Subgroups — C₃₁×#34200 #21490959

Order 7936.

3534 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#525	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2361	C₂	1	4	yes	maximal, complemented
5	C₃₁×#2360	C₂	1	4	yes	maximal, complemented
6	C₃₁×#2352	C₂	1	4	yes	maximal, complemented
7	D₄×C₄⋊C₄×C₃₁	C₂	1	4	yes	maximal, complemented
8	C₃₁×#2322	C₂	1	4	yes	maximal, complemented
9	C₃₁×#2317	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2311	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₃₁×#120	C₂	1	4	yes	maximal, complemented
12	C₃₁×#2280	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#2274	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₃₁	C₂²	1	2	yes	—
17	C₃₁×#525	C₄	1	16	yes	complemented
18	C₂×C₃₁×#123	C₂²	1	2	yes	—
19	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₃₁×#121	C₂²	1	2	yes	—
21	C₂×C₃₁×#120	C₂²	1	2	yes	—
22	C₃₁×#520	—	2	8	no	—
23	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
24	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
25	C₂×C₄×D₄×C₃₁	C₂²	1	8	yes	—
26	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
27	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
28	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
32	C₂²×C₄⋊C₄×C₃₁	—	2	8	no	—
33	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
34	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
35	C₂²×C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
36	C₂²×C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
37	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
39	C₃₁×#391	C₂²	1	2	yes	complemented
40	C₃₁×#390	C₂²	1	2	yes	complemented
41	C₃₁×#389	C₂²	1	4	yes	complemented
42	C₃₁×#389	C₂²	1	8	yes	complemented
43	C₃₁×#388	C₂²	1	8	yes	complemented
44	C₃₁×#387	C₂²	1	8	yes	complemented
45	C₃₁×#386	C₂²	1	4	yes	—
46	C₃₁×#386	C₂²	1	8	yes	—
47	C₃₁×#385	C₂²	1	4	yes	—
48	C₃₁×#385	C₂²	1	8	yes	—
49	C₃₁×#385	C₂²	1	8	yes	complemented
50	C₃₁×#384	C₂²	1	2	yes	complemented
51	C₃₁×#382	C₂²	1	2	yes	complemented
52	C₃₁×#381	C₂²	1	2	yes	—
53	C₃₁×#380	C₂²	1	2	yes	—
54	C₃₁×#380	C₂²	1	2	yes	—
55	C₃₁×#380	C₂²	1	4	yes	complemented
56	C₃₁×#379	C₂²	1	2	yes	—
57	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	complemented
58	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	complemented
59	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
60	C₄×C₂²⋊C₄×C₃₁	C₂²	1	8	yes	—
61	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
62	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
63	C₂×#41×C₃₁	—	2	4	no	—
64	C₂×#41×C₃₁	—	2	4	no	—
65	C₂×#41×C₃₁	C₂×C₄	1	8	yes	complemented
66	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
68	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
69	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₃₁	—	2	4	no	—
71	C₂³×C₄×C₃₁	—	2	4	no	—
72	C₂³×C₄×C₃₁	—	2	8	no	—
73	C₂³×C₄×C₃₁	—	4	8	no	—
74	C₂³×C₄×C₃₁	C₂×C₄	1	8	yes	complemented
75	C₂³×C₄×C₃₁	C₂³	1	8	yes	—
76	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
77	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
78	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
80	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
81	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
