Subgroups — C₃₁×#34322 #21491081

Order 7936.

2228 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#556	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2373	C₂	1	4	yes	maximal, complemented
3	C₃₁×#2367	C₂	1	2	yes	maximal
4	C₃₁×#2365	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2360	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2355	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2351	C₂	1	2	yes	maximal, complemented
8	D₄×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
9	C₃₁×#2346	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2334	C₂	1	4	yes	maximal, complemented
11	C₃₁×#2323	C₂	1	2	yes	maximal, complemented
12	C₄×C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₃₁×#124	C₂	1	2	yes	maximal
14	C₃₁×#2295	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2293	C₂	1	1	yes	maximal, characteristic
16	C₃₁×#2274	C₂	1	2	yes	maximal, complemented
17	C₄²×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#556	C₄	1	16	yes	complemented
19	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₃₁×#126	C₂²	1	4	yes	—
21	C₂×C₃₁×#124	C₂²	1	2	yes	—
22	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×#117	C₂²	1	2	yes	—
32	C₂×C₃₁×#117	C₂²	1	2	yes	—
33	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
34	C₃₁×#391	C₂²	1	2	yes	—
35	C₃₁×#391	C₂²	1	2	yes	—
36	C₃₁×#391	C₂²	1	2	yes	—
37	C₃₁×#390	C₂²	1	1	yes	characteristic
38	C₃₁×#390	C₂²	1	1	yes	characteristic
39	C₃₁×#389	C₂²	1	2	yes	—
40	C₃₁×#389	C₂²	1	2	yes	—
41	C₃₁×#389	C₂²	1	2	yes	—
42	C₃₁×#389	C₂²	1	4	yes	—
43	C₃₁×#389	C₂²	1	4	yes	—
44	C₃₁×#389	C₂²	1	2	yes	—
45	C₃₁×#389	C₂²	1	1	yes	characteristic
46	C₃₁×#389	C₂²	1	1	yes	characteristic
47	C₃₁×#388	C₂²	1	4	yes	—
48	C₃₁×#388	C₂²	1	4	yes	—
49	C₃₁×#388	C₂²	1	2	yes	—
50	C₃₁×#388	C₂²	1	4	yes	—
51	C₃₁×#388	C₂²	1	4	yes	—
52	C₃₁×#388	C₂²	1	2	yes	—
53	C₃₁×#387	C₂²	1	4	yes	—
54	C₃₁×#387	C₂²	1	4	yes	—
55	C₃₁×#387	C₂²	1	4	yes	—
56	C₃₁×#387	C₂²	1	4	yes	—
57	C₃₁×#385	C₂²	1	4	yes	—
58	C₃₁×#385	C₂²	1	4	yes	—
59	C₃₁×#384	C₂²	1	1	yes	characteristic
60	C₃₁×#382	C₂²	1	4	yes	—
61	C₃₁×#382	C₂²	1	2	yes	—
62	C₃₁×#380	C₂²	1	2	yes	—
63	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
64	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
65	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
66	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
67	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
68	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
69	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
70	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
72	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
77	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
78	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
79	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
80	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
81	C₃₁×#376	C₂²	1	4	yes	—
82	C₄³×C₃₁	C₂²	1	1	yes	characteristic
83	C₄³×C₃₁	C₂²	1	2	yes	—
84	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
85	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
86	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
88	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
89	C₃₁×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
90	C₃₁×#126	C₂×C₄	1	32	yes	complemented
91	C₃₁×#124	C₂×C₄	1	16	yes	—
92	C₃₁×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
93	C₄×Q₈×C₃₁	—	2	4	no	—
94	C₄×Q₈×C₃₁	—	2	4	no	—
95	C₄×Q₈×C₃₁	—	4	4	no	—
96	C₄×Q₈×C₃₁	—	4	4	no	—
97	C₄×Q₈×C₃₁	C₂×C₄	1	16	yes	complemented
98	C₄×Q₈×C₃₁	C₂×C₄	1	8	yes	complemented
99	C₄×D₄×C₃₁	—	4	4	no	—
100	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	—
101	C₃₁×#117	—	2	8	no	—
102	C₃₁×#117	C₂×C₄	1	16	yes	complemented
103	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
104	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
106	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
114	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	2	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×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
