4	yes	—
158	C₃₁×#95	C₂³	1	4	yes	—
159	C₃₁×#95	C₂³	1	4	yes	—
160	C₃₁×#95	C₂³	1	4	yes	—
161	C₃₁×#95	C₂³	1	2	yes	—
162	C₃₁×#95	C₂³	1	2	yes	—
163	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
164	C₂×Q₈×C₃₁	—	2	4	no	—
165	C₂×Q₈×C₃₁	—	2	4	no	—
166	C₂×Q₈×C₃₁	—	2	2	no	—
167	C₂×Q₈×C₃₁	—	2	2	no	—
168	C₂×Q₈×C₃₁	—	4	4	no	—
169	C₂×Q₈×C₃₁	—	4	4	no	—
170	C₂×Q₈×C₃₁	—	4	32	no	—
171	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
172	C₂×Q₈×C₃₁	C₂²×C₄	1	8	yes	—
173	C₂×Q₈×C₃₁	C₂²×C₄	1	16	yes	—
174	C₂×D₄×C₃₁	—	2	2	no	—
175	C₂×D₄×C₃₁	—	2	2	no	—
176	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
177	C₂²×C₄×C₃₁	—	2	4	no	—
178	C₂²×C₄×C₃₁	—	2	4	no	—
179	C₂²×C₄×C₃₁	—	4	4	no	—
180	C₂²×C₄×C₃₁	—	4	4	no	—
181	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
182	C₂²×C₄×C₃₁	C₂²×C₄	1	16	yes	—
183	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
185	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
190	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
193	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
196	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
199	C₄⋊C₄×C₃₁	—	2	2	no	—
200	C₄⋊C₄×C₃₁	—	2	4	no	—
201	C₄⋊C₄×C₃₁	—	2	2	no	—
202	C₄⋊C₄×C₃₁	—	2	4	no	—
203	C₄⋊C₄×C₃₁	—	2	2	no	—
204	C₄⋊C₄×C₃₁	—	2	2	no	—
205	C₄⋊C₄×C₃₁	—	2	4	no	—
206	C₄⋊C₄×C₃₁	—	4	2	no	—
207	C₄⋊C₄×C₃₁	—	4	2	no	—
208	C₄⋊C₄×C₃₁	—	4	2	no	—
209	C₄⋊C₄×C₃₁	—	4	2	no	—
210	C₄⋊C₄×C₃₁	—	4	4	no	—
211	C₄⋊C₄×C₃₁	—	4	4	no	—
212	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
213	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
214	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
215	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
216	C₄⋊C₄×C₃₁	C₂²×C₄	1	16	yes	—
217	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
218	C₂²⋊C₄×C₃₁	—	2	4	no	—
219	C₂²⋊C₄×C₃₁	—	4	2	no	—
220	C₂²⋊C₄×C₃₁	—	4	4	no	—
221	C₂²⋊C₄×C₃₁	—	4	2	no	—
222	C₂²⋊C₄×C₃₁	—	4	2	no	—
223	C₂²⋊C₄×C₃₁	—	4	4	no	—
224	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
225	C₂²⋊C₄×C₃₁	C₂²×C₄	1	16	yes	—
226	C₄²×C₃₁	—	2	2	no	—
227	C₄²×C₃₁	—	2	4	no	—
228	C₄²×C₃₁	—	2	2	no	—
229	C₄²×C₃₁	—	2	2	no	—
230	C₄²×C₃₁	—	2	2	no	—
231	C₄²×C₃₁	—	2	4	no	—
232	C₄²×C₃₁	—	2	2	no	—
233	C₄²×C₃₁	—	4	4	no	—
234	C₄²×C₃₁	—	4	1	no	—
235	C₄²×C₃₁	—	4	4	no	—
236	C₄²×C₃₁	—	4	4	no	—
237	C₄²×C₃₁	—	4	4	no	—
238	C₄²×C₃₁	C₂²×C₄	1	8	yes	—
239	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
240	#34487	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
241	C₂³×C₃₁	—	2	2	no	—
242	C₂³×C₃₁	—	2	2	no	—
243	C₂³×C₃₁	—	2	2	no	—
244	C₂³×C₃₁	—	2	2	no	—
245	C₂³×C₃₁	—	2	2	no	—
246	C₂³×C₃₁	—	2	2	no	—
247	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
248	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
249	Q₈×C₃₁	—	2	8	no	—
250	Q₈×C₃₁	—	2	16	no	—
251	Q₈×C₃₁	—	4	16	no	—
252	D₄×C₃₁	—	2	8	no	—
253	C₂×C₄×C₃₁	—	2	1	no	—
254	C₂×C₄×C₃₁	—	2	2	no	—
255	C₂×C₄×C₃₁	—	2	4	no	—
256	C₂×C₄×C₃₁	—	2	4	no	—
257	C₂×C₄×C₃₁	—	2	2	no	—
258	C₂×C₄×C₃₁	—	2	2	no	—
259	C₂×C₄×C₃₁	—	2	2	no	—
260	C₂×C₄×C₃₁	—	2	1	no	—
261	C₂×C₄×C₃₁	—	2	1	no	—
262	C₂×C₄×C₃₁	—	2	2	no	—
263	C₂×C₄×C₃₁	—	2	2	no	—
