Subgroups — C₂×C₃₁×#2412 #21491416

Order 7936.

5162 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×#123	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃₁×#120	C₂	1	1	yes	maximal, characteristic
3	C₂³×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2412	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₃₁×#397	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₁×#394	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₁×#386	C₂	1	2	yes	maximal, complemented
9	C₂×C₃₁×#386	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₁×#385	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃₁×#381	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#380	C₂	1	2	yes	maximal, complemented
13	C₂⁶×C₃₁	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₃₁	C₂²	1	2	yes	—
19	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
20	C₂×C₃₁×#123	—	2	8	no	—
21	C₂×C₃₁×#123	C₂²	1	8	yes	complemented
22	C₂×C₃₁×#120	—	2	8	no	—
23	C₂×C₃₁×#120	C₂²	1	8	yes	—
24	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
25	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
26	C₂²×C₂²⋊C₄×C₃₁	—	2	8	no	—
27	C₂²×C₂²⋊C₄×C₃₁	—	2	8	no	—
28	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
30	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
32	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
35	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	8	yes	complemented
37	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	8	yes	complemented
38	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
39	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
40	C₃₁×#397	C₂²	1	16	yes	complemented
41	C₃₁×#394	C₂²	1	16	yes	complemented
42	C₃₁×#386	C₂²	1	8	yes	complemented
43	C₃₁×#386	C₂²	1	16	yes	complemented
44	C₃₁×#385	C₂²	1	8	yes	complemented
45	C₃₁×#381	C₂²	1	8	yes	complemented
46	C₃₁×#380	C₂²	1	16	yes	complemented
47	C₂×C₃₁×#95	C₂²	1	2	yes	complemented
48	C₂×C₃₁×#95	C₂²	1	2	yes	complemented
49	C₂×C₃₁×#95	C₂²	1	2	yes	complemented
50	C₂×C₃₁×#95	C₂²	1	2	yes	complemented
51	C₂⁵×C₃₁	—	2	4	no	—
52	C₂⁵×C₃₁	—	2	4	no	—
53	C₂⁵×C₃₁	—	2	8	no	—
54	C₂⁵×C₃₁	—	4	4	no	—
55	C₂⁵×C₃₁	D₄	1	8	yes	—
56	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
57	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
58	C₂⁵×C₃₁	C₂³	1	4	yes	—
59	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
60	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₃₁	—	2	4	no	—
62	C₂²×D₄×C₃₁	—	2	4	no	—
63	C₂²×D₄×C₃₁	—	2	4	no	—
64	C₂²×D₄×C₃₁	—	2	4	no	—
65	C₂²×D₄×C₃₁	—	2	4	no	—
66	C₂²×D₄×C₃₁	—	2	8	no	—
67	C₂²×D₄×C₃₁	—	4	4	no	—
68	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
69	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
70	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
71	C₂³×C₄×C₃₁	—	2	4	no	—
72	C₂³×C₄×C₃₁	—	2	4	no	—
73	C₂³×C₄×C₃₁	—	2	4	no	—
74	C₂³×C₄×C₃₁	—	2	8	no	—
75	C₂³×C₄×C₃₁	—	2	4	no	—
76	C₂³×C₄×C₃₁	—	2	8	no	—
77	C₂³×C₄×C₃₁	—	4	4	no	—
78	C₂³×C₄×C₃₁	—	4	4	no	—
79	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
80	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
81	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
82	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
83	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₃₁	C₂³	1	8	yes	—