132	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
133	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
134	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
136	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
138	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
140	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
142	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
143	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
144	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
146	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
147	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
149	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
150	C₃₁×#95	C₂³	1	2	yes	—
151	C₃₁×#95	C₂³	1	4	yes	—
152	C₃₁×#95	C₂³	1	4	yes	—
153	C₃₁×#95	C₂³	1	4	yes	—
154	C₃₁×#95	C₂³	1	2	yes	—
155	C₃₁×#95	C₂³	1	4	yes	—
156	C₃₁×#95	C₂³	1	4	yes	—
157	C₃₁×#95	C₂³	1	4	yes	—
158	C₃₁×#95	C₂³	1	2	yes	—
159	C₃₁×#95	C₂³	1	4	yes	—
160	C₃₁×#95	C₂³	1	2	yes	—
161	C₃₁×#95	C₂³	1	2	yes	—
162	C₃₁×#95	C₂³	1	4	yes	—
163	C₃₁×#95	C₂³	1	2	yes	—
164	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
165	C₂×Q₈×C₃₁	—	2	2	no	—
166	C₂×Q₈×C₃₁	—	2	2	no	—
167	C₂×Q₈×C₃₁	—	2	4	no	—
168	C₂×Q₈×C₃₁	—	2	4	no	—
169	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
170	C₂×Q₈×C₃₁	C₂²×C₄	1	8	yes	—
171	C₂×D₄×C₃₁	—	2	2	no	—
172	C₂×D₄×C₃₁	—	2	2	no	—
173	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
174	C₂²×C₄×C₃₁	—	2	4	no	—
175	C₂²×C₄×C₃₁	—	2	4	no	—
176	C₂²×C₄×C₃₁	—	2	8	no	—
177	C₂²×C₄×C₃₁	—	4	4	no	—
178	C₂²×C₄×C₃₁	—	4	4	no	—
179	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
180	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₃₁	C₂⁴	1	4	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	4	yes	—
189	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
193	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
194	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
195	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
196	C₄⋊C₄×C₃₁	—	2	8	no	—
197	C₄⋊C₄×C₃₁	—	2	4	no	—
198	C₄⋊C₄×C₃₁	—	2	4	no	—
199	C₄⋊C₄×C₃₁	—	2	4	no	—
200	C₄⋊C₄×C₃₁	—	2	4	no	—
201	C₄⋊C₄×C₃₁	—	2	4	no	—
202	C₄⋊C₄×C₃₁	—	2	2	no	—
203	C₄⋊C₄×C₃₁	—	2	4	no	—
204	C₄⋊C₄×C₃₁	—	2	2	no	—
205	C₄⋊C₄×C₃₁	—	2	2	no	—
206	C₄⋊C₄×C₃₁	—	4	2	no	—
207	C₄⋊C₄×C₃₁	—	4	4	no	—
208	C₄⋊C₄×C₃₁	—	4	4	no	—
209	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
210	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
211	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
212	C₄⋊C₄×C₃₁	C₂²×C₄	1	16	yes	—
213	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
214	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
215	C₄⋊C₄×C₃₁	#41	1	4	yes	—
216	C₂²⋊C₄×C₃₁	—	2	4	no	—
217	C₂²⋊C₄×C₃₁	—	2	4	no	—
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	C₂²×C₄	1	16	yes	—
222	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
223	C₂²⋊C₄×C₃₁	C₂²×C₄	1	16	yes	—
224	C₄²×C₃₁	—	2	4	no	—
225	C₄²×C₃₁	—	2	4	no	—
226	C₄²×C₃₁	—	2	2	no	—
227	C₄²×C₃₁	—	2	4	no	—
228	C₄²×C₃₁	—	2	4	no	—
229	C₄²×C₃₁	—	2	2	no	—
230	C₄²×C₃₁	—	2	2	no	—
231	C₄²×C₃₁	—	2	2	no	—
232	C₄²×C₃₁	—	2	4	no	—
233	C₄²×C₃₁	—	4	2	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	16	yes	—
239	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
240	C₄²×C₃₁	C₂²×C₄	1	8	yes	—
241	C₄²×C₃₁	#41	1	4	yes	—
242	#34322	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	2	2	no	—
248	C₂³×C₃₁	—	2	2	no	—
249	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
250	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
251	Q₈×C₃₁	—	2	8	no	—
252	Q₈×C₃₁	—	2	16	no	—
253	D₄×C₃₁	—	2	8	no	—
254	C₂×C₄×C₃₁	—	2	1	no	—
255	C₂×C₄×C₃₁	—	2	2	no	—
256	C₂×C₄×C₃₁	—	2	2	no	—
257	C₂×C₄×C₃₁	—	2	2	no	—
258	C₂×C₄×C₃₁	—	2	2	no	—
259	C₂×C₄×C₃₁	—	2	1	no	—
260	C₂×C₄×C₃₁	—	2	2	no	—
261	C₂×C₄×C₃₁	—	2	4	no	—
262	C₂×C₄×C₃₁	—	2	2	no	—
263	C₂×C₄×C₃₁	—	2	1	no	—
264	C₂×C₄×C₃₁	—	2	1	no	—
265	C₂×C₄×C₃₁	—	2	1	no	—
266	C₂×C₄×C₃₁	—	2	1	no	—