82	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
83	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
84	C₃₁×#123	C₂×C₄	1	16	yes	complemented
85	C₃₁×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
86	C₃₁×#121	C₂×C₄	1	16	yes	complemented
87	C₃₁×#120	C₂×C₄	1	16	yes	complemented
88	C₄×Q₈×C₃₁	—	2	8	no	—
89	C₄×D₄×C₃₁	—	2	16	no	—
90	C₄×D₄×C₃₁	—	2	8	no	—
91	C₄×D₄×C₃₁	—	4	16	no	—
92	C₄×D₄×C₃₁	C₂×C₄	1	32	yes	complemented
93	C₃₁×#117	—	2	4	no	—
94	C₃₁×#117	—	2	4	no	—
95	C₃₁×#117	—	2	8	no	—
96	C₃₁×#117	C₂×C₄	1	8	yes	complemented
97	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
98	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
99	C₂×C₄⋊C₄×C₃₁	—	2	16	no	—
100	C₂×C₄⋊C₄×C₃₁	—	2	16	no	—
101	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
102	C₂×C₄⋊C₄×C₃₁	D₄	1	8	yes	complemented
103	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
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	4	yes	—
108	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
111	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
115	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
116	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
117	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
119	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
121	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
124	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
125	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
126	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
127	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
128	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
129	C₃₁×#95	C₂³	1	8	yes	—
130	C₃₁×#95	C₂³	1	4	yes	—
131	C₃₁×#95	C₂³	1	4	yes	—
132	C₃₁×#95	C₂³	1	8	yes	—
133	C₃₁×#95	C₂³	1	8	yes	—
134	C₂⁴×C₃₁	—	2	2	no	—
135	C₂⁴×C₃₁	—	2	2	no	—
136	C₂⁴×C₃₁	—	2	4	no	—
137	C₂⁴×C₃₁	—	2	4	no	—
138	C₂⁴×C₃₁	C₂²×C₄	1	4	yes	—
139	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
140	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
141	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
142	#41×C₃₁	—	2	32	no	—
143	C₂×Q₈×C₃₁	—	2	2	no	—
144	C₂×Q₈×C₃₁	—	2	2	no	—
145	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	complemented
146	C₂×D₄×C₃₁	—	2	4	no	—
147	C₂×D₄×C₃₁	—	2	4	no	—
148	C₂×D₄×C₃₁	—	2	8	no	—
149	C₂×D₄×C₃₁	—	2	8	no	—
150	C₂×D₄×C₃₁	—	2	2	no	—
151	C₂×D₄×C₃₁	—	2	2	no	—
152	C₂×D₄×C₃₁	C₂²×C₄	1	16	yes	—
153	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
154	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	complemented
155	C₂²×C₄×C₃₁	—	2	2	no	—
156	C₂²×C₄×C₃₁	—	2	2	no	—
157	C₂²×C₄×C₃₁	—	2	32	no	—
158	C₂²×C₄×C₃₁	—	2	4	no	—
159	C₂²×C₄×C₃₁	—	2	4	no	—
160	C₂²×C₄×C₃₁	—	2	4	no	—
161	C₂²×C₄×C₃₁	—	2	4	no	—
162	C₂²×C₄×C₃₁	—	2	4	no	—
163	C₂²×C₄×C₃₁	—	2	4	no	—
164	C₂²×C₄×C₃₁	—	2	4	no	—
165	C₂²×C₄×C₃₁	—	2	16	no	—
166	C₂²×C₄×C₃₁	—	2	16	no	—
167	C₂²×C₄×C₃₁	—	2	8	no	—
168	C₂²×C₄×C₃₁	—	4	4	no	—
169	C₂²×C₄×C₃₁	—	4	8	no	—
170	C₂²×C₄×C₃₁	—	4	4	no	—
171	C₂²×C₄×C₃₁	—	4	8	no	—
172	C₂²×C₄×C₃₁	—	4	32	no	—
173	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
174	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
175	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
176	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