87	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
88	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
89	C₃₁×#123	—	2	32	no	—
90	C₃₁×#120	—	2	32	no	—
91	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
92	C₂×C₄⋊C₄×C₃₁	—	4	4	no	—
93	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	complemented
94	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	complemented
95	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
96	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
97	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
98	C₂×C₂²⋊C₄×C₃₁	—	2	32	no	—
99	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
100	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
101	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
102	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
103	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
104	C₂×C₂²⋊C₄×C₃₁	—	2	32	no	—
105	C₂×C₂²⋊C₄×C₃₁	—	4	4	no	—
106	C₂×C₂²⋊C₄×C₃₁	D₄	1	8	yes	complemented
107	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
108	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
109	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
110	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
111	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
112	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
113	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
114	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
115	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	complemented
116	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	complemented
117	C₃₁×#95	C₂³	1	8	yes	complemented
118	C₃₁×#95	C₂³	1	8	yes	complemented
119	C₃₁×#95	C₂³	1	8	yes	complemented
120	C₃₁×#95	C₂³	1	8	yes	complemented
121	C₂⁴×C₃₁	—	2	2	no	—
122	C₂⁴×C₃₁	—	2	2	no	—
123	C₂⁴×C₃₁	—	2	4	no	—
124	C₂⁴×C₃₁	—	2	4	no	—
125	C₂⁴×C₃₁	—	2	4	no	—
126	C₂⁴×C₃₁	—	2	32	no	—
127	C₂⁴×C₃₁	—	2	32	no	—
128	C₂⁴×C₃₁	—	2	8	no	—
129	C₂⁴×C₃₁	—	2	2	no	—
130	C₂⁴×C₃₁	—	2	8	no	—
131	C₂⁴×C₃₁	—	2	16	no	—
132	C₂⁴×C₃₁	—	2	2	no	—
133	C₂⁴×C₃₁	—	2	4	no	—
134	C₂⁴×C₃₁	—	2	4	no	—
135	C₂⁴×C₃₁	—	2	2	no	—
136	C₂⁴×C₃₁	—	2	2	no	—
137	C₂⁴×C₃₁	—	2	2	no	—
138	C₂⁴×C₃₁	—	2	4	no	—
139	C₂⁴×C₃₁	—	2	4	no	—
140	C₂⁴×C₃₁	—	4	16	no	—
141	C₂⁴×C₃₁	—	4	8	no	—
142	C₂⁴×C₃₁	—	4	32	no	—
143	C₂⁴×C₃₁	—	4	32	no	—
144	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
145	C₂⁴×C₃₁	C₂×D₄	1	16	yes	—
146	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
147	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
148	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
149	C₂⁴×C₃₁	#41	1	4	yes	—
150	C₂⁴×C₃₁	#41	1	8	yes	—
151	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
152	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
153	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
154	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
155	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
156	C₂×D₄×C₃₁	—	2	8	no	—
157	C₂×D₄×C₃₁	—	2	8	no	—
158	C₂×D₄×C₃₁	—	2	8	no	—
159	C₂×D₄×C₃₁	—	2	8	no	—
160	C₂×D₄×C₃₁	—	2	8	no	—
161	C₂×D₄×C₃₁	—	2	16	no	—
162	C₂×D₄×C₃₁	—	4	8	no	—
163	C₂×D₄×C₃₁	—	4	16	no	—
164	C₂×D₄×C₃₁	—	4	16	no	—
165	C₂×D₄×C₃₁	—	4	16	no	—
166	C₂²×C₄×C₃₁	—	2	4	no	—
167	C₂²×C₄×C₃₁	—	2	4	no	—