267	C₂×C₄×C₃₁	—	2	4	no	—
268	C₂×C₄×C₃₁	—	2	2	no	—
269	C₂×C₄×C₃₁	—	2	1	no	—
270	C₂×C₄×C₃₁	—	2	1	no	—
271	C₂×C₄×C₃₁	—	2	2	no	—
272	C₂×C₄×C₃₁	—	2	16	no	—
273	C₂×C₄×C₃₁	—	2	2	no	—
274	C₂×C₄×C₃₁	—	2	2	no	—
275	C₂×C₄×C₃₁	—	2	2	no	—
276	C₂×C₄×C₃₁	—	2	1	no	—
277	C₂×C₄×C₃₁	—	2	4	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	4	no	—
282	C₂×C₄×C₃₁	—	2	2	no	—
283	C₂×C₄×C₃₁	—	2	2	no	—
284	C₂×C₄×C₃₁	—	2	2	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	—	8	8	no	—
289	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
290	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
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	8	yes	—
294	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
295	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
296	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
297	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
298	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
299	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
300	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
301	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
302	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
303	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
304	C₂×#556	C₂×C₃₁	1	1	yes	characteristic
305	#2373	C₂×C₃₁	1	4	yes	complemented
306	#2367	C₂×C₃₁	1	2	yes	—
307	#2365	C₂×C₃₁	1	1	yes	characteristic, complemented
308	#2360	C₂×C₃₁	1	2	yes	complemented
309	#2355	C₂×C₃₁	1	1	yes	characteristic, complemented
310	#2351	C₂×C₃₁	1	2	yes	complemented
311	D₄×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic
312	#2346	C₂×C₃₁	1	2	yes	complemented
313	#2334	C₂×C₃₁	1	4	yes	complemented
314	#2323	C₂×C₃₁	1	2	yes	complemented
315	C₄×C₄⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
316	C₄×#124	C₂×C₃₁	1	2	yes	—
317	#2295	C₂×C₃₁	1	2	yes	complemented
318	#2293	C₂×C₃₁	1	1	yes	characteristic
319	#2274	C₂×C₃₁	1	2	yes	complemented
320	C₄²×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
321	C₂²×C₃₁	—	2	4	no	—
322	C₂²×C₃₁	—	2	4	no	—
323	C₂²×C₃₁	—	2	4	no	—
324	C₂²×C₃₁	—	4	2	no	—
325	C₂²×C₃₁	—	4	2	no	—
326	C₂²×C₃₁	—	4	2	no	—
327	C₂²×C₃₁	—	4	2	no	—
328	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
329	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
330	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
331	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
332	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
333	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
334	C₂²×C₃₁	#585	1	1	yes	characteristic
335	C₄×C₃₁	—	2	4	no	—
336	C₄×C₃₁	—	2	4	no	—
337	C₄×C₃₁	—	2	8	no	—
338	C₄×C₃₁	—	2	4	no	—
339	C₄×C₃₁	—	2	2	no	—
340	C₄×C₃₁	—	2	2	no	—
341	C₄×C₃₁	—	2	2	no	—
342	C₄×C₃₁	—	2	4	no	—
343	C₄×C₃₁	—	2	2	no	—
344	C₄×C₃₁	—	4	2	no	—
345	C₄×C₃₁	—	4	2	no	—
346	C₄×C₃₁	—	4	2	no	—
347	C₄×C₃₁	—	4	1	no	—
348	C₄×C₃₁	—	4	4	no	—
349	C₄×C₃₁	C₄×#41	1	4	yes	—
350	C₄×C₃₁	#520	1	4	yes	—
351	#556	C₄×C₃₁	1	16	yes	complemented
352	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
353	C₂×#126	C₂²×C₃₁	1	4	yes	—
354	C₂×#124	C₂²×C₃₁	1	2	yes	—
355	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
356	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
357	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
358	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
359	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
360	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
361	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
362	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
363	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
364	C₂×#117	C₂²×C₃₁	1	2	yes	—
365	C₂×#117	C₂²×C₃₁	1	2	yes	—
366	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
367	#391	C₂²×C₃₁	1	2	yes	—
368	#391	C₂²×C₃₁	1	2	yes	—
369	#391	C₂²×C₃₁	1	2	yes	—
370	#390	C₂²×C₃₁	1	1	yes	characteristic
371	#390	C₂²×C₃₁	1	1	yes	characteristic
372	#389	C₂²×C₃₁	1	2	yes	—
373	#389	C₂²×C₃₁	1	2	yes	—
374	#389	C₂²×C₃₁	1	2	yes	—