177	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	complemented
178	C₂²×C₄×C₃₁	C₂×D₄	1	8	yes	—
179	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
180	C₂²×C₄×C₃₁	#41	1	4	yes	—
181	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
189	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
191	C₄⋊C₄×C₃₁	—	2	16	no	—
192	C₄⋊C₄×C₃₁	—	2	4	no	—
193	C₄⋊C₄×C₃₁	—	2	4	no	—
194	C₄⋊C₄×C₃₁	—	2	2	no	—
195	C₄⋊C₄×C₃₁	—	2	8	no	—
196	C₄⋊C₄×C₃₁	—	2	2	no	—
197	C₄⋊C₄×C₃₁	—	2	4	no	—
198	C₄⋊C₄×C₃₁	—	4	8	no	—
199	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	complemented
200	C₄⋊C₄×C₃₁	C₂²×C₄	1	16	yes	complemented
201	C₄⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
202	C₄⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
203	C₂²⋊C₄×C₃₁	—	2	4	no	—
204	C₂²⋊C₄×C₃₁	—	2	4	no	—
205	C₂²⋊C₄×C₃₁	—	2	8	no	—
206	C₂²⋊C₄×C₃₁	—	2	8	no	—
207	C₂²⋊C₄×C₃₁	—	2	8	no	—
208	C₂²⋊C₄×C₃₁	—	4	8	no	—
209	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
210	C₂²⋊C₄×C₃₁	C₂²×C₄	1	16	yes	—
211	C₂²⋊C₄×C₃₁	C₂²×C₄	1	16	yes	complemented
212	C₄²×C₃₁	—	2	8	no	—
213	C₄²×C₃₁	—	2	4	no	—
214	C₄²×C₃₁	—	2	4	no	—
215	C₄²×C₃₁	—	4	8	no	—
216	C₄²×C₃₁	C₂²×C₄	1	8	yes	complemented
217	#34200	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂³×C₃₁	—	2	8	no	—
219	C₂³×C₃₁	—	2	8	no	—
220	C₂³×C₃₁	—	2	16	no	—
221	C₂³×C₃₁	—	2	8	no	—
222	C₂³×C₃₁	—	2	16	no	—
223	C₂³×C₃₁	—	2	2	no	—
224	C₂³×C₃₁	—	2	2	no	—
225	C₂³×C₃₁	—	2	2	no	—
226	C₂³×C₃₁	—	2	2	no	—
227	C₂³×C₃₁	—	2	2	no	—
228	C₂³×C₃₁	—	2	2	no	—
229	C₂³×C₃₁	—	2	2	no	—
230	C₂³×C₃₁	—	2	2	no	—
231	C₂³×C₃₁	—	2	4	no	—
232	C₂³×C₃₁	—	2	4	no	—
233	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
234	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
235	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
236	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
237	C₂³×C₃₁	C₂×#41	1	2	yes	—
238	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
239	C₂³×C₃₁	2₋¹⁺⁴	1	4	yes	—
240	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
241	Q₈×C₃₁	—	2	8	no	—
242	D₄×C₃₁	—	2	16	no	—
243	D₄×C₃₁	—	2	32	no	—
244	D₄×C₃₁	—	2	8	no	—
245	C₂×C₄×C₃₁	—	2	8	no	—
246	C₂×C₄×C₃₁	—	2	2	no	—
247	C₂×C₄×C₃₁	—	2	2	no	—
248	C₂×C₄×C₃₁	—	2	2	no	—
249	C₂×C₄×C₃₁	—	2	2	no	—
250	C₂×C₄×C₃₁	—	2	4	no	—
251	C₂×C₄×C₃₁	—	2	8	no	—
252	C₂×C₄×C₃₁	—	2	4	no	—
253	C₂×C₄×C₃₁	—	2	16	no	—
254	C₂×C₄×C₃₁	—	2	16	no	—
255	C₂×C₄×C₃₁	—	2	16	no	—
256	C₂×C₄×C₃₁	—	2	2	no	—
257	C₂×C₄×C₃₁	—	2	2	no	—
258	C₂×C₄×C₃₁	—	2	4	no	—
259	C₂×C₄×C₃₁	—	2	4	no	—
260	C₂×C₄×C₃₁	—	2	4	no	—
261	C₂×C₄×C₃₁	—	2	4	no	—
262	C₂×C₄×C₃₁	—	2	8	no	—
263	C₂×C₄×C₃₁	—	2	4	no	—
264	C₂×C₄×C₃₁	—	2	4	no	—
265	C₂×C₄×C₃₁	—	4	8	no	—
266	C₂×C₄×C₃₁	—	4	32	no	—
267	C₂×C₄×C₃₁	—	4	8	no	—
268	C₂×C₄×C₃₁	—	8	8	no	—
269	C₂×C₄×C₃₁	C₄×D₄	1	16	yes	complemented
270	C₂×C₄×C₃₁	C₂³×C₄	1	8	yes	—
271	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
272	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
273	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
274	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
275	C₂×C₄×C₃₁	C₂²×D₄	1	8	yes	—
276	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
277	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
278	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