168	C₂²×C₄×C₃₁	—	2	8	no	—
169	C₂²×C₄×C₃₁	—	2	8	no	—
170	C₂²×C₄×C₃₁	—	2	4	no	—
171	C₂²×C₄×C₃₁	—	2	4	no	—
172	C₂²×C₄×C₃₁	—	2	4	no	—
173	C₂²×C₄×C₃₁	—	2	2	no	—
174	C₂²×C₄×C₃₁	—	2	2	no	—
175	C₂²×C₄×C₃₁	—	2	2	no	—
176	C₂²×C₄×C₃₁	—	2	4	no	—
177	C₂²×C₄×C₃₁	—	2	2	no	—
178	C₂²×C₄×C₃₁	—	2	8	no	—
179	C₂²×C₄×C₃₁	—	2	16	no	—
180	C₂²×C₄×C₃₁	—	2	8	no	—
181	C₂²×C₄×C₃₁	—	2	4	no	—
182	C₂²×C₄×C₃₁	—	2	4	no	—
183	C₂²×C₄×C₃₁	—	2	2	no	—
184	C₂²×C₄×C₃₁	—	2	4	no	—
185	C₂²×C₄×C₃₁	—	2	4	no	—
186	C₂²×C₄×C₃₁	—	2	4	no	—
187	C₂²×C₄×C₃₁	—	2	4	no	—
188	C₂²×C₄×C₃₁	—	2	4	no	—
189	C₂²×C₄×C₃₁	—	2	16	no	—
190	C₂²×C₄×C₃₁	—	4	8	no	—
191	C₂²×C₄×C₃₁	—	4	8	no	—
192	C₂²×C₄×C₃₁	—	4	32	no	—
193	C₂²×C₄×C₃₁	—	4	16	no	—
194	C₂²×C₄×C₃₁	—	4	16	no	—
195	C₂²×C₄×C₃₁	C₂×D₄	1	8	yes	—
196	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
198	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
199	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
203	C₄⋊C₄×C₃₁	—	2	16	no	—
204	C₄⋊C₄×C₃₁	—	4	8	no	—
205	C₂²⋊C₄×C₃₁	—	2	16	no	—
206	C₂²⋊C₄×C₃₁	—	2	8	no	—
207	C₂²⋊C₄×C₃₁	—	2	16	no	—
208	C₂²⋊C₄×C₃₁	—	2	8	no	—
209	C₂²⋊C₄×C₃₁	—	2	8	no	—
210	C₂²⋊C₄×C₃₁	—	2	8	no	—
211	C₂²⋊C₄×C₃₁	—	2	16	no	—
212	C₂²⋊C₄×C₃₁	—	2	16	no	—
213	C₂²⋊C₄×C₃₁	—	4	8	no	—
214	C₂²⋊C₄×C₃₁	C₂×D₄	1	16	yes	complemented
215	C₂×#2412	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂³×C₃₁	—	2	8	no	—
217	C₂³×C₃₁	—	2	8	no	—
218	C₂³×C₃₁	—	2	8	no	—
219	C₂³×C₃₁	—	2	8	no	—
220	C₂³×C₃₁	—	2	16	no	—
221	C₂³×C₃₁	—	2	16	no	—
222	C₂³×C₃₁	—	2	16	no	—
223	C₂³×C₃₁	—	2	16	no	—
224	C₂³×C₃₁	—	2	2	no	—
225	C₂³×C₃₁	—	2	2	no	—
226	C₂³×C₃₁	—	2	4	no	—
227	C₂³×C₃₁	—	2	4	no	—
228	C₂³×C₃₁	—	2	4	no	—
229	C₂³×C₃₁	—	2	32	no	—
230	C₂³×C₃₁	—	2	8	no	—
231	C₂³×C₃₁	—	2	8	no	—
232	C₂³×C₃₁	—	2	32	no	—
233	C₂³×C₃₁	—	2	8	no	—
234	C₂³×C₃₁	—	2	2	no	—
235	C₂³×C₃₁	—	2	2	no	—
236	C₂³×C₃₁	—	2	4	no	—
237	C₂³×C₃₁	—	2	4	no	—
238	C₂³×C₃₁	—	2	2	no	—
239	C₂³×C₃₁	—	2	2	no	—
240	C₂³×C₃₁	—	2	2	no	—
241	C₂³×C₃₁	—	2	4	no	—
242	C₂³×C₃₁	—	2	4	no	—
243	C₂³×C₃₁	—	4	16	no	—
244	C₂³×C₃₁	—	4	128	no	—
245	C₂³×C₃₁	—	4	32	no	—
246	C₂³×C₃₁	—	4	32	no	—
247	C₂³×C₃₁	—	4	8	no	—
248	C₂³×C₃₁	—	4	8	no	—
249	C₂³×C₃₁	—	4	4	no	—
250	C₂³×C₃₁	—	4	4	no	—
251	C₂³×C₃₁	—	4	4	no	—
252	C₂³×C₃₁	—	4	8	no	—
253	C₂³×C₃₁	—	4	8	no	—
254	C₂³×C₃₁	#121	1	16	yes	—
255	C₂³×C₃₁	#123	1	16	yes	complemented
256	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
257	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
258	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
259	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
260	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
261	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
262	C₂³×C₃₁	C₂×#41	1	4	yes	—
263	C₂³×C₃₁	C₂×#41	1	8	yes	—
264	C₂³×C₃₁	C₂×#41	1	2	yes	—
265	C₂³×C₃₁	C₂×#41	1	4	yes	—
266	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
267	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
268	D₄×C₃₁	—	4	16	no	—
269	D₄×C₃₁	—	4	16	no	—
270	D₄×C₃₁	—	4	16	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	2	no	—
278	C₂×C₄×C₃₁	—	2	2	no	—
279	C₂×C₄×C₃₁	—	2	2	no	—
280	C₂×C₄×C₃₁	—	2	4	no	—
281	C₂×C₄×C₃₁	—	2	2	no	—
282	C₂×C₄×C₃₁	—	2	4	no	—
283	C₂×C₄×C₃₁	—	2	4	no	—
284	C₂×C₄×C₃₁	—	2	2	no	—
285	C₂×C₄×C₃₁	—	2	4	no	—
