Subgroups — C₃₁×#34382 #21491141

Order 7936.

2218 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×#529	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2382	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2379	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2359	C₂	1	4	yes	maximal, complemented
5	C₃₁×#2355	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2352	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2352	C₂	1	2	yes	maximal, complemented
8	D₄×C₄⋊C₄×C₃₁	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2334	C₂	1	4	yes	maximal, complemented
10	C₃₁×#2329	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2325	C₂	1	2	yes	maximal
12	C₃₁×#2317	C₂	1	2	yes	maximal, complemented
13	C₃₁×#2314	C₂	1	2	yes	maximal, complemented
14	C₃₁×#2285	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃₁×#382	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#529	C₄	1	16	yes	complemented
17	C₂×C₃₁×#126	C₂²	1	2	yes	—
18	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
20	C₂×C₃₁×#123	C₂²	1	2	yes	—
21	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
25	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#117	C₂²	1	2	yes	—
28	C₂×C₃₁×#117	C₂²	1	2	yes	—
29	C₂×C₃₁×#117	C₂²	1	2	yes	—
30	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
31	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
34	C₃₁×#391	C₂²	1	4	yes	—
35	C₃₁×#389	C₂²	1	4	yes	—
36	C₃₁×#389	C₂²	1	4	yes	—
37	C₃₁×#389	C₂²	1	4	yes	—
38	C₃₁×#388	C₂²	1	4	yes	—
39	C₃₁×#388	C₂²	1	4	yes	—
40	C₃₁×#388	C₂²	1	4	yes	—
41	C₃₁×#388	C₂²	1	4	yes	—
42	C₃₁×#387	C₂²	1	4	yes	—
43	C₃₁×#387	C₂²	1	4	yes	—
44	C₃₁×#387	C₂²	1	4	yes	—
45	C₃₁×#387	C₂²	1	4	yes	—
46	C₃₁×#387	C₂²	1	4	yes	—
47	C₃₁×#387	C₂²	1	4	yes	—
48	C₃₁×#386	C₂²	1	4	yes	—
49	C₃₁×#386	C₂²	1	4	yes	—
50	C₃₁×#385	C₂²	1	4	yes	—
51	C₃₁×#385	C₂²	1	4	yes	—
52	C₃₁×#385	C₂²	1	4	yes	—
53	C₃₁×#385	C₂²	1	4	yes	—
54	C₃₁×#384	C₂²	1	1	yes	characteristic
55	C₃₁×#384	C₂²	1	1	yes	characteristic
56	C₃₁×#384	C₂²	1	2	yes	—
57	C₃₁×#382	C₂²	1	2	yes	—
58	C₃₁×#382	C₂²	1	2	yes	—
59	C₃₁×#382	C₂²	1	2	yes	—
60	C₃₁×#382	C₂²	1	2	yes	—
61	C₃₁×#382	C₂²	1	2	yes	—
62	C₃₁×#382	C₂²	1	2	yes	—
63	C₃₁×#380	C₂²	1	2	yes	—
64	C₃₁×#380	C₂²	1	2	yes	—
65	C₃₁×#380	C₂²	1	2	yes	—
66	C₃₁×#380	C₂²	1	2	yes	—
67	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
68	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
69	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
70	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
71	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
72	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
73	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
74	C₂×C₃₁×#95	C₂²	1	2	yes	—
75	C₂×C₃₁×#95	C₂²	1	2	yes	—
76	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
78	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
82	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
83	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
84	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
85	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
86	C₃₁×#126	C₂×C₄	1	16	yes	complemented
87	C₃₁×#125	C₂×C₄	1	8	yes	complemented
88	C₃₁×#124	C₂×C₄	1	8	yes	complemented
89	C₃₁×#123	C₂×C₄	1	16	yes	complemented
90	C₃₁×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
91	C₃₁×#121	C₂×C₄	1	8	yes	—
92	C₄×Q₈×C₃₁	C₂×C₄	1	8	yes	complemented
93	C₄×D₄×C₃₁	—	4	8	no	—