279	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
280	C₂×#525	C₂×C₃₁	1	1	yes	characteristic
281	C₂×#520	C₂×C₃₁	1	1	yes	characteristic, complemented
282	C₂³×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
283	#2361	C₂×C₃₁	1	4	yes	complemented
284	#2360	C₂×C₃₁	1	4	yes	complemented
285	#2352	C₂×C₃₁	1	4	yes	complemented
286	D₄×C₄⋊C₄	C₂×C₃₁	1	4	yes	complemented
287	#2322	C₂×C₃₁	1	4	yes	complemented
288	#2317	C₂×C₃₁	1	1	yes	characteristic, complemented
289	#2311	C₂×C₃₁	1	1	yes	characteristic, complemented
290	C₄×#120	C₂×C₃₁	1	4	yes	complemented
291	#2280	C₂×C₃₁	1	1	yes	characteristic, complemented
292	#2274	C₂×C₃₁	1	1	yes	characteristic, complemented
293	C₂²×C₃₁	—	2	32	no	—
294	C₂²×C₃₁	—	2	4	no	—
295	C₂²×C₃₁	—	2	4	no	—
296	C₂²×C₃₁	—	2	4	no	—
297	C₂²×C₃₁	—	2	2	no	—
298	C₂²×C₃₁	—	2	4	no	—
299	C₂²×C₃₁	—	2	2	no	—
300	C₂²×C₃₁	—	2	4	no	—
301	C₂²×C₃₁	—	2	4	no	—
302	C₂²×C₃₁	—	2	4	no	—
303	C₂²×C₃₁	—	2	4	no	—
304	C₂²×C₃₁	—	2	4	no	—
305	C₂²×C₃₁	—	2	8	no	—
306	C₂²×C₃₁	—	4	2	no	—
307	C₂²×C₃₁	—	4	2	no	—
308	C₂²×C₃₁	—	4	4	no	—
309	C₂²×C₃₁	C₂×C₄×D₄	1	4	yes	—
310	C₂²×C₃₁	#520	1	8	yes	complemented
311	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
312	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
313	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
314	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
315	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
316	C₄×C₃₁	—	2	4	no	—
317	C₄×C₃₁	—	2	4	no	—
318	C₄×C₃₁	—	2	8	no	—
319	C₄×C₃₁	—	2	8	no	—
320	C₄×C₃₁	—	4	4	no	—
321	C₄×C₃₁	—	4	2	no	—
322	C₄×C₃₁	—	4	2	no	—
323	C₄×C₃₁	—	4	4	no	—
324	C₄×C₃₁	C₂×C₄×D₄	1	4	yes	—
325	C₄×C₃₁	C₂×C₄×D₄	1	4	yes	—
326	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
327	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
328	C₂⁴×C₄	C₂²×C₃₁	1	2	yes	—
329	#525	C₄×C₃₁	1	16	yes	complemented
330	C₂×#123	C₂²×C₃₁	1	2	yes	—
331	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
332	C₂×#121	C₂²×C₃₁	1	2	yes	—
333	C₂×#120	C₂²×C₃₁	1	2	yes	—
334	#520	—	2	8	no	—
335	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
336	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
337	C₂×C₄×D₄	C₂²×C₃₁	1	8	yes	—
338	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
339	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
340	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
341	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
342	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
343	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
344	C₂²×C₄⋊C₄	—	2	8	no	—
345	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
346	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
347	C₂²×C₄⋊C₄	C₂²×C₃₁	1	4	yes	—
348	C₂²×C₄⋊C₄	C₂²×C₃₁	1	4	yes	—
349	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
350	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
351	#391	C₂²×C₃₁	1	2	yes	complemented
352	#390	C₂²×C₃₁	1	2	yes	complemented
353	#389	C₂²×C₃₁	1	4	yes	complemented
354	#389	C₂²×C₃₁	1	8	yes	complemented
355	#388	C₂²×C₃₁	1	8	yes	complemented
356	#387	C₂²×C₃₁	1	8	yes	complemented
357	#386	C₂²×C₃₁	1	4	yes	—
358	#386	C₂²×C₃₁	1	8	yes	—
359	#385	C₂²×C₃₁	1	4	yes	—
360	#385	C₂²×C₃₁	1	8	yes	—
