Subgroups — C₂×C₃₁×#2312 #21490804

Order 7936.

4142 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2312	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₃₁×#388	C₂	1	8	yes	maximal, complemented
4	C₂×C₃₁×#380	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₁×#379	C₂	1	2	yes	maximal
6	C₂×C₄×C₂²⋊C₄×C₃₁	C₂	1	2	yes	maximal, complemented
7	C₂⁶×C₃₁	C₂²	1	1	yes	characteristic
8	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₃₁	C₂²	1	4	yes	complemented
11	C₂²×C₂²⋊C₄×C₃₁	C₄	1	16	yes	complemented
12	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
13	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
14	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
15	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
16	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	8	yes	—
17	C₂²×C₄²×C₃₁	C₂²	1	4	yes	complemented
18	C₃₁×#388	C₂²	1	64	yes	complemented
19	C₃₁×#380	C₂²	1	16	yes	complemented
20	C₃₁×#379	C₂²	1	16	yes	—
21	C₄×C₂²⋊C₄×C₃₁	C₂²	1	16	yes	complemented
22	C₂×C₃₁×#95	C₂²	1	4	yes	complemented
23	C₂×C₃₁×#95	C₂²	1	4	yes	complemented
24	C₂⁵×C₃₁	—	2	8	no	—
25	C₂⁵×C₃₁	—	4	4	no	—
26	C₂⁵×C₃₁	—	4	4	no	—
27	C₂⁵×C₃₁	C₂×C₄	1	8	yes	—
28	C₂⁵×C₃₁	C₂³	1	2	yes	—
29	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
30	C₂⁵×C₃₁	C₂³	1	4	yes	—
31	C₂³×C₄×C₃₁	—	4	4	no	—
32	C₂³×C₄×C₃₁	—	4	4	no	—
33	C₂³×C₄×C₃₁	C₂×C₄	1	8	yes	—
34	C₂³×C₄×C₃₁	C₂×C₄	1	8	yes	—
35	C₂³×C₄×C₃₁	C₂³	1	8	yes	—
36	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
37	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
38	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
39	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
40	C₂×C₄⋊C₄×C₃₁	—	4	8	no	—
41	C₂×C₄⋊C₄×C₃₁	C₂³	1	16	yes	complemented
42	C₂×C₂²⋊C₄×C₃₁	—	2	16	no	—
43	C₂×C₂²⋊C₄×C₃₁	—	4	8	no	—
44	C₂×C₂²⋊C₄×C₃₁	—	4	8	no	—
45	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	32	yes	—
46	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	64	yes	complemented
47	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	—
48	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	—
49	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	—
50	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	—
51	C₂×C₄²×C₃₁	—	4	8	no	—
52	C₂×C₄²×C₃₁	C₂³	1	16	yes	complemented
53	C₃₁×#95	C₂³	1	16	yes	complemented
54	C₃₁×#95	C₂³	1	16	yes	complemented
55	C₂⁴×C₃₁	—	2	4	no	—
56	C₂⁴×C₃₁	—	2	4	no	—
57	C₂⁴×C₃₁	—	2	32	no	—
58	C₂⁴×C₃₁	—	2	16	no	—
59	C₂⁴×C₃₁	—	2	8	no	—
60	C₂⁴×C₃₁	—	2	8	no	—
61	C₂⁴×C₃₁	—	2	8	no	—
62	C₂⁴×C₃₁	—	4	16	no	—
63	C₂⁴×C₃₁	—	4	16	no	—
64	C₂⁴×C₃₁	—	4	8	no	—
65	C₂⁴×C₃₁	—	4	8	no	—
66	C₂⁴×C₃₁	—	4	64	no	—
67	C₂⁴×C₃₁	C₂²×C₄	1	8	yes	—
68	C₂⁴×C₃₁	C₂²×C₄	1	4	yes	—
69	C₂⁴×C₃₁	C₂²×C₄	1	16	yes	—
70	C₂⁴×C₃₁	#41	1	8	yes	—
71	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
72	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
73	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
74	C₂²×C₄×C₃₁	—	2	8	no	—
75	C₂²×C₄×C₃₁	—	2	8	no	—
76	C₂²×C₄×C₃₁	—	2	16	no	—
77	C₂²×C₄×C₃₁	—	2	16	no	—
78	C₂²×C₄×C₃₁	—	2	16	no	—
79	C₂²×C₄×C₃₁	—	4	16	no	—
80	C₂²×C₄×C₃₁	—	4	16	no	—