286	C₂×C₄×C₃₁	—	2	4	no	—
287	C₂×C₄×C₃₁	—	2	4	no	—
288	C₂×C₄×C₃₁	—	2	4	no	—
289	C₂×C₄×C₃₁	—	2	4	no	—
290	C₂×C₄×C₃₁	—	4	32	no	—
291	C₂×C₄×C₃₁	—	4	16	no	—
292	C₂×C₄×C₃₁	—	4	16	no	—
293	C₂×C₄×C₃₁	—	4	8	no	—
294	C₂×C₄×C₃₁	—	4	4	no	—
295	C₂×C₄×C₃₁	—	4	4	no	—
296	C₂×C₄×C₃₁	—	4	8	no	—
297	C₂×C₄×C₃₁	—	4	4	no	—
298	C₂×C₄×C₃₁	—	4	8	no	—
299	C₂×C₄×C₃₁	C₂²×D₄	1	8	yes	—
300	C₂²×#123	C₂×C₃₁	1	1	yes	characteristic, complemented
301	C₂²×#120	C₂×C₃₁	1	1	yes	characteristic
302	C₂³×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
303	C₂³×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
304	#2412	C₂×C₃₁	1	16	yes	direct product factor
305	C₂×#397	C₂×C₃₁	1	2	yes	complemented
306	C₂×#394	C₂×C₃₁	1	2	yes	complemented
307	C₂×#386	C₂×C₃₁	1	2	yes	complemented
308	C₂×#386	C₂×C₃₁	1	1	yes	characteristic, complemented
309	C₂×#385	C₂×C₃₁	1	1	yes	characteristic, complemented
310	C₂×#381	C₂×C₃₁	1	1	yes	characteristic, complemented
311	C₂×#380	C₂×C₃₁	1	2	yes	complemented
312	C₂²×C₃₁	—	2	4	no	—
313	C₂²×C₃₁	—	2	4	no	—
314	C₂²×C₃₁	—	2	32	no	—
315	C₂²×C₃₁	—	2	32	no	—
316	C₂²×C₃₁	—	2	4	no	—
317	C₂²×C₃₁	—	2	4	no	—
318	C₂²×C₃₁	—	2	8	no	—
319	C₂²×C₃₁	—	2	8	no	—
320	C₂²×C₃₁	—	2	8	no	—
321	C₂²×C₃₁	—	2	8	no	—
322	C₂²×C₃₁	—	2	4	no	—
323	C₂²×C₃₁	—	2	4	no	—
324	C₂²×C₃₁	—	2	4	no	—
325	C₂²×C₃₁	—	4	64	no	—
326	C₂²×C₃₁	—	4	16	no	—
327	C₂²×C₃₁	—	4	4	no	—
328	C₂²×C₃₁	—	4	4	no	—
329	C₂²×C₃₁	—	4	2	no	—
330	C₂²×C₃₁	—	4	2	no	—
331	C₂²×C₃₁	—	4	2	no	—
332	C₂²×C₃₁	—	4	4	no	—
333	C₂²×C₃₁	—	4	4	no	—
334	C₂²×C₃₁	—	8	8	no	—
335	C₂²×C₃₁	C₂×#121	1	8	yes	—
336	C₂²×C₃₁	C₂×#121	1	4	yes	—
337	C₂²×C₃₁	C₂×#123	1	4	yes	—
338	C₂²×C₃₁	C₂×#123	1	8	yes	complemented
339	C₂²×C₃₁	#534	1	4	yes	—
340	C₂²×C₃₁	#546	1	8	yes	—
341	C₂²×C₃₁	#551	1	8	yes	—
342	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
343	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
344	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
345	C₂²×C₃₁	C₂²×#41	1	2	yes	—
346	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
347	C₄×C₃₁	—	2	8	no	—
348	C₄×C₃₁	—	4	4	no	—
349	C₄×C₃₁	—	4	2	no	—
350	C₄×C₃₁	—	4	2	no	—
351	C₄×C₃₁	—	4	4	no	—
352	C₄×C₃₁	—	4	2	no	—
353	C₄×C₃₁	—	4	4	no	—
354	C₂⁶	C₂²×C₃₁	1	1	yes	characteristic
355	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
356	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
357	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
358	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
359	C₂⁴×C₄	C₂²×C₃₁	1	2	yes	—
360	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
361	C₂×#123	—	2	8	no	—
362	C₂×#123	C₂²×C₃₁	1	8	yes	complemented
363	C₂×#120	—	2	8	no	—
364	C₂×#120	C₂²×C₃₁	1	8	yes	—
365	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
366	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
367	C₂²×C₂²⋊C₄	—	2	8	no	—
368	C₂²×C₂²⋊C₄	—	2	8	no	—
369	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
370	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
371	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
372	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
373	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
374	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
375	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