361	#385	C₂²×C₃₁	1	8	yes	complemented
362	#384	C₂²×C₃₁	1	2	yes	complemented
363	#382	C₂²×C₃₁	1	2	yes	complemented
364	#381	C₂²×C₃₁	1	2	yes	—
365	#380	C₂²×C₃₁	1	2	yes	—
366	#380	C₂²×C₃₁	1	2	yes	—
367	#380	C₂²×C₃₁	1	4	yes	complemented
368	#379	C₂²×C₃₁	1	2	yes	—
369	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	complemented
370	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	complemented
371	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
372	C₄×C₂²⋊C₄	C₂²×C₃₁	1	8	yes	—
373	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
374	C₂×C₃₁	—	2	4	no	—
375	C₂×C₃₁	—	2	8	no	—
376	C₂×C₃₁	—	4	4	no	—
377	C₂×C₃₁	C₂²×C₄×D₄	1	1	yes	characteristic
378	C₂×C₃₁	C₂×#520	1	2	yes	—
379	C₂×C₃₁	#3484	1	1	yes	characteristic
380	C₂×C₃₁	#3486	1	1	yes	characteristic
381	C₂×C₃₁	#3492	1	2	yes	—
382	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
383	C₂×#41	—	2	4	no	—
384	C₂×#41	—	2	4	no	—
385	C₂×#41	C₂×C₄×C₃₁	1	8	yes	complemented
386	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
387	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
388	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
389	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
390	C₂³×C₄	—	2	4	no	—
391	C₂³×C₄	—	2	4	no	—
392	C₂³×C₄	—	2	8	no	—
393	C₂³×C₄	—	4	8	no	—
394	C₂³×C₄	C₂×C₄×C₃₁	1	8	yes	complemented
395	C₂³×C₄	C₂³×C₃₁	1	8	yes	—
396	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
397	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
398	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
399	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
400	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
401	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
402	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
403	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
404	#123	C₂×C₄×C₃₁	1	16	yes	complemented
405	C₂²⋊Q₈	C₂×C₄×C₃₁	1	16	yes	complemented
406	#121	C₂×C₄×C₃₁	1	16	yes	complemented
407	#120	C₂×C₄×C₃₁	1	16	yes	complemented
408	C₄×Q₈	—	2	8	no	—
409	C₄×D₄	—	2	16	no	—
410	C₄×D₄	—	2	8	no	—
411	C₄×D₄	—	4	16	no	—
412	C₄×D₄	C₂×C₄×C₃₁	1	32	yes	complemented
413	#117	—	2	4	no	—
414	#117	—	2	4	no	—
415	#117	—	2	8	no	—
416	#117	C₂×C₄×C₃₁	1	8	yes	complemented
417	C₂×C₄⋊C₄	—	2	8	no	—
418	C₂×C₄⋊C₄	—	2	4	no	—
419	C₂×C₄⋊C₄	—	2	16	no	—
420	C₂×C₄⋊C₄	—	2	16	no	—
421	C₂×C₄⋊C₄	—	2	8	no	—
422	C₂×C₄⋊C₄	D₄×C₃₁	1	8	yes	complemented
423	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
424	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
425	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
426	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
428	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
430	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
431	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
432	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
433	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
434	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
443	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
444	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
445	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
446	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