375	#389	C₂²×C₃₁	1	4	yes	—
376	#389	C₂²×C₃₁	1	4	yes	—
377	#389	C₂²×C₃₁	1	2	yes	—
378	#389	C₂²×C₃₁	1	1	yes	characteristic
379	#389	C₂²×C₃₁	1	1	yes	characteristic
380	#388	C₂²×C₃₁	1	4	yes	—
381	#388	C₂²×C₃₁	1	4	yes	—
382	#388	C₂²×C₃₁	1	2	yes	—
383	#388	C₂²×C₃₁	1	4	yes	—
384	#388	C₂²×C₃₁	1	4	yes	—
385	#388	C₂²×C₃₁	1	2	yes	—
386	#387	C₂²×C₃₁	1	4	yes	—
387	#387	C₂²×C₃₁	1	4	yes	—
388	#387	C₂²×C₃₁	1	4	yes	—
389	#387	C₂²×C₃₁	1	4	yes	—
390	#385	C₂²×C₃₁	1	4	yes	—
391	#385	C₂²×C₃₁	1	4	yes	—
392	#384	C₂²×C₃₁	1	1	yes	characteristic
393	#382	C₂²×C₃₁	1	4	yes	—
394	#382	C₂²×C₃₁	1	2	yes	—
395	#380	C₂²×C₃₁	1	2	yes	—
396	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
397	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
398	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
399	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	—
400	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
401	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
402	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
403	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
404	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	—
405	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
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	2	yes	—
409	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
410	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
411	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
412	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
413	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
414	#376	C₂²×C₃₁	1	4	yes	—
415	C₄³	C₂²×C₃₁	1	1	yes	characteristic
416	C₄³	C₂²×C₃₁	1	2	yes	—
417	C₂×C₃₁	—	4	4	no	—
418	C₂×C₃₁	C₂×C₄×#41	1	1	yes	characteristic
419	C₂×C₃₁	C₂×#520	1	1	yes	characteristic
420	C₂×C₃₁	C₄×2₋¹⁺⁴	1	1	yes	characteristic
421	C₂×C₃₁	#3507	1	1	yes	characteristic
422	C₂×C₃₁	#3511	1	1	yes	characteristic
423	C₂×C₃₁	#3514	1	1	yes	characteristic
424	C₂×C₃₁	#3523	1	1	yes	characteristic
425	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
426	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
427	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
428	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
429	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
430	C₄⋊Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
431	#126	C₂×C₄×C₃₁	1	32	yes	complemented
432	#124	C₂×C₄×C₃₁	1	16	yes	—
433	C₂²⋊Q₈	C₂×C₄×C₃₁	1	16	yes	complemented
434	C₄×Q₈	—	2	4	no	—
435	C₄×Q₈	—	2	4	no	—
436	C₄×Q₈	—	4	4	no	—
437	C₄×Q₈	—	4	4	no	—
438	C₄×Q₈	C₂×C₄×C₃₁	1	16	yes	complemented
439	C₄×Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
440	C₄×D₄	—	4	4	no	—
441	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	—
442	#117	—	2	8	no	—
443	#117	C₂×C₄×C₃₁	1	16	yes	complemented
444	C₂×C₄⋊C₄	—	2	8	no	—
445	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
446	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
447	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
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	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
453	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
454	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
455	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
456	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	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	2	yes	—
460	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
462	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
463	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
464	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
465	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
473	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
474	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
475	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
476	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
477	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