94	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
95	C₄×D₄×C₃₁	C₂×C₄	1	16	yes	complemented
96	C₃₁×#117	—	4	4	no	—
97	C₃₁×#117	—	4	4	no	—
98	C₃₁×#117	C₂×C₄	1	16	yes	complemented
99	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
100	C₂×C₄⋊C₄×C₃₁	—	4	4	no	—
101	C₂×C₄⋊C₄×C₃₁	—	4	2	no	—
102	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	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	4	yes	—
109	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
112	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	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	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	2	yes	—
121	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	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	2	yes	—
128	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
130	C₂×C₄²×C₃₁	C₂×C₄	1	8	yes	complemented
131	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
132	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
133	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
134	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
135	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
140	C₃₁×#95	C₂³	1	4	yes	—
141	C₃₁×#95	C₂³	1	4	yes	—
142	C₃₁×#95	C₂³	1	4	yes	—
143	C₃₁×#95	C₂³	1	4	yes	—
144	C₃₁×#95	C₂³	1	4	yes	—
145	C₃₁×#95	C₂³	1	4	yes	—
146	C₃₁×#95	C₂³	1	4	yes	—
147	C₃₁×#95	C₂³	1	4	yes	—
148	C₃₁×#95	C₂³	1	4	yes	—
149	C₃₁×#95	C₂³	1	4	yes	—
150	C₃₁×#95	C₂³	1	4	yes	—
151	C₃₁×#95	C₂³	1	4	yes	—
152	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
153	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
154	C₂×Q₈×C₃₁	—	4	1	no	—
155	C₂×Q₈×C₃₁	—	4	1	no	—
156	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
157	C₂×D₄×C₃₁	—	2	4	no	—
158	C₂×D₄×C₃₁	—	2	4	no	—
159	C₂×D₄×C₃₁	—	4	1	no	—
160	C₂×D₄×C₃₁	—	4	1	no	—
161	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
162	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
163	C₂²×C₄×C₃₁	—	2	2	no	—
164	C₂²×C₄×C₃₁	—	2	2	no	—
165	C₂²×C₄×C₃₁	—	2	2	no	—
166	C₂²×C₄×C₃₁	—	2	4	no	—
167	C₂²×C₄×C₃₁	—	2	2	no	—
168	C₂²×C₄×C₃₁	—	2	4	no	—
169	C₂²×C₄×C₃₁	—	2	4	no	—
170	C₂²×C₄×C₃₁	—	2	4	no	—
171	C₂²×C₄×C₃₁	—	4	1	no	—
172	C₂²×C₄×C₃₁	—	4	1	no	—
173	C₂²×C₄×C₃₁	—	4	2	no	—
174	C₂²×C₄×C₃₁	—	4	4	no	—
175	C₂²×C₄×C₃₁	—	4	2	no	—
176	C₂²×C₄×C₃₁	—	4	4	no	—
177	C₂²×C₄×C₃₁	—	4	2	no	—
178	C₂²×C₄×C₃₁	—	4	4	no	—
179	C₂²×C₄×C₃₁	—	4	2	no	—
180	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
181	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
182	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
183	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
184	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
187	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
188	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
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	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	—	4	4	no	—
202	C₄⋊C₄×C₃₁	—	4	2	no	—
203	C₄⋊C₄×C₃₁	—	4	2	no	—
204	C₄⋊C₄×C₃₁	—	4	2	no	—
205	C₄⋊C₄×C₃₁	—	4	2	no	—
206	C₄⋊C₄×C₃₁	—	4	4	no	—
207	C₄⋊C₄×C₃₁	—	4	2	no	—
208	C₄⋊C₄×C₃₁	—	4	2	no	—
209	C₄⋊C₄×C₃₁	—	4	4	no	—
210	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
211	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
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	4	yes	—
215	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