447	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
448	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
449	#95	C₂³×C₃₁	1	8	yes	—
450	#95	C₂³×C₃₁	1	4	yes	—
451	#95	C₂³×C₃₁	1	4	yes	—
452	#95	C₂³×C₃₁	1	8	yes	—
453	#95	C₂³×C₃₁	1	8	yes	—
454	C₃₁	#34200	1	1	yes	characteristic, direct product factor, Sylow
455	C₂⁴	—	2	2	no	—
456	C₂⁴	—	2	2	no	—
457	C₂⁴	—	2	4	no	—
458	C₂⁴	—	2	4	no	—
459	C₂⁴	C₂²×C₄×C₃₁	1	4	yes	—
460	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
461	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
462	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
463	#41	—	2	32	no	—
464	C₂×Q₈	—	2	2	no	—
465	C₂×Q₈	—	2	2	no	—
466	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	complemented
467	C₂×D₄	—	2	4	no	—
468	C₂×D₄	—	2	4	no	—
469	C₂×D₄	—	2	8	no	—
470	C₂×D₄	—	2	8	no	—
471	C₂×D₄	—	2	2	no	—
472	C₂×D₄	—	2	2	no	—
473	C₂×D₄	C₂²×C₄×C₃₁	1	16	yes	—
474	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
475	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	complemented
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	32	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	4	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	4	no	—
486	C₂²×C₄	—	2	16	no	—
487	C₂²×C₄	—	2	16	no	—
488	C₂²×C₄	—	2	8	no	—
489	C₂²×C₄	—	4	4	no	—
490	C₂²×C₄	—	4	8	no	—
491	C₂²×C₄	—	4	4	no	—
492	C₂²×C₄	—	4	8	no	—
493	C₂²×C₄	—	4	32	no	—
494	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
495	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
496	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
497	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
498	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	complemented
499	C₂²×C₄	C₂×D₄×C₃₁	1	8	yes	—
500	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
501	C₂²×C₄	#41×C₃₁	1	4	yes	—
502	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
503	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
504	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
505	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
506	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
507	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
508	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
509	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
510	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
511	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
512	C₄⋊C₄	—	2	16	no	—
513	C₄⋊C₄	—	2	4	no	—
514	C₄⋊C₄	—	2	4	no	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	2	8	no	—
517	C₄⋊C₄	—	2	2	no	—
518	C₄⋊C₄	—	2	4	no	—
519	C₄⋊C₄	—	4	8	no	—
520	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	complemented
521	C₄⋊C₄	C₂²×C₄×C₃₁	1	16	yes	complemented
522	C₄⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
523	C₄⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
524	C₂²⋊C₄	—	2	4	no	—
525	C₂²⋊C₄	—	2	4	no	—
526	C₂²⋊C₄	—	2	8	no	—
527	C₂²⋊C₄	—	2	8	no	—
528	C₂²⋊C₄	—	2	8	no	—
529	C₂²⋊C₄	—	4	8	no	—
530	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
531	C₂²⋊C₄	C₂²×C₄×C₃₁	1	16	yes	—
532	C₂²⋊C₄	C₂²×C₄×C₃₁	1	16	yes	complemented
533	C₄²	—	2	8	no	—
534	C₄²	—	2	4	no	—
535	C₄²	—	2	4	no	—
536	C₄²	—	4	8	no	—
537	C₄²	C₂²×C₄×C₃₁	1	8	yes	complemented
538	C₂³	—	2	8	no	—