478	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
479	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
480	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
481	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
482	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
483	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
484	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
485	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
486	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
487	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
488	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
489	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
490	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
491	#95	C₂³×C₃₁	1	2	yes	—
492	#95	C₂³×C₃₁	1	4	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	2	yes	—
500	#95	C₂³×C₃₁	1	4	yes	—
501	#95	C₂³×C₃₁	1	2	yes	—
502	#95	C₂³×C₃₁	1	2	yes	—
503	#95	C₂³×C₃₁	1	4	yes	—
504	#95	C₂³×C₃₁	1	2	yes	—
505	C₃₁	#34322	1	1	yes	characteristic, direct product factor, Sylow
506	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
507	C₂×Q₈	—	2	2	no	—
508	C₂×Q₈	—	2	2	no	—
509	C₂×Q₈	—	2	4	no	—
510	C₂×Q₈	—	2	4	no	—
511	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
512	C₂×Q₈	C₂²×C₄×C₃₁	1	8	yes	—
513	C₂×D₄	—	2	2	no	—
514	C₂×D₄	—	2	2	no	—
515	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
516	C₂²×C₄	—	2	4	no	—
517	C₂²×C₄	—	2	4	no	—
518	C₂²×C₄	—	2	8	no	—
519	C₂²×C₄	—	4	4	no	—
520	C₂²×C₄	—	4	4	no	—
521	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
522	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
523	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
524	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
525	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
526	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
527	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
528	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
529	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
530	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
531	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
532	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
533	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
534	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
535	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
536	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
537	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
538	C₄⋊C₄	—	2	8	no	—
539	C₄⋊C₄	—	2	4	no	—
540	C₄⋊C₄	—	2	4	no	—
541	C₄⋊C₄	—	2	4	no	—
542	C₄⋊C₄	—	2	4	no	—
543	C₄⋊C₄	—	2	4	no	—
544	C₄⋊C₄	—	2	2	no	—
545	C₄⋊C₄	—	2	4	no	—
546	C₄⋊C₄	—	2	2	no	—
547	C₄⋊C₄	—	2	2	no	—
548	C₄⋊C₄	—	4	2	no	—
549	C₄⋊C₄	—	4	4	no	—
550	C₄⋊C₄	—	4	4	no	—
551	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
552	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
553	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
554	C₄⋊C₄	C₂²×C₄×C₃₁	1	16	yes	—
555	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
556	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
557	C₄⋊C₄	#41×C₃₁	1	4	yes	—
558	C₂²⋊C₄	—	2	4	no	—
559	C₂²⋊C₄	—	2	4	no	—
560	C₂²⋊C₄	—	2	4	no	—
561	C₂²⋊C₄	—	4	2	no	—
562	C₂²⋊C₄	—	4	4	no	—
563	C₂²⋊C₄	C₂²×C₄×C₃₁	1	16	yes	—
564	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
565	C₂²⋊C₄	C₂²×C₄×C₃₁	1	16	yes	—
566	C₄²	—	2	4	no	—
567	C₄²	—	2	4	no	—
568	C₄²	—	2	2	no	—
569	C₄²	—	2	4	no	—
570	C₄²	—	2	4	no	—
571	C₄²	—	2	2	no	—
572	C₄²	—	2	2	no	—
573	C₄²	—	2	2	no	—
574	C₄²	—	2	4	no	—
575	C₄²	—	4	2	no	—
576	C₄²	—	4	1	no	—
577	C₄²	—	4	4	no	—
578	C₄²	—	4	4	no	—
579	C₄²	—	4	4	no	—
580	C₄²	C₂²×C₄×C₃₁	1	16	yes	—
581	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
582	C₄²	C₂²×C₄×C₃₁	1	8	yes	—
583	C₄²	#41×C₃₁	1	4	yes	—
584	C₂³	—	2	2	no	—
585	C₂³	—	2	2	no	—
586	C₂³	—	2	2	no	—
587	C₂³	—	2	2	no	—
588	C₂³	—	2	2	no	—
589	C₂³	—	2	2	no	—
590	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