376	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
377	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	8	yes	complemented
378	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	8	yes	complemented
379	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
380	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
381	#397	C₂²×C₃₁	1	16	yes	complemented
382	#394	C₂²×C₃₁	1	16	yes	complemented
383	#386	C₂²×C₃₁	1	8	yes	complemented
384	#386	C₂²×C₃₁	1	16	yes	complemented
385	#385	C₂²×C₃₁	1	8	yes	complemented
386	#381	C₂²×C₃₁	1	8	yes	complemented
387	#380	C₂²×C₃₁	1	16	yes	complemented
388	C₂×#95	C₂²×C₃₁	1	2	yes	complemented
389	C₂×#95	C₂²×C₃₁	1	2	yes	complemented
390	C₂×#95	C₂²×C₃₁	1	2	yes	complemented
391	C₂×#95	C₂²×C₃₁	1	2	yes	complemented
392	C₂×C₃₁	—	2	8	no	—
393	C₂×C₃₁	—	2	8	no	—
394	C₂×C₃₁	—	4	4	no	—
395	C₂×C₃₁	—	8	2	no	—
396	C₂×C₃₁	#2412	1	8	yes	direct product factor
397	C₂×C₃₁	C₂²×#121	1	1	yes	characteristic
398	C₂×C₃₁	C₂²×#123	1	1	yes	characteristic
399	C₂×C₃₁	C₂×#534	1	1	yes	characteristic
400	C₂×C₃₁	C₂×#546	1	2	yes	—
401	C₂×C₃₁	C₂×#551	1	2	yes	—
402	C₂⁵	—	2	4	no	—
403	C₂⁵	—	2	4	no	—
404	C₂⁵	—	2	8	no	—
405	C₂⁵	—	4	4	no	—
406	C₂⁵	D₄×C₃₁	1	8	yes	—
407	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
408	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
409	C₂⁵	C₂³×C₃₁	1	4	yes	—
410	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
411	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
412	C₂²×D₄	—	2	4	no	—
413	C₂²×D₄	—	2	4	no	—
414	C₂²×D₄	—	2	4	no	—
415	C₂²×D₄	—	2	4	no	—
416	C₂²×D₄	—	2	4	no	—
417	C₂²×D₄	—	2	8	no	—
418	C₂²×D₄	—	4	4	no	—
419	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
420	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
421	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
422	C₂³×C₄	—	2	4	no	—
423	C₂³×C₄	—	2	4	no	—
424	C₂³×C₄	—	2	4	no	—
425	C₂³×C₄	—	2	8	no	—
426	C₂³×C₄	—	2	4	no	—
427	C₂³×C₄	—	2	8	no	—
428	C₂³×C₄	—	4	4	no	—
429	C₂³×C₄	—	4	4	no	—
430	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
431	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
432	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
433	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
434	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
435	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
436	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
437	C₂³×C₄	C₂³×C₃₁	1	8	yes	—
438	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
439	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
440	#123	—	2	32	no	—
441	#120	—	2	32	no	—
442	C₂×C₄⋊C₄	—	2	8	no	—
443	C₂×C₄⋊C₄	—	4	4	no	—
444	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	complemented
445	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	complemented
446	C₂×C₂²⋊C₄	—	2	8	no	—
447	C₂×C₂²⋊C₄	—	2	4	no	—
448	C₂×C₂²⋊C₄	—	2	8	no	—
449	C₂×C₂²⋊C₄	—	2	32	no	—
450	C₂×C₂²⋊C₄	—	2	4	no	—
451	C₂×C₂²⋊C₄	—	2	4	no	—
452	C₂×C₂²⋊C₄	—	2	4	no	—
453	C₂×C₂²⋊C₄	—	2	8	no	—
454	C₂×C₂²⋊C₄	—	2	8	no	—
455	C₂×C₂²⋊C₄	—	2	32	no	—
456	C₂×C₂²⋊C₄	—	4	4	no	—
457	C₂×C₂²⋊C₄	D₄×C₃₁	1	8	yes	complemented
458	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	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	8	yes	complemented