539	C₂³	—	2	8	no	—
540	C₂³	—	2	16	no	—
541	C₂³	—	2	8	no	—
542	C₂³	—	2	16	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	2	2	no	—
547	C₂³	—	2	2	no	—
548	C₂³	—	2	2	no	—
549	C₂³	—	2	2	no	—
550	C₂³	—	2	2	no	—
551	C₂³	—	2	4	no	—
552	C₂³	—	2	4	no	—
553	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
554	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
555	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
556	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
557	C₂³	C₂×#41×C₃₁	1	2	yes	—
558	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
559	C₂³	C₃₁×2₋¹⁺⁴	1	4	yes	—
560	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
561	Q₈	—	2	8	no	—
562	D₄	—	2	16	no	—
563	D₄	—	2	32	no	—
564	D₄	—	2	8	no	—
565	C₂×C₄	—	2	8	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	8	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	16	no	—
574	C₂×C₄	—	2	16	no	—
575	C₂×C₄	—	2	16	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	8	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	4	8	no	—
586	C₂×C₄	—	4	32	no	—
587	C₂×C₄	—	4	8	no	—
588	C₂×C₄	—	8	8	no	—
589	C₂×C₄	C₄×D₄×C₃₁	1	16	yes	complemented
590	C₂×C₄	C₂³×C₄×C₃₁	1	8	yes	—
591	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
592	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
593	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
594	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
595	C₂×C₄	C₂²×D₄×C₃₁	1	8	yes	—
596	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
597	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
598	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
599	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
600	C₂²	—	2	32	no	—
601	C₂²	—	2	4	no	—
602	C₂²	—	2	4	no	—
603	C₂²	—	2	4	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	2	4	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	4	no	—
608	C₂²	—	2	4	no	—
609	C₂²	—	2	4	no	—
610	C₂²	—	2	4	no	—
611	C₂²	—	2	4	no	—
612	C₂²	—	2	8	no	—
613	C₂²	—	4	2	no	—
614	C₂²	—	4	2	no	—
615	C₂²	—	4	4	no	—
616	C₂²	C₂×C₄×D₄×C₃₁	1	4	yes	—
617	C₂²	C₃₁×#520	1	8	yes	complemented
618	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
619	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
620	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
621	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
622	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
623	C₄	—	2	4	no	—
624	C₄	—	2	4	no	—
625	C₄	—	2	8	no	—
626	C₄	—	2	8	no	—
627	C₄	—	4	4	no	—
628	C₄	—	4	2	no	—
629	C₄	—	4	2	no	—
630	C₄	—	4	4	no	—
631	C₄	C₂×C₄×D₄×C₃₁	1	4	yes	—
632	C₄	C₂×C₄×D₄×C₃₁	1	4	yes	—
633	C₂	—	2	4	no	—
634	C₂	—	2	8	no	—
635	C₂	—	4	4	no	—
636	C₂	C₂²×C₄×D₄×C₃₁	1	1	yes	characteristic
637	C₂	C₂×C₃₁×#520	1	2	yes	—
638	C₂	C₃₁×#3484	1	1	yes	characteristic
639	C₂	C₃₁×#3486	1	1	yes	characteristic
640	C₂	C₃₁×#3492	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#525	C₂
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. C₂×C₃₁×#520	C₂	semidirect
3. C₂³×C₄⋊C₄×C₃₁	C₂	semidirect
4. C₃₁×#2361	C₂	semidirect
5. C₃₁×#2360	C₂	semidirect
6. C₃₁×#2352	C₂	semidirect
7. D₄×C₄⋊C₄×C₃₁	C₂	semidirect
8. C₃₁×#2322	C₂	semidirect
9. C₃₁×#2317	C₂	semidirect
10. C₃₁×#2311	C₂	semidirect
11. C₄×C₃₁×#120	C₂	semidirect