591	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
592	Q₈	—	2	8	no	—
593	Q₈	—	2	16	no	—
594	D₄	—	2	8	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	2	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	2	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	16	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	8	8	no	—
630	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
631	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
632	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
633	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
634	C₂×C₄	C₂³×C₄×C₃₁	1	8	yes	—
635	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
636	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
637	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
638	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
639	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
640	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
641	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
642	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
643	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
644	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
645	C₂²	—	2	4	no	—
646	C₂²	—	2	4	no	—
647	C₂²	—	2	4	no	—
648	C₂²	—	4	2	no	—
649	C₂²	—	4	2	no	—
650	C₂²	—	4	2	no	—
651	C₂²	—	4	2	no	—
652	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
653	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
654	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
655	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
656	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
657	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
658	C₂²	C₃₁×#585	1	1	yes	characteristic
659	C₄	—	2	4	no	—
660	C₄	—	2	4	no	—
661	C₄	—	2	8	no	—
662	C₄	—	2	4	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	4	no	—
667	C₄	—	2	2	no	—
668	C₄	—	4	2	no	—
669	C₄	—	4	2	no	—
670	C₄	—	4	2	no	—
671	C₄	—	4	4	no	—
672	C₄	—	4	1	no	—
673	C₄	C₄×#41×C₃₁	1	4	yes	—
674	C₄	C₃₁×#520	1	4	yes	—
675	C₂	—	4	4	no	—
676	C₂	C₂×C₄×#41×C₃₁	1	1	yes	characteristic
677	C₂	C₂×C₃₁×#520	1	1	yes	characteristic
678	C₂	C₄×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
679	C₂	C₃₁×#3507	1	1	yes	characteristic
680	C₂	C₃₁×#3511	1	1	yes	characteristic
681	C₂	C₃₁×#3514	1	1	yes	characteristic
682	C₂	C₃₁×#3523	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×#2373	C₂	semidirect
4. C₃₁×#2365	C₂	semidirect
5. C₃₁×#2360	C₂	semidirect
6. C₃₁×#2355	C₂	semidirect
7. C₃₁×#2351	C₂	semidirect
9. C₃₁×#2346	C₂	semidirect
10. C₃₁×#2334	C₂	semidirect
11. C₃₁×#2323	C₂	semidirect
12. C₄×C₃₁×C₄⋊Q₈	C₂	semidirect
14. C₃₁×#2295	C₂	semidirect
16. C₃₁×#2274	C₂	semidirect
17. C₄²×Q₈×C₃₁	C₂	semidirect
18. C₃₁×#556	C₄	semidirect
89. C₃₁×C₄⋊Q₈	C₂×C₄	semidirect
90. C₃₁×#126	C₂×C₄	semidirect
92. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
97. C₄×Q₈×C₃₁	C₂×C₄	semidirect
98. C₄×Q₈×C₃₁	C₂×C₄	semidirect
102. C₃₁×#117	C₂×C₄	semidirect
242. #34322	C₃₁	direct (N × H)
305. #2373	C₂×C₃₁	semidirect
307. #2365	C₂×C₃₁	semidirect
308. #2360	C₂×C₃₁	semidirect
309. #2355	C₂×C₃₁	semidirect
310. #2351	C₂×C₃₁	semidirect
312. #2346	C₂×C₃₁	semidirect
313. #2334	C₂×C₃₁	semidirect
314. #2323	C₂×C₃₁	semidirect
315. C₄×C₄⋊Q₈	C₂×C₃₁	semidirect
317. #2295	C₂×C₃₁	semidirect
319. #2274	C₂×C₃₁	semidirect
320. C₄²×Q₈	C₂×C₃₁	semidirect
351. #556	C₄×C₃₁	semidirect
430. C₄⋊Q₈	C₂×C₄×C₃₁	semidirect
431. #126	C₂×C₄×C₃₁	semidirect
433. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
438. C₄×Q₈	C₂×C₄×C₃₁	semidirect
439. C₄×Q₈	C₂×C₄×C₃₁	semidirect
443. #117	C₂×C₄×C₃₁	semidirect
505. C₃₁	#34322	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×C₃₁×#556	2
C₃₁×#2373	2
C₃₁×#2367	2
C₃₁×#2365	2
C₃₁×#2360	2
C₃₁×#2355	2
C₃₁×#2351	2
D₄×C₄⋊C₄×C₃₁	2
C₃₁×#2346	2
C₃₁×#2334	2
C₃₁×#2323	2
C₄×C₃₁×C₄⋊Q₈	2
C₄×C₃₁×#124	2
C₃₁×#2295	2
C₃₁×#2293	2
C₃₁×#2274	2
C₄²×Q₈×C₃₁	2
#34322	31

Subgroups — C31×#34322 #21491081

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34322 #21491081