81	C₂²×C₄×C₃₁	—	4	8	no	—
82	C₂²×C₄×C₃₁	—	4	8	no	—
83	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
84	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
85	C₂²×C₄×C₃₁	C₂²×C₄	1	16	yes	—
86	C₂²×C₄×C₃₁	C₂²×C₄	1	16	yes	—
87	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
88	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
89	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
90	C₄⋊C₄×C₃₁	—	4	16	no	—
91	C₂²⋊C₄×C₃₁	—	2	32	no	—
92	C₂²⋊C₄×C₃₁	—	4	16	no	—
93	C₂²⋊C₄×C₃₁	—	4	16	no	—
94	C₂²⋊C₄×C₃₁	C₂²×C₄	1	64	yes	—
95	C₄²×C₃₁	—	4	16	no	—
96	C₂×#2312	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₂³×C₃₁	—	2	8	no	—
98	C₂³×C₃₁	—	2	8	no	—
99	C₂³×C₃₁	—	2	32	no	—
100	C₂³×C₃₁	—	2	4	no	—
101	C₂³×C₃₁	—	2	4	no	—
102	C₂³×C₃₁	—	2	32	no	—
103	C₂³×C₃₁	—	2	16	no	—
104	C₂³×C₃₁	—	2	16	no	—
105	C₂³×C₃₁	—	2	16	no	—
106	C₂³×C₃₁	—	2	8	no	—
107	C₂³×C₃₁	—	2	8	no	—
108	C₂³×C₃₁	—	2	8	no	—
109	C₂³×C₃₁	—	4	16	no	—
110	C₂³×C₃₁	—	4	16	no	—
111	C₂³×C₃₁	—	4	128	no	—
112	C₂³×C₃₁	—	4	64	no	—
113	C₂³×C₃₁	—	4	32	no	—
114	C₂³×C₃₁	#117	1	16	yes	—
115	C₂³×C₃₁	C₂³×C₄	1	8	yes	—
116	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
117	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
118	C₂³×C₃₁	C₂×#41	1	8	yes	—
119	C₂³×C₃₁	C₂×#41	1	4	yes	—
120	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
121	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
122	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
123	C₂×C₄×C₃₁	—	2	16	no	—
124	C₂×C₄×C₃₁	—	2	16	no	—
125	C₂×C₄×C₃₁	—	2	8	no	—
126	C₂×C₄×C₃₁	—	2	8	no	—
127	C₂×C₄×C₃₁	—	2	16	no	—
128	C₂×C₄×C₃₁	—	2	16	no	—
129	C₂×C₄×C₃₁	—	2	16	no	—
130	C₂×C₄×C₃₁	—	4	16	no	—
131	C₂×C₄×C₃₁	—	4	16	no	—
132	C₂×C₄×C₃₁	—	4	32	no	—
133	C₂×C₄×C₃₁	C₂³×C₄	1	8	yes	—
134	C₂×C₄×C₃₁	C₂³×C₄	1	8	yes	—
135	C₂³×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic
136	#2312	C₂×C₃₁	1	16	yes	direct product factor
137	C₂×#388	C₂×C₃₁	1	8	yes	complemented
138	C₂×#380	C₂×C₃₁	1	2	yes	complemented
139	C₂×#379	C₂×C₃₁	1	2	yes	—
140	C₂×C₄×C₂²⋊C₄	C₂×C₃₁	1	2	yes	complemented
141	C₂²×C₃₁	—	2	32	no	—
142	C₂²×C₃₁	—	2	4	no	—
143	C₂²×C₃₁	—	2	4	no	—
144	C₂²×C₃₁	—	2	16	no	—
145	C₂²×C₃₁	—	2	8	no	—
146	C₂²×C₃₁	—	2	8	no	—
147	C₂²×C₃₁	—	2	8	no	—
148	C₂²×C₃₁	—	4	64	no	—
149	C₂²×C₃₁	—	4	32	no	—
150	C₂²×C₃₁	—	4	16	no	—
151	C₂²×C₃₁	C₂×#117	1	8	yes	—
152	C₂²×C₃₁	C₂×#117	1	4	yes	—
153	C₂²×C₃₁	#518	1	4	yes	—
154	C₂²×C₃₁	#518	1	4	yes	—
155	C₂²×C₃₁	#538	1	16	yes	—
156	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
157	C₂²×C₃₁	C₂²×#41	1	2	yes	—
158	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
159	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
160	C₄×C₃₁	—	2	8	no	—
161	C₄×C₃₁	—	2	8	no	—
162	C₄×C₃₁	—	4	16	no	—
163	C₂⁶	C₂²×C₃₁	1	1	yes	characteristic
164	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
165	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
166	C₂²×C₄⋊C₄	C₂²×C₃₁	1	4	yes	complemented
167	C₂²×C₂²⋊C₄	C₄×C₃₁	1	16	yes	complemented
168	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
169	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