216	C₂²⋊C₄×C₃₁	—	2	8	no	—
217	C₂²⋊C₄×C₃₁	—	4	4	no	—
218	C₂²⋊C₄×C₃₁	—	4	4	no	—
219	C₂²⋊C₄×C₃₁	—	4	4	no	—
220	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
221	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
222	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
223	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
224	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
225	C₄²×C₃₁	—	4	4	no	—
226	C₄²×C₃₁	—	4	4	no	—
227	C₄²×C₃₁	—	4	4	no	—
228	C₄²×C₃₁	—	4	4	no	—
229	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
230	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
231	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
232	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
233	C₄²×C₃₁	C₂²×C₄	1	8	yes	—
234	#34382	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂³×C₃₁	—	2	1	no	—
236	C₂³×C₃₁	—	2	1	no	—
237	C₂³×C₃₁	—	2	1	no	—
238	C₂³×C₃₁	—	2	1	no	—
239	C₂³×C₃₁	—	2	2	no	—
240	C₂³×C₃₁	—	2	2	no	—
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	C₂³×C₄	1	4	yes	—
246	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
247	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
248	C₂³×C₃₁	2₋¹⁺⁴	1	2	yes	—
249	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
250	Q₈×C₃₁	—	4	4	no	—
251	D₄×C₃₁	—	2	16	no	—
252	D₄×C₃₁	—	4	4	no	—
253	C₂×C₄×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	1	no	—
258	C₂×C₄×C₃₁	—	2	1	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	1	no	—
263	C₂×C₄×C₃₁	—	2	2	no	—
264	C₂×C₄×C₃₁	—	2	2	no	—
265	C₂×C₄×C₃₁	—	2	1	no	—
266	C₂×C₄×C₃₁	—	2	1	no	—
267	C₂×C₄×C₃₁	—	2	2	no	—
268	C₂×C₄×C₃₁	—	2	1	no	—
269	C₂×C₄×C₃₁	—	2	1	no	—
270	C₂×C₄×C₃₁	—	2	8	no	—
271	C₂×C₄×C₃₁	—	2	16	no	—
272	C₂×C₄×C₃₁	—	2	4	no	—
273	C₂×C₄×C₃₁	—	2	4	no	—
274	C₂×C₄×C₃₁	—	2	4	no	—
275	C₂×C₄×C₃₁	—	2	4	no	—
276	C₂×C₄×C₃₁	—	2	4	no	—
277	C₂×C₄×C₃₁	—	2	4	no	—
278	C₂×C₄×C₃₁	—	2	4	no	—
279	C₂×C₄×C₃₁	—	2	4	no	—
280	C₂×C₄×C₃₁	—	2	4	no	—
281	C₂×C₄×C₃₁	—	2	4	no	—
282	C₂×C₄×C₃₁	—	2	4	no	—
283	C₂×C₄×C₃₁	—	2	4	no	—
284	C₂×C₄×C₃₁	—	4	4	no	—
285	C₂×C₄×C₃₁	—	8	4	no	—
286	C₂×C₄×C₃₁	—	8	4	no	—
287	C₂×C₄×C₃₁	—	8	8	no	—
288	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
289	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
290	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
291	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
292	C₂×C₄×C₃₁	C₂³×C₄	1	2	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	4	yes	—
296	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
297	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
298	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
299	C₂×#529	C₂×C₃₁	1	1	yes	characteristic
300	#2382	C₂×C₃₁	1	2	yes	complemented
301	#2379	C₂×C₃₁	1	2	yes	complemented
302	#2359	C₂×C₃₁	1	4	yes	complemented
303	#2355	C₂×C₃₁	1	2	yes	complemented
304	#2352	C₂×C₃₁	1	2	yes	complemented
305	#2352	C₂×C₃₁	1	2	yes	complemented
306	D₄×C₄⋊C₄	C₂×C₃₁	1	2	yes	complemented
307	#2334	C₂×C₃₁	1	4	yes	complemented
308	#2329	C₂×C₃₁	1	2	yes	complemented
309	#2325	C₂×C₃₁	1	2	yes	—
310	#2317	C₂×C₃₁	1	2	yes	complemented
311	#2314	C₂×C₃₁	1	2	yes	complemented
312	#2285	C₂×C₃₁	1	1	yes	characteristic, complemented
313	C₂×#382	C₂×C₃₁	1	1	yes	characteristic, complemented
314	C₂²×C₃₁	—	2	2	no	—
315	C₂²×C₃₁	—	2	2	no	—
316	C₂²×C₃₁	—	2	2	no	—
317	C₂²×C₃₁	—	2	2	no	—
318	C₂²×C₃₁	—	2	2	no	—
319	C₂²×C₃₁	—	2	2	no	—
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	#520	1	4	yes	—