264	C₂×C₄×C₃₁	—	2	1	no	—
265	C₂×C₄×C₃₁	—	2	16	no	—
266	C₂×C₄×C₃₁	—	2	2	no	—
267	C₂×C₄×C₃₁	—	2	1	no	—
268	C₂×C₄×C₃₁	—	2	1	no	—
269	C₂×C₄×C₃₁	—	2	2	no	—
270	C₂×C₄×C₃₁	—	2	1	no	—
271	C₂×C₄×C₃₁	—	2	2	no	—
272	C₂×C₄×C₃₁	—	2	4	no	—
273	C₂×C₄×C₃₁	—	2	2	no	—
274	C₂×C₄×C₃₁	—	2	1	no	—
275	C₂×C₄×C₃₁	—	2	2	no	—
276	C₂×C₄×C₃₁	—	2	1	no	—
277	C₂×C₄×C₃₁	—	2	1	no	—
278	C₂×C₄×C₃₁	—	2	2	no	—
279	C₂×C₄×C₃₁	—	2	1	no	—
280	C₂×C₄×C₃₁	—	2	2	no	—
281	C₂×C₄×C₃₁	—	2	2	no	—
282	C₂×C₄×C₃₁	—	2	2	no	—
283	C₂×C₄×C₃₁	—	2	2	no	—
284	C₂×C₄×C₃₁	—	2	4	no	—
285	C₂×C₄×C₃₁	—	2	2	no	—
286	C₂×C₄×C₃₁	—	2	1	no	—
287	C₂×C₄×C₃₁	—	2	4	no	—
288	C₂×C₄×C₃₁	—	2	1	no	—
289	C₂×C₄×C₃₁	—	2	2	no	—
290	C₂×C₄×C₃₁	—	4	16	no	—
291	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
292	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
293	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
294	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
295	C₂×C₄×C₃₁	C₂³×C₄	1	8	yes	—
296	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
297	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
298	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
299	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
300	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
301	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
302	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
303	C₂×D₄×Q₈	C₂×C₃₁	1	1	yes	characteristic
304	#2378	C₂×C₃₁	1	4	yes	complemented
305	#2369	C₂×C₃₁	1	2	yes	complemented
306	#2365	C₂×C₃₁	1	1	yes	characteristic, complemented
307	#2362	C₂×C₃₁	1	2	yes	complemented
308	#2357	C₂×C₃₁	1	2	yes	—
309	#2355	C₂×C₃₁	1	1	yes	characteristic, complemented
310	#2354	C₂×C₃₁	1	1	yes	characteristic
311	Q₈×C₂²⋊C₄	C₂×C₃₁	1	2	yes	complemented
312	#2332	C₂×C₃₁	1	4	yes	complemented
313	#2331	C₂×C₃₁	1	2	yes	complemented
314	#2323	C₂×C₃₁	1	2	yes	complemented
315	#2319	C₂×C₃₁	1	2	yes	—
316	#2310	C₂×C₃₁	1	2	yes	complemented
317	C₄×C₄⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
318	#2295	C₂×C₃₁	1	1	yes	characteristic, complemented
319	#2293	C₂×C₃₁	1	1	yes	characteristic
320	C₂²×C₃₁	—	2	4	no	—
321	C₂²×C₃₁	—	2	4	no	—
322	C₂²×C₃₁	—	2	4	no	—
323	C₂²×C₃₁	—	4	2	no	—
324	C₂²×C₃₁	—	4	2	no	—
325	C₂²×C₃₁	—	4	2	no	—
326	C₂²×C₃₁	—	4	2	no	—
327	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
328	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
329	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
330	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
331	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
332	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
333	C₂²×C₃₁	#585	1	1	yes	characteristic
334	C₄×C₃₁	—	2	4	no	—
335	C₄×C₃₁	—	2	4	no	—
336	C₄×C₃₁	—	2	8	no	—
337	C₄×C₃₁	—	2	2	no	—
338	C₄×C₃₁	—	2	4	no	—
339	C₄×C₃₁	—	2	2	no	—
340	C₄×C₃₁	—	4	1	no	—
341	C₄×C₃₁	—	4	2	no	—
342	C₄×C₃₁	—	4	2	no	—
343	C₄×C₃₁	—	4	2	no	—
344	C₄×C₃₁	—	4	1	no	—
345	C₄×C₃₁	—	4	2	no	—
346	C₄×C₃₁	—	4	1	no	—
347	C₄×C₃₁	—	4	4	no	—
348	C₄×C₃₁	#518	1	4	yes	—
349	C₄×C₃₁	#519	1	4	yes	—
350	C₂³×Q₈	C₂²×C₃₁	1	2	yes	—
351	D₄×Q₈	C₄×C₃₁	1	16	yes	complemented