170	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
171	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
172	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	8	yes	—
173	C₂²×C₄²	C₂²×C₃₁	1	4	yes	complemented
174	#388	C₂²×C₃₁	1	64	yes	complemented
175	#380	C₂²×C₃₁	1	16	yes	complemented
176	#379	C₂²×C₃₁	1	16	yes	—
177	C₄×C₂²⋊C₄	C₂²×C₃₁	1	16	yes	complemented
178	C₂×#95	C₂²×C₃₁	1	4	yes	complemented
179	C₂×#95	C₂²×C₃₁	1	4	yes	complemented
180	C₂×C₃₁	—	2	8	no	—
181	C₂×C₃₁	—	4	8	no	—
182	C₂×C₃₁	#2312	1	8	yes	direct product factor
183	C₂×C₃₁	C₂²×#117	1	1	yes	characteristic
184	C₂×C₃₁	C₂×#518	1	1	yes	characteristic
185	C₂×C₃₁	C₂×#518	1	1	yes	characteristic
186	C₂×C₃₁	C₂×#538	1	4	yes	—
187	C₂⁵	—	2	8	no	—
188	C₂⁵	—	4	4	no	—
189	C₂⁵	—	4	4	no	—
190	C₂⁵	C₂×C₄×C₃₁	1	8	yes	—
191	C₂⁵	C₂³×C₃₁	1	2	yes	—
192	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
193	C₂⁵	C₂³×C₃₁	1	4	yes	—
194	C₂³×C₄	—	4	4	no	—
195	C₂³×C₄	—	4	4	no	—
196	C₂³×C₄	C₂×C₄×C₃₁	1	8	yes	—
197	C₂³×C₄	C₂×C₄×C₃₁	1	8	yes	—
198	C₂³×C₄	C₂³×C₃₁	1	8	yes	—
199	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
200	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
201	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
202	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
203	C₂×C₄⋊C₄	—	4	8	no	—
204	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	complemented
205	C₂×C₂²⋊C₄	—	2	16	no	—
206	C₂×C₂²⋊C₄	—	4	8	no	—
207	C₂×C₂²⋊C₄	—	4	8	no	—
208	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	32	yes	—
209	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	64	yes	complemented
210	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	—
211	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	—
212	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	—
213	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	—
214	C₂×C₄²	—	4	8	no	—
215	C₂×C₄²	C₂³×C₃₁	1	16	yes	complemented
216	#95	C₂³×C₃₁	1	16	yes	complemented
217	#95	C₂³×C₃₁	1	16	yes	complemented
218	C₃₁	C₂×#2312	1	1	yes	characteristic, direct product factor, Sylow
219	C₂⁴	—	2	4	no	—
220	C₂⁴	—	2	4	no	—
221	C₂⁴	—	2	32	no	—
222	C₂⁴	—	2	16	no	—
223	C₂⁴	—	2	8	no	—
224	C₂⁴	—	2	8	no	—
225	C₂⁴	—	2	8	no	—
226	C₂⁴	—	4	16	no	—
227	C₂⁴	—	4	16	no	—
228	C₂⁴	—	4	8	no	—
229	C₂⁴	—	4	8	no	—
230	C₂⁴	—	4	64	no	—
231	C₂⁴	C₂²×C₄×C₃₁	1	8	yes	—
232	C₂⁴	C₂²×C₄×C₃₁	1	4	yes	—
233	C₂⁴	C₂²×C₄×C₃₁	1	16	yes	—
234	C₂⁴	#41×C₃₁	1	8	yes	—
235	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
236	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
237	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
238	C₂²×C₄	—	2	8	no	—
239	C₂²×C₄	—	2	8	no	—
240	C₂²×C₄	—	2	16	no	—
241	C₂²×C₄	—	2	16	no	—
242	C₂²×C₄	—	2	16	no	—
243	C₂²×C₄	—	4	16	no	—
244	C₂²×C₄	—	4	16	no	—
245	C₂²×C₄	—	4	8	no	—
246	C₂²×C₄	—	4	8	no	—
247	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
248	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
249	C₂²×C₄	C₂²×C₄×C₃₁	1	16	yes	—
250	C₂²×C₄	C₂²×C₄×C₃₁	1	16	yes	—
251	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
252	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