328	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
329	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
330	C₂²×C₃₁	C₂×H(5,𝔽₂)	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	C₂²×C₃₁	#585	1	1	yes	characteristic
335	C₄×C₃₁	—	2	2	no	—
336	C₄×C₃₁	—	2	2	no	—
337	C₄×C₃₁	—	2	4	no	—
338	C₄×C₃₁	—	2	2	no	—
339	C₄×C₃₁	—	2	4	no	—
340	C₄×C₃₁	—	2	2	no	—
341	C₄×C₃₁	—	2	2	no	—
342	C₄×C₃₁	—	2	4	no	—
343	C₄×C₃₁	—	4	4	no	—
344	C₄×C₃₁	—	4	4	no	—
345	C₄×C₃₁	—	4	4	no	—
346	C₄×C₃₁	—	4	4	no	—
347	C₄×C₃₁	#520	1	4	yes	—
348	#529	C₄×C₃₁	1	16	yes	complemented
349	C₂×#126	C₂²×C₃₁	1	2	yes	—
350	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
351	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
352	C₂×#123	C₂²×C₃₁	1	2	yes	—
353	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
354	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
355	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
356	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
357	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
358	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
359	C₂×#117	C₂²×C₃₁	1	2	yes	—
360	C₂×#117	C₂²×C₃₁	1	2	yes	—
361	C₂×#117	C₂²×C₃₁	1	2	yes	—
362	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
363	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
364	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
365	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
366	#391	C₂²×C₃₁	1	4	yes	—
367	#389	C₂²×C₃₁	1	4	yes	—
368	#389	C₂²×C₃₁	1	4	yes	—
369	#389	C₂²×C₃₁	1	4	yes	—
370	#388	C₂²×C₃₁	1	4	yes	—
371	#388	C₂²×C₃₁	1	4	yes	—
372	#388	C₂²×C₃₁	1	4	yes	—
373	#388	C₂²×C₃₁	1	4	yes	—
374	#387	C₂²×C₃₁	1	4	yes	—
375	#387	C₂²×C₃₁	1	4	yes	—
376	#387	C₂²×C₃₁	1	4	yes	—
377	#387	C₂²×C₃₁	1	4	yes	—
378	#387	C₂²×C₃₁	1	4	yes	—
379	#387	C₂²×C₃₁	1	4	yes	—
380	#386	C₂²×C₃₁	1	4	yes	—
381	#386	C₂²×C₃₁	1	4	yes	—
382	#385	C₂²×C₃₁	1	4	yes	—
383	#385	C₂²×C₃₁	1	4	yes	—
384	#385	C₂²×C₃₁	1	4	yes	—
385	#385	C₂²×C₃₁	1	4	yes	—
386	#384	C₂²×C₃₁	1	1	yes	characteristic
387	#384	C₂²×C₃₁	1	1	yes	characteristic
388	#384	C₂²×C₃₁	1	2	yes	—
389	#382	C₂²×C₃₁	1	2	yes	—
390	#382	C₂²×C₃₁	1	2	yes	—
391	#382	C₂²×C₃₁	1	2	yes	—
392	#382	C₂²×C₃₁	1	2	yes	—
393	#382	C₂²×C₃₁	1	2	yes	—
394	#382	C₂²×C₃₁	1	2	yes	—
395	#380	C₂²×C₃₁	1	2	yes	—
396	#380	C₂²×C₃₁	1	2	yes	—
397	#380	C₂²×C₃₁	1	2	yes	—
398	#380	C₂²×C₃₁	1	2	yes	—
399	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
400	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
401	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
402	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	—
403	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
404	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
405	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
406	C₂×#95	C₂²×C₃₁	1	2	yes	—
407	C₂×#95	C₂²×C₃₁	1	2	yes	—
408	C₂×C₃₁	—	2	4	no	—
409	C₂×C₃₁	—	4	4	no	—
410	C₂×C₃₁	C₂×#520	1	1	yes	characteristic
411	C₂×C₃₁	C₂×#520	1	1	yes	characteristic
412	C₂×C₃₁	#3428	1	1	yes	characteristic
413	C₂×C₃₁	#3558	1	1	yes	characteristic
414	C₂×C₃₁	#3559	1	1	yes	characteristic
415	C₂×C₃₁	#3561	1	1	yes	characteristic
416	C₂×C₃₁	#3563	1	1	yes	characteristic
417	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
418	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
419	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