352	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
353	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
354	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
355	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	—
356	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
357	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
358	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
359	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
360	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
361	C₂×#117	C₂²×C₃₁	1	2	yes	—
362	C₂×#117	C₂²×C₃₁	1	2	yes	—
363	#391	C₂²×C₃₁	1	2	yes	—
364	#391	C₂²×C₃₁	1	1	yes	characteristic
365	#391	C₂²×C₃₁	1	4	yes	—
366	#391	C₂²×C₃₁	1	2	yes	—
367	#391	C₂²×C₃₁	1	2	yes	—
368	#391	C₂²×C₃₁	1	4	yes	—
369	#391	C₂²×C₃₁	1	4	yes	—
370	#391	C₂²×C₃₁	1	4	yes	—
371	#391	C₂²×C₃₁	1	1	yes	characteristic
372	#390	C₂²×C₃₁	1	1	yes	characteristic
373	#390	C₂²×C₃₁	1	2	yes	—
374	#390	C₂²×C₃₁	1	1	yes	characteristic
375	#389	C₂²×C₃₁	1	2	yes	—
376	#389	C₂²×C₃₁	1	2	yes	—
377	#389	C₂²×C₃₁	1	2	yes	—
378	#389	C₂²×C₃₁	1	1	yes	characteristic
379	#389	C₂²×C₃₁	1	4	yes	—
380	#389	C₂²×C₃₁	1	1	yes	characteristic
381	#389	C₂²×C₃₁	1	1	yes	characteristic
382	#389	C₂²×C₃₁	1	1	yes	characteristic
383	#388	C₂²×C₃₁	1	4	yes	—
384	#388	C₂²×C₃₁	1	4	yes	—
385	#388	C₂²×C₃₁	1	4	yes	—
386	#388	C₂²×C₃₁	1	2	yes	—
387	#388	C₂²×C₃₁	1	4	yes	—
388	#388	C₂²×C₃₁	1	4	yes	—
389	#388	C₂²×C₃₁	1	2	yes	—
390	#387	C₂²×C₃₁	1	4	yes	—
391	#387	C₂²×C₃₁	1	4	yes	—
392	#387	C₂²×C₃₁	1	2	yes	—
393	#387	C₂²×C₃₁	1	4	yes	—
394	#387	C₂²×C₃₁	1	4	yes	—
395	#387	C₂²×C₃₁	1	2	yes	—
396	#384	C₂²×C₃₁	1	1	yes	characteristic
397	#382	C₂²×C₃₁	1	2	yes	—
398	#381	C₂²×C₃₁	1	4	yes	—
399	#381	C₂²×C₃₁	1	4	yes	—
400	#380	C₂²×C₃₁	1	4	yes	—
401	#380	C₂²×C₃₁	1	2	yes	—
402	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
403	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
404	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
405	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
406	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
407	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
408	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	—
409	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
410	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
411	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
412	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
413	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
414	#376	C₂²×C₃₁	1	2	yes	—
415	C₄³	C₂²×C₃₁	1	1	yes	characteristic
416	C₂×C₃₁	—	4	4	no	—
417	C₂×C₃₁	C₂×#518	1	1	yes	characteristic
418	C₂×C₃₁	C₂×#519	1	1	yes	characteristic
419	C₂×C₃₁	C₄×2₋¹⁺⁴	1	1	yes	characteristic
420	C₂×C₃₁	#3547	1	1	yes	characteristic
421	C₂×C₃₁	#3550	1	1	yes	characteristic
422	C₂×C₃₁	#3552	1	1	yes	characteristic
423	C₂×C₃₁	#3554	1	1	yes	characteristic
424	C₂²×Q₈	—	4	4	no	—
425	C₂²×Q₈	—	4	4	no	—
426	C₂²×Q₈	C₂×C₄×C₃₁	1	16	yes	—
427	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
428	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