467	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	complemented
468	#95	C₂³×C₃₁	1	8	yes	complemented
469	#95	C₂³×C₃₁	1	8	yes	complemented
470	#95	C₂³×C₃₁	1	8	yes	complemented
471	#95	C₂³×C₃₁	1	8	yes	complemented
472	C₃₁	C₂×#2412	1	1	yes	characteristic, direct product factor, Sylow
473	C₂⁴	—	2	2	no	—
474	C₂⁴	—	2	2	no	—
475	C₂⁴	—	2	4	no	—
476	C₂⁴	—	2	4	no	—
477	C₂⁴	—	2	4	no	—
478	C₂⁴	—	2	32	no	—
479	C₂⁴	—	2	32	no	—
480	C₂⁴	—	2	8	no	—
481	C₂⁴	—	2	2	no	—
482	C₂⁴	—	2	8	no	—
483	C₂⁴	—	2	16	no	—
484	C₂⁴	—	2	2	no	—
485	C₂⁴	—	2	4	no	—
486	C₂⁴	—	2	4	no	—
487	C₂⁴	—	2	2	no	—
488	C₂⁴	—	2	2	no	—
489	C₂⁴	—	2	2	no	—
490	C₂⁴	—	2	4	no	—
491	C₂⁴	—	2	4	no	—
492	C₂⁴	—	4	16	no	—
493	C₂⁴	—	4	8	no	—
494	C₂⁴	—	4	32	no	—
495	C₂⁴	—	4	32	no	—
496	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
497	C₂⁴	C₂×D₄×C₃₁	1	16	yes	—
498	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
499	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
500	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
501	C₂⁴	#41×C₃₁	1	4	yes	—
502	C₂⁴	#41×C₃₁	1	8	yes	—
503	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
504	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
505	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
506	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
507	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
508	C₂×D₄	—	2	8	no	—
509	C₂×D₄	—	2	8	no	—
510	C₂×D₄	—	2	8	no	—
511	C₂×D₄	—	2	8	no	—
512	C₂×D₄	—	2	8	no	—
513	C₂×D₄	—	2	16	no	—
514	C₂×D₄	—	4	8	no	—
515	C₂×D₄	—	4	16	no	—
516	C₂×D₄	—	4	16	no	—
517	C₂×D₄	—	4	16	no	—
518	C₂²×C₄	—	2	4	no	—
519	C₂²×C₄	—	2	4	no	—
520	C₂²×C₄	—	2	8	no	—
521	C₂²×C₄	—	2	8	no	—
522	C₂²×C₄	—	2	4	no	—
523	C₂²×C₄	—	2	4	no	—
524	C₂²×C₄	—	2	4	no	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	4	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	8	no	—
531	C₂²×C₄	—	2	16	no	—
532	C₂²×C₄	—	2	8	no	—
533	C₂²×C₄	—	2	4	no	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	2	no	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	2	4	no	—
539	C₂²×C₄	—	2	4	no	—
540	C₂²×C₄	—	2	4	no	—
541	C₂²×C₄	—	2	16	no	—
542	C₂²×C₄	—	4	8	no	—
543	C₂²×C₄	—	4	8	no	—
544	C₂²×C₄	—	4	32	no	—
545	C₂²×C₄	—	4	16	no	—
546	C₂²×C₄	—	4	16	no	—
547	C₂²×C₄	C₂×D₄×C₃₁	1	8	yes	—
548	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
550	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
551	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
552	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
553	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
554	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
555	C₄⋊C₄	—	2	16	no	—
556	C₄⋊C₄	—	4	8	no	—
557	C₂²⋊C₄	—	2	16	no	—
558	C₂²⋊C₄	—	2	8	no	—
559	C₂²⋊C₄	—	2	16	no	—
560	C₂²⋊C₄	—	2	8	no	—
561	C₂²⋊C₄	—	2	8	no	—
562	C₂²⋊C₄	—	2	8	no	—
563	C₂²⋊C₄	—	2	16	no	—
564	C₂²⋊C₄	—	2	16	no	—
565	C₂²⋊C₄	—	4	8	no	—
566	C₂²⋊C₄	C₂×D₄×C₃₁	1	16	yes	complemented
567	C₂³	—	2	8	no	—
568	C₂³	—	2	8	no	—
569	C₂³	—	2	8	no	—
570	C₂³	—	2	8	no	—
571	C₂³	—	2	16	no	—
572	C₂³	—	2	16	no	—
573	C₂³	—	2	16	no	—
574	C₂³	—	2	16	no	—
575	C₂³	—	2	2	no	—
576	C₂³	—	2	2	no	—
577	C₂³	—	2	4	no	—
578	C₂³	—	2	4	no	—
579	C₂³	—	2	4	no	—
580	C₂³	—	2	32	no	—
581	C₂³	—	2	8	no	—
582	C₂³	—	2	8	no	—
583	C₂³	—	2	32	no	—
584	C₂³	—	2	8	no	—
585	C₂³	—	2	2	no	—