420	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
421	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
422	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
423	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
424	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
425	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
426	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
427	#126	C₂×C₄×C₃₁	1	16	yes	complemented
428	#125	C₂×C₄×C₃₁	1	8	yes	complemented
429	#124	C₂×C₄×C₃₁	1	8	yes	complemented
430	#123	C₂×C₄×C₃₁	1	16	yes	complemented
431	C₂²⋊Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
432	#121	C₂×C₄×C₃₁	1	8	yes	—
433	C₄×Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
434	C₄×D₄	—	4	8	no	—
435	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
436	C₄×D₄	C₂×C₄×C₃₁	1	16	yes	complemented
437	#117	—	4	4	no	—
438	#117	—	4	4	no	—
439	#117	C₂×C₄×C₃₁	1	16	yes	complemented
440	C₂×C₄⋊C₄	—	4	2	no	—
441	C₂×C₄⋊C₄	—	4	4	no	—
442	C₂×C₄⋊C₄	—	4	2	no	—
443	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
444	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
445	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
446	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	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	4	yes	—
450	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
451	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
452	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
453	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
454	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
455	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	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	2	yes	—
460	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	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	2	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
471	C₂×C₄²	C₂×C₄×C₃₁	1	8	yes	complemented
472	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
473	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
474	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
475	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
476	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
477	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
478	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
479	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
480	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
481	#95	C₂³×C₃₁	1	4	yes	—
482	#95	C₂³×C₃₁	1	4	yes	—
483	#95	C₂³×C₃₁	1	4	yes	—
484	#95	C₂³×C₃₁	1	4	yes	—
485	#95	C₂³×C₃₁	1	4	yes	—
486	#95	C₂³×C₃₁	1	4	yes	—
487	#95	C₂³×C₃₁	1	4	yes	—
488	#95	C₂³×C₃₁	1	4	yes	—
489	#95	C₂³×C₃₁	1	4	yes	—
490	#95	C₂³×C₃₁	1	4	yes	—
491	#95	C₂³×C₃₁	1	4	yes	—
492	#95	C₂³×C₃₁	1	4	yes	—
493	C₃₁	#34382	1	1	yes	characteristic, direct product factor, Sylow
494	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
495	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
496	C₂×Q₈	—	4	1	no	—
497	C₂×Q₈	—	4	1	no	—
498	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
499	C₂×D₄	—	2	4	no	—
500	C₂×D₄	—	2	4	no	—
501	C₂×D₄	—	4	1	no	—
502	C₂×D₄	—	4	1	no	—
503	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
504	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	2	2	no	—
507	C₂²×C₄	—	2	2	no	—
508	C₂²×C₄	—	2	4	no	—
509	C₂²×C₄	—	2	2	no	—
510	C₂²×C₄	—	2	4	no	—
511	C₂²×C₄	—	2	4	no	—