429	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
430	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
431	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
432	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
433	C₄⋊Q₈	C₂×C₄×C₃₁	1	8	yes	—
434	C₄⋊Q₈	C₂×C₄×C₃₁	1	16	yes	—
435	C₂²⋊Q₈	C₂×C₄×C₃₁	1	16	yes	—
436	C₂²⋊Q₈	C₂×C₄×C₃₁	1	32	yes	—
437	C₄×Q₈	—	4	4	no	—
438	C₄×Q₈	—	4	4	no	—
439	C₄×Q₈	C₂×C₄×C₃₁	1	8	yes	—
440	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	—
441	C₄×D₄	C₂×C₄×C₃₁	1	16	yes	—
442	#117	—	4	4	no	—
443	#117	—	4	4	no	—
444	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
445	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
446	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
449	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
450	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
451	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
452	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
453	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
454	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
455	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
456	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
457	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
458	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
461	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
462	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
471	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
472	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
473	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
474	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
475	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
476	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
477	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
478	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
479	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
480	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
481	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
482	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
483	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
484	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
485	#95	C₂³×C₃₁	1	2	yes	—
486	#95	C₂³×C₃₁	1	2	yes	—
487	#95	C₂³×C₃₁	1	2	yes	—
488	#95	C₂³×C₃₁	1	2	yes	—
489	#95	C₂³×C₃₁	1	2	yes	—
490	#95	C₂³×C₃₁	1	2	yes	—
491	#95	C₂³×C₃₁	1	4	yes	—
492	#95	C₂³×C₃₁	1	2	yes	—
493	#95	C₂³×C₃₁	1	4	yes	—
494	#95	C₂³×C₃₁	1	4	yes	—
495	#95	C₂³×C₃₁	1	2	yes	—
496	#95	C₂³×C₃₁	1	4	yes	—
497	#95	C₂³×C₃₁	1	4	yes	—
498	#95	C₂³×C₃₁	1	4	yes	—
499	#95	C₂³×C₃₁	1	4	yes	—
500	#95	C₂³×C₃₁	1	4	yes	—
501	#95	C₂³×C₃₁	1	2	yes	—
502	#95	C₂³×C₃₁	1	2	yes	—
503	C₃₁	#34487	1	1	yes	characteristic, direct product factor, Sylow
504	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
505	C₂×Q₈	—	2	4	no	—
506	C₂×Q₈	—	2	4	no	—
507	C₂×Q₈	—	2	2	no	—
508	C₂×Q₈	—	2	2	no	—
509	C₂×Q₈	—	4	4	no	—
510	C₂×Q₈	—	4	4	no	—
511	C₂×Q₈	—	4	32	no	—
512	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