12. C₃₁×#2280	C₂	semidirect
13. C₃₁×#2274	C₂	semidirect
17. C₃₁×#525	C₄	semidirect
23. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
27. C₂×C₄×D₄×C₃₁	C₂²	semidirect
31. C₂×C₃₁×#117	C₂²	semidirect
38. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
39. C₃₁×#391	C₂²	semidirect
40. C₃₁×#390	C₂²	semidirect
41. C₃₁×#389	C₂²	semidirect
42. C₃₁×#389	C₂²	semidirect
43. C₃₁×#388	C₂²	semidirect
44. C₃₁×#387	C₂²	semidirect
49. C₃₁×#385	C₂²	semidirect
50. C₃₁×#384	C₂²	semidirect
51. C₃₁×#382	C₂²	semidirect
55. C₃₁×#380	C₂²	semidirect
57. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
58. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
65. C₂×#41×C₃₁	C₂×C₄	semidirect
74. C₂³×C₄×C₃₁	C₂×C₄	semidirect
84. C₃₁×#123	C₂×C₄	semidirect
85. C₃₁×C₂²⋊Q₈	C₂×C₄	semidirect
86. C₃₁×#121	C₂×C₄	semidirect
87. C₃₁×#120	C₂×C₄	semidirect
92. C₄×D₄×C₃₁	C₂×C₄	semidirect
96. C₃₁×#117	C₂×C₄	semidirect
102. C₂×C₄⋊C₄×C₃₁	D₄	semidirect
145. C₂×Q₈×C₃₁	C₂²×C₄	semidirect
154. C₂×D₄×C₃₁	C₂²×C₄	semidirect
177. C₂²×C₄×C₃₁	C₂²×C₄	semidirect
199. C₄⋊C₄×C₃₁	C₂²×C₄	semidirect
200. C₄⋊C₄×C₃₁	C₂²×C₄	semidirect
211. C₂²⋊C₄×C₃₁	C₂²×C₄	semidirect
216. C₄²×C₃₁	C₂²×C₄	semidirect
217. #34200	C₃₁	direct (N × H)
269. C₂×C₄×C₃₁	C₄×D₄	semidirect
281. C₂×#520	C₂×C₃₁	semidirect
282. C₂³×C₄⋊C₄	C₂×C₃₁	semidirect
283. #2361	C₂×C₃₁	semidirect
284. #2360	C₂×C₃₁	semidirect
285. #2352	C₂×C₃₁	semidirect
286. D₄×C₄⋊C₄	C₂×C₃₁	semidirect
287. #2322	C₂×C₃₁	semidirect
288. #2317	C₂×C₃₁	semidirect
289. #2311	C₂×C₃₁	semidirect
290. C₄×#120	C₂×C₃₁	semidirect
291. #2280	C₂×C₃₁	semidirect
292. #2274	C₂×C₃₁	semidirect
310. C₂²×C₃₁	#520	semidirect
329. #525	C₄×C₃₁	semidirect
335. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
339. C₂×C₄×D₄	C₂²×C₃₁	semidirect
343. C₂×#117	C₂²×C₃₁	semidirect
350. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
351. #391	C₂²×C₃₁	semidirect
352. #390	C₂²×C₃₁	semidirect
353. #389	C₂²×C₃₁	semidirect
354. #389	C₂²×C₃₁	semidirect
355. #388	C₂²×C₃₁	semidirect
356. #387	C₂²×C₃₁	semidirect
361. #385	C₂²×C₃₁	semidirect
362. #384	C₂²×C₃₁	semidirect
363. #382	C₂²×C₃₁	semidirect
367. #380	C₂²×C₃₁	semidirect
369. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
370. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
385. C₂×#41	C₂×C₄×C₃₁	semidirect
394. C₂³×C₄	C₂×C₄×C₃₁	semidirect
404. #123	C₂×C₄×C₃₁	semidirect
405. C₂²⋊Q₈	C₂×C₄×C₃₁	semidirect
406. #121	C₂×C₄×C₃₁	semidirect
407. #120	C₂×C₄×C₃₁	semidirect
412. C₄×D₄	C₂×C₄×C₃₁	semidirect
416. #117	C₂×C₄×C₃₁	semidirect
422. C₂×C₄⋊C₄	D₄×C₃₁	semidirect
454. C₃₁	#34200	direct (N × H)
466. C₂×Q₈	C₂²×C₄×C₃₁	semidirect
475. C₂×D₄	C₂²×C₄×C₃₁	semidirect
498. C₂²×C₄	C₂²×C₄×C₃₁	semidirect
520. C₄⋊C₄	C₂²×C₄×C₃₁	semidirect
521. C₄⋊C₄	C₂²×C₄×C₃₁	semidirect
532. C₂²⋊C₄	C₂²×C₄×C₃₁	semidirect
537. C₄²	C₂²×C₄×C₃₁	semidirect
589. C₂×C₄	C₄×D₄×C₃₁	semidirect
617. C₂²	C₃₁×#520	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃₁×#525	2
C₂×C₃₁×#520	2
C₂³×C₄⋊C₄×C₃₁	2
C₃₁×#2361	2
C₃₁×#2360	2
C₃₁×#2352	2
D₄×C₄⋊C₄×C₃₁	2
C₃₁×#2322	2
C₃₁×#2317	2
C₃₁×#2311	2
C₄×C₃₁×#120	2
C₃₁×#2280	2
C₃₁×#2274	2
#34200	31

Subgroups — C31×#34200 #21490959

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34200 #21490959