512	C₂²×C₄	—	2	4	no	—
513	C₂²×C₄	—	4	1	no	—
514	C₂²×C₄	—	4	1	no	—
515	C₂²×C₄	—	4	2	no	—
516	C₂²×C₄	—	4	4	no	—
517	C₂²×C₄	—	4	2	no	—
518	C₂²×C₄	—	4	4	no	—
519	C₂²×C₄	—	4	2	no	—
520	C₂²×C₄	—	4	4	no	—
521	C₂²×C₄	—	4	2	no	—
522	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
523	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
524	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
525	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
526	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
527	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
528	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
529	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
530	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
531	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
532	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
533	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
534	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
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	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
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	—	4	4	no	—
544	C₄⋊C₄	—	4	2	no	—
545	C₄⋊C₄	—	4	2	no	—
546	C₄⋊C₄	—	4	2	no	—
547	C₄⋊C₄	—	4	2	no	—
548	C₄⋊C₄	—	4	4	no	—
549	C₄⋊C₄	—	4	2	no	—
550	C₄⋊C₄	—	4	2	no	—
551	C₄⋊C₄	—	4	4	no	—
552	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
553	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
554	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	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	8	yes	—
558	C₂²⋊C₄	—	2	8	no	—
559	C₂²⋊C₄	—	4	4	no	—
560	C₂²⋊C₄	—	4	4	no	—
561	C₂²⋊C₄	—	4	4	no	—
562	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
563	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
564	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
565	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
566	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
567	C₄²	—	4	4	no	—
568	C₄²	—	4	4	no	—
569	C₄²	—	4	4	no	—
570	C₄²	—	4	4	no	—
571	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
572	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
573	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
574	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
575	C₄²	C₂²×C₄×C₃₁	1	8	yes	—
576	C₂³	—	2	1	no	—
577	C₂³	—	2	1	no	—
578	C₂³	—	2	1	no	—
579	C₂³	—	2	1	no	—
580	C₂³	—	2	2	no	—
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	C₂³×C₄×C₃₁	1	4	yes	—
587	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
588	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
589	C₂³	C₃₁×2₋¹⁺⁴	1	2	yes	—
590	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
591	Q₈	—	4	4	no	—
592	D₄	—	2	16	no	—
593	D₄	—	4	4	no	—
594	C₂×C₄	—	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	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	8	no	—
612	C₂×C₄	—	2	16	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	4	4	no	—
626	C₂×C₄	—	8	4	no	—
627	C₂×C₄	—	8	4	no	—
628	C₂×C₄	—	8	8	no	—
629	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
630	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
631	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
632	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
633	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
634	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