513	C₂×Q₈	C₂²×C₄×C₃₁	1	8	yes	—
514	C₂×Q₈	C₂²×C₄×C₃₁	1	16	yes	—
515	C₂×D₄	—	2	2	no	—
516	C₂×D₄	—	2	2	no	—
517	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
518	C₂²×C₄	—	2	4	no	—
519	C₂²×C₄	—	2	4	no	—
520	C₂²×C₄	—	4	4	no	—
521	C₂²×C₄	—	4	4	no	—
522	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
523	C₂²×C₄	C₂²×C₄×C₃₁	1	16	yes	—
524	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
525	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
526	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
527	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
528	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
529	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
530	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
531	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
532	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
533	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
534	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
535	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
536	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
537	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
538	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
539	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	2	4	no	—
542	C₄⋊C₄	—	2	2	no	—
543	C₄⋊C₄	—	2	4	no	—
544	C₄⋊C₄	—	2	2	no	—
545	C₄⋊C₄	—	2	2	no	—
546	C₄⋊C₄	—	2	4	no	—
547	C₄⋊C₄	—	4	2	no	—
548	C₄⋊C₄	—	4	2	no	—
549	C₄⋊C₄	—	4	2	no	—
550	C₄⋊C₄	—	4	2	no	—
551	C₄⋊C₄	—	4	4	no	—
552	C₄⋊C₄	—	4	4	no	—
553	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
554	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
555	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
556	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
557	C₄⋊C₄	C₂²×C₄×C₃₁	1	16	yes	—
558	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
559	C₂²⋊C₄	—	2	4	no	—
560	C₂²⋊C₄	—	4	2	no	—
561	C₂²⋊C₄	—	4	4	no	—
562	C₂²⋊C₄	—	4	2	no	—
563	C₂²⋊C₄	—	4	2	no	—
564	C₂²⋊C₄	—	4	4	no	—
565	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
566	C₂²⋊C₄	C₂²×C₄×C₃₁	1	16	yes	—
567	C₄²	—	2	2	no	—
568	C₄²	—	2	4	no	—
569	C₄²	—	2	2	no	—
570	C₄²	—	2	2	no	—
571	C₄²	—	2	2	no	—
572	C₄²	—	2	4	no	—
573	C₄²	—	2	2	no	—
574	C₄²	—	4	4	no	—
575	C₄²	—	4	1	no	—
576	C₄²	—	4	4	no	—
577	C₄²	—	4	4	no	—
578	C₄²	—	4	4	no	—
579	C₄²	C₂²×C₄×C₃₁	1	8	yes	—
580	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
581	C₂³	—	2	2	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	2	2	no	—
584	C₂³	—	2	2	no	—
585	C₂³	—	2	2	no	—
586	C₂³	—	2	2	no	—
587	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
588	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
589	Q₈	—	2	8	no	—
590	Q₈	—	2	16	no	—
591	Q₈	—	4	16	no	—
592	D₄	—	2	8	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	4	no	—
596	C₂×C₄	—	2	4	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	16	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	4	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	4	16	no	—
631	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