586	C₂³	—	2	2	no	—
587	C₂³	—	2	4	no	—
588	C₂³	—	2	4	no	—
589	C₂³	—	2	2	no	—
590	C₂³	—	2	2	no	—
591	C₂³	—	2	2	no	—
592	C₂³	—	2	4	no	—
593	C₂³	—	2	4	no	—
594	C₂³	—	4	16	no	—
595	C₂³	—	4	128	no	—
596	C₂³	—	4	32	no	—
597	C₂³	—	4	32	no	—
598	C₂³	—	4	8	no	—
599	C₂³	—	4	8	no	—
600	C₂³	—	4	4	no	—
601	C₂³	—	4	4	no	—
602	C₂³	—	4	4	no	—
603	C₂³	—	4	8	no	—
604	C₂³	—	4	8	no	—
605	C₂³	C₃₁×#121	1	16	yes	—
606	C₂³	C₃₁×#123	1	16	yes	complemented
607	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
608	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
609	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
610	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
611	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
612	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
613	C₂³	C₂×#41×C₃₁	1	4	yes	—
614	C₂³	C₂×#41×C₃₁	1	8	yes	—
615	C₂³	C₂×#41×C₃₁	1	2	yes	—
616	C₂³	C₂×#41×C₃₁	1	4	yes	—
617	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
618	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
619	D₄	—	4	16	no	—
620	D₄	—	4	16	no	—
621	D₄	—	4	16	no	—
622	C₂×C₄	—	2	16	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	2	4	no	—
627	C₂×C₄	—	2	4	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	4	no	—
640	C₂×C₄	—	2	4	no	—
641	C₂×C₄	—	4	32	no	—
642	C₂×C₄	—	4	16	no	—
643	C₂×C₄	—	4	16	no	—
644	C₂×C₄	—	4	8	no	—
645	C₂×C₄	—	4	4	no	—
646	C₂×C₄	—	4	4	no	—
647	C₂×C₄	—	4	8	no	—
648	C₂×C₄	—	4	4	no	—
649	C₂×C₄	—	4	8	no	—
650	C₂×C₄	C₂²×D₄×C₃₁	1	8	yes	—
651	C₂²	—	2	4	no	—
652	C₂²	—	2	4	no	—
653	C₂²	—	2	32	no	—
654	C₂²	—	2	32	no	—
655	C₂²	—	2	4	no	—
656	C₂²	—	2	4	no	—
657	C₂²	—	2	8	no	—
658	C₂²	—	2	8	no	—
659	C₂²	—	2	8	no	—
660	C₂²	—	2	8	no	—
661	C₂²	—	2	4	no	—
662	C₂²	—	2	4	no	—
663	C₂²	—	2	4	no	—
664	C₂²	—	4	64	no	—
665	C₂²	—	4	16	no	—
666	C₂²	—	4	4	no	—
667	C₂²	—	4	4	no	—
668	C₂²	—	4	2	no	—
669	C₂²	—	4	2	no	—
670	C₂²	—	4	2	no	—
671	C₂²	—	4	4	no	—
672	C₂²	—	4	4	no	—
673	C₂²	—	8	8	no	—
674	C₂²	C₂×C₃₁×#121	1	8	yes	—
675	C₂²	C₂×C₃₁×#121	1	4	yes	—
676	C₂²	C₂×C₃₁×#123	1	4	yes	—
677	C₂²	C₂×C₃₁×#123	1	8	yes	complemented
678	C₂²	C₃₁×#534	1	4	yes	—
679	C₂²	C₃₁×#546	1	8	yes	—
680	C₂²	C₃₁×#551	1	8	yes	—
681	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
682	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
683	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
684	C₂²	C₂²×#41×C₃₁	1	2	yes	—
685	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
686	C₄	—	2	8	no	—
687	C₄	—	4	4	no	—
688	C₄	—	4	2	no	—
689	C₄	—	4	2	no	—
690	C₄	—	4	4	no	—
691	C₄	—	4	2	no	—
692	C₄	—	4	4	no	—
693	C₂	—	2	8	no	—
694	C₂	—	2	8	no	—
695	C₂	—	4	4	no	—
696	C₂	—	8	2	no	—
697	C₂	C₃₁×#2412	1	8	yes	direct product factor
698	C₂	C₂²×C₃₁×#121	1	1	yes	characteristic
699	C₂	C₂²×C₃₁×#123	1	1	yes	characteristic
700	C₂	C₂×C₃₁×#534	1	1	yes	characteristic
701	C₂	C₂×C₃₁×#546	1	2	yes	—
702	C₂	C₂×C₃₁×#551	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂²×C₃₁×#120	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃₁×#123	C₂	semidirect
3. C₂³×C₂²⋊C₄×C₃₁	C₂	semidirect
4. C₂³×C₂²⋊C₄×C₃₁	C₂	semidirect
5. C₃₁×#2412	C₂	direct (N × H)
6. C₂×C₃₁×#397	C₂	semidirect
7. C₂×C₃₁×#394	C₂	semidirect
8. C₂×C₃₁×#386	C₂	semidirect
9. C₂×C₃₁×#386	C₂	semidirect
10. C₂×C₃₁×#385	C₂	semidirect