635	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
636	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
637	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
638	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
639	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	4	no	—
647	C₂²	—	2	4	no	—
648	C₂²	—	2	4	no	—
649	C₂²	—	4	2	no	—
650	C₂²	—	4	2	no	—
651	C₂²	—	4	2	no	—
652	C₂²	—	4	2	no	—
653	C₂²	C₃₁×#520	1	4	yes	—
654	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
655	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
656	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
657	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
658	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
659	C₂²	C₃₁×#585	1	1	yes	characteristic
660	C₂²	C₃₁×#585	1	1	yes	characteristic
661	C₄	—	2	2	no	—
662	C₄	—	2	2	no	—
663	C₄	—	2	4	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	4	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	4	no	—
669	C₄	—	4	4	no	—
670	C₄	—	4	4	no	—
671	C₄	—	4	4	no	—
672	C₄	—	4	4	no	—
673	C₄	C₃₁×#520	1	4	yes	—
674	C₂	—	2	4	no	—
675	C₂	—	4	4	no	—
676	C₂	C₂×C₃₁×#520	1	1	yes	characteristic
677	C₂	C₂×C₃₁×#520	1	1	yes	characteristic
678	C₂	C₃₁×#3428	1	1	yes	characteristic
679	C₂	C₃₁×#3558	1	1	yes	characteristic
680	C₂	C₃₁×#3559	1	1	yes	characteristic
681	C₂	C₃₁×#3561	1	1	yes	characteristic
682	C₂	C₃₁×#3563	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#121	C₂²
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×#2382	C₂	semidirect
3. C₃₁×#2379	C₂	semidirect
4. C₃₁×#2359	C₂	semidirect
5. C₃₁×#2355	C₂	semidirect
6. C₃₁×#2352	C₂	semidirect
7. C₃₁×#2352	C₂	semidirect
8. D₄×C₄⋊C₄×C₃₁	C₂	semidirect
9. C₃₁×#2334	C₂	semidirect
10. C₃₁×#2329	C₂	semidirect
12. C₃₁×#2317	C₂	semidirect
13. C₃₁×#2314	C₂	semidirect
14. C₃₁×#2285	C₂	semidirect
15. C₂×C₃₁×#382	C₂	semidirect
16. C₃₁×#529	C₄	semidirect
86. C₃₁×#126	C₂×C₄	semidirect
87. C₃₁×#125	C₂×C₄	semidirect
88. C₃₁×#124	C₂×C₄	semidirect
89. C₃₁×#123	C₂×C₄	semidirect
90. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
92. C₄×Q₈×C₃₁	C₂×C₄	semidirect
94. C₄×D₄×C₃₁	C₂×C₄	semidirect
95. C₄×D₄×C₃₁	C₂×C₄	semidirect
98. C₃₁×#117	C₂×C₄	semidirect
130. C₂×C₄²×C₃₁	C₂×C₄	semidirect
234. #34382	C₃₁	direct (N × H)
300. #2382	C₂×C₃₁	semidirect
301. #2379	C₂×C₃₁	semidirect
302. #2359	C₂×C₃₁	semidirect
303. #2355	C₂×C₃₁	semidirect
304. #2352	C₂×C₃₁	semidirect
305. #2352	C₂×C₃₁	semidirect
306. D₄×C₄⋊C₄	C₂×C₃₁	semidirect
307. #2334	C₂×C₃₁	semidirect
308. #2329	C₂×C₃₁	semidirect
310. #2317	C₂×C₃₁	semidirect
311. #2314	C₂×C₃₁	semidirect
312. #2285	C₂×C₃₁	semidirect
313. C₂×#382	C₂×C₃₁	semidirect
348. #529	C₄×C₃₁	semidirect
427. #126	C₂×C₄×C₃₁	semidirect
428. #125	C₂×C₄×C₃₁	semidirect
429. #124	C₂×C₄×C₃₁	semidirect
430. #123	C₂×C₄×C₃₁	semidirect
431. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
433. C₄×Q₈	C₂×C₄×C₃₁	semidirect
435. C₄×D₄	C₂×C₄×C₃₁	semidirect
436. C₄×D₄	C₂×C₄×C₃₁	semidirect
439. #117	C₂×C₄×C₃₁	semidirect
471. C₂×C₄²	C₂×C₄×C₃₁	semidirect
493. C₃₁	#34382	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×#529	2
C₃₁×#2382	2
C₃₁×#2379	2
C₃₁×#2359	2
C₃₁×#2355	2
C₃₁×#2352	2
D₄×C₄⋊C₄×C₃₁	2
C₃₁×#2334	2
C₃₁×#2329	2
C₃₁×#2325	2
C₃₁×#2317	2
C₃₁×#2314	2
C₃₁×#2285	2
C₂×C₃₁×#382	2
#34382	31

Subgroups — C31×#34382 #21491141

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34382 #21491141