632	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
633	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
634	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
635	C₂×C₄	C₂³×C₄×C₃₁	1	8	yes	—
636	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
637	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
638	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
639	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
640	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
641	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
642	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
643	C₂²	—	2	4	no	—
644	C₂²	—	2	4	no	—
645	C₂²	—	2	4	no	—
646	C₂²	—	4	2	no	—
647	C₂²	—	4	2	no	—
648	C₂²	—	4	2	no	—
649	C₂²	—	4	2	no	—
650	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
651	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
652	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
653	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
654	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
655	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
656	C₂²	C₃₁×#585	1	1	yes	characteristic
657	C₄	—	2	4	no	—
658	C₄	—	2	4	no	—
659	C₄	—	2	8	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	4	no	—
662	C₄	—	2	2	no	—
663	C₄	—	4	1	no	—
664	C₄	—	4	2	no	—
665	C₄	—	4	2	no	—
666	C₄	—	4	2	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	2	no	—
669	C₄	—	4	1	no	—
670	C₄	—	4	4	no	—
671	C₄	C₃₁×#518	1	4	yes	—
672	C₄	C₃₁×#519	1	4	yes	—
673	C₂	—	4	4	no	—
674	C₂	C₂×C₃₁×#518	1	1	yes	characteristic
675	C₂	C₂×C₃₁×#519	1	1	yes	characteristic
676	C₂	C₄×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
677	C₂	C₃₁×#3547	1	1	yes	characteristic
678	C₂	C₃₁×#3550	1	1	yes	characteristic
679	C₂	C₃₁×#3552	1	1	yes	characteristic
680	C₂	C₃₁×#3554	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂²×D₄×C₃₁	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2378	C₂	semidirect
3. C₃₁×#2369	C₂	semidirect
4. C₃₁×#2365	C₂	semidirect
5. C₃₁×#2362	C₂	semidirect
7. C₃₁×#2355	C₂	semidirect
9. Q₈×C₂²⋊C₄×C₃₁	C₂	semidirect
10. C₃₁×#2332	C₂	semidirect
11. C₃₁×#2331	C₂	semidirect
12. C₃₁×#2323	C₂	semidirect
14. C₃₁×#2310	C₂	semidirect
15. C₄×C₃₁×C₄⋊Q₈	C₂	semidirect
16. C₃₁×#2295	C₂	semidirect
19. D₄×Q₈×C₃₁	C₄	semidirect
240. #34487	C₃₁	direct (N × H)
304. #2378	C₂×C₃₁	semidirect
305. #2369	C₂×C₃₁	semidirect
306. #2365	C₂×C₃₁	semidirect
307. #2362	C₂×C₃₁	semidirect
309. #2355	C₂×C₃₁	semidirect
311. Q₈×C₂²⋊C₄	C₂×C₃₁	semidirect
312. #2332	C₂×C₃₁	semidirect
313. #2331	C₂×C₃₁	semidirect
314. #2323	C₂×C₃₁	semidirect
316. #2310	C₂×C₃₁	semidirect
317. C₄×C₄⋊Q₈	C₂×C₃₁	semidirect
318. #2295	C₂×C₃₁	semidirect
351. D₄×Q₈	C₄×C₃₁	semidirect
503. C₃₁	#34487	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
C₃₁×#2378	2
C₃₁×#2369	2
C₃₁×#2365	2
C₃₁×#2362	2
C₃₁×#2357	2
C₃₁×#2355	2
C₃₁×#2354	2
Q₈×C₂²⋊C₄×C₃₁	2
C₃₁×#2332	2
C₃₁×#2331	2
C₃₁×#2323	2
C₃₁×#2319	2
C₃₁×#2310	2
C₄×C₃₁×C₄⋊Q₈	2
C₃₁×#2295	2
C₃₁×#2293	2
#34487	31

Subgroups — C31×#34487 #21491246

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34487 #21491246