11. C₂×C₃₁×#381	C₂	semidirect
12. C₂×C₃₁×#380	C₂	semidirect
21. C₂×C₃₁×#123	C₂²	semidirect
24. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
25. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
36. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
37. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
38. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
39. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
40. C₃₁×#397	C₂²	semidirect
41. C₃₁×#394	C₂²	semidirect
42. C₃₁×#386	C₂²	semidirect
43. C₃₁×#386	C₂²	semidirect
44. C₃₁×#385	C₂²	semidirect
45. C₃₁×#381	C₂²	semidirect
46. C₃₁×#380	C₂²	semidirect
47. C₂×C₃₁×#95	C₂²	semidirect
48. C₂×C₃₁×#95	C₂²	semidirect
49. C₂×C₃₁×#95	C₂²	semidirect
50. C₂×C₃₁×#95	C₂²	semidirect
93. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
94. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
106. C₂×C₂²⋊C₄×C₃₁	D₄	semidirect
115. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
116. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
117. C₃₁×#95	C₂³	semidirect
118. C₃₁×#95	C₂³	semidirect
119. C₃₁×#95	C₂³	semidirect
120. C₃₁×#95	C₂³	semidirect
214. C₂²⋊C₄×C₃₁	C₂×D₄	semidirect
215. C₂×#2412	C₃₁	direct (N × H)
255. C₂³×C₃₁	#123	semidirect
300. C₂²×#123	C₂×C₃₁	semidirect
302. C₂³×C₂²⋊C₄	C₂×C₃₁	semidirect
303. C₂³×C₂²⋊C₄	C₂×C₃₁	semidirect
304. #2412	C₂×C₃₁	direct (N × H)
305. C₂×#397	C₂×C₃₁	semidirect
306. C₂×#394	C₂×C₃₁	semidirect
307. C₂×#386	C₂×C₃₁	semidirect
308. C₂×#386	C₂×C₃₁	semidirect
309. C₂×#385	C₂×C₃₁	semidirect
310. C₂×#381	C₂×C₃₁	semidirect
311. C₂×#380	C₂×C₃₁	semidirect
338. C₂²×C₃₁	C₂×#123	semidirect
362. C₂×#123	C₂²×C₃₁	semidirect
365. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
366. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
377. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
378. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
379. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
380. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
381. #397	C₂²×C₃₁	semidirect
382. #394	C₂²×C₃₁	semidirect
383. #386	C₂²×C₃₁	semidirect
384. #386	C₂²×C₃₁	semidirect
385. #385	C₂²×C₃₁	semidirect
386. #381	C₂²×C₃₁	semidirect
387. #380	C₂²×C₃₁	semidirect
388. C₂×#95	C₂²×C₃₁	semidirect
389. C₂×#95	C₂²×C₃₁	semidirect
390. C₂×#95	C₂²×C₃₁	semidirect
391. C₂×#95	C₂²×C₃₁	semidirect
396. C₂×C₃₁	#2412	direct (N × H)
444. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
445. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
457. C₂×C₂²⋊C₄	D₄×C₃₁	semidirect
466. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
467. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
468. #95	C₂³×C₃₁	semidirect
469. #95	C₂³×C₃₁	semidirect
470. #95	C₂³×C₃₁	semidirect
471. #95	C₂³×C₃₁	semidirect
472. C₃₁	C₂×#2412	direct (N × H)
566. C₂²⋊C₄	C₂×D₄×C₃₁	semidirect
606. C₂³	C₃₁×#123	semidirect
677. C₂²	C₂×C₃₁×#123	semidirect
697. C₂	C₃₁×#2412	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×#123	2
C₂²×C₃₁×#120	2
C₂³×C₂²⋊C₄×C₃₁	2
C₃₁×#2412	2
C₂×C₃₁×#397	2
C₂×C₃₁×#394	2
C₂×C₃₁×#386	2
C₂×C₃₁×#385	2
C₂×C₃₁×#381	2
C₂×C₃₁×#380	2
C₂×#2412	31

Subgroups — C2×C31×#2412 #21491416

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#2412 #21491416