253	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
254	C₄⋊C₄	—	4	16	no	—
255	C₂²⋊C₄	—	2	32	no	—
256	C₂²⋊C₄	—	4	16	no	—
257	C₂²⋊C₄	—	4	16	no	—
258	C₂²⋊C₄	C₂²×C₄×C₃₁	1	64	yes	—
259	C₄²	—	4	16	no	—
260	C₂³	—	2	8	no	—
261	C₂³	—	2	8	no	—
262	C₂³	—	2	32	no	—
263	C₂³	—	2	4	no	—
264	C₂³	—	2	4	no	—
265	C₂³	—	2	32	no	—
266	C₂³	—	2	16	no	—
267	C₂³	—	2	16	no	—
268	C₂³	—	2	16	no	—
269	C₂³	—	2	8	no	—
270	C₂³	—	2	8	no	—
271	C₂³	—	2	8	no	—
272	C₂³	—	4	16	no	—
273	C₂³	—	4	16	no	—
274	C₂³	—	4	128	no	—
275	C₂³	—	4	64	no	—
276	C₂³	—	4	32	no	—
277	C₂³	C₃₁×#117	1	16	yes	—
278	C₂³	C₂³×C₄×C₃₁	1	8	yes	—
279	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
280	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
281	C₂³	C₂×#41×C₃₁	1	8	yes	—
282	C₂³	C₂×#41×C₃₁	1	4	yes	—
283	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
284	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
285	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
286	C₂×C₄	—	2	16	no	—
287	C₂×C₄	—	2	16	no	—
288	C₂×C₄	—	2	8	no	—
289	C₂×C₄	—	2	8	no	—
290	C₂×C₄	—	2	16	no	—
291	C₂×C₄	—	2	16	no	—
292	C₂×C₄	—	2	16	no	—
293	C₂×C₄	—	4	16	no	—
294	C₂×C₄	—	4	16	no	—
295	C₂×C₄	—	4	32	no	—
296	C₂×C₄	C₂³×C₄×C₃₁	1	8	yes	—
297	C₂×C₄	C₂³×C₄×C₃₁	1	8	yes	—
298	C₂²	—	2	32	no	—
299	C₂²	—	2	4	no	—
300	C₂²	—	2	4	no	—
301	C₂²	—	2	16	no	—
302	C₂²	—	2	8	no	—
303	C₂²	—	2	8	no	—
304	C₂²	—	2	8	no	—
305	C₂²	—	4	64	no	—
306	C₂²	—	4	32	no	—
307	C₂²	—	4	16	no	—
308	C₂²	C₂×C₃₁×#117	1	8	yes	—
309	C₂²	C₂×C₃₁×#117	1	4	yes	—
310	C₂²	C₃₁×#518	1	4	yes	—
311	C₂²	C₃₁×#518	1	4	yes	—
312	C₂²	C₃₁×#538	1	16	yes	—
313	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
314	C₂²	C₂²×#41×C₃₁	1	2	yes	—
315	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
316	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
317	C₄	—	2	8	no	—
318	C₄	—	2	8	no	—
319	C₄	—	4	16	no	—
320	C₂	—	2	8	no	—
321	C₂	—	4	8	no	—
322	C₂	C₃₁×#2312	1	8	yes	direct product factor
323	C₂	C₂²×C₃₁×#117	1	1	yes	characteristic
324	C₂	C₂×C₃₁×#518	1	1	yes	characteristic
325	C₂	C₂×C₃₁×#518	1	1	yes	characteristic
326	C₂	C₂×C₃₁×#538	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₃₁	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂⁶×C₃₁	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2312	C₂	direct (N × H)
3. C₂×C₃₁×#388	C₂	semidirect
4. C₂×C₃₁×#380	C₂	semidirect
6. C₂×C₄×C₂²⋊C₄×C₃₁	C₂	semidirect
10. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
11. C₂²×C₂²⋊C₄×C₃₁	C₄	semidirect
17. C₂²×C₄²×C₃₁	C₂²	semidirect
18. C₃₁×#388	C₂²	semidirect
19. C₃₁×#380	C₂²	semidirect
21. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
22. C₂×C₃₁×#95	C₂²	semidirect
23. C₂×C₃₁×#95	C₂²	semidirect
41. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
46. C₂×C₂²⋊C₄×C₃₁	C₂×C₄	semidirect
52. C₂×C₄²×C₃₁	C₂³	semidirect
53. C₃₁×#95	C₂³	semidirect
54. C₃₁×#95	C₂³	semidirect
96. C₂×#2312	C₃₁	direct (N × H)
136. #2312	C₂×C₃₁	direct (N × H)
137. C₂×#388	C₂×C₃₁	semidirect
138. C₂×#380	C₂×C₃₁	semidirect
140. C₂×C₄×C₂²⋊C₄	C₂×C₃₁	semidirect
166. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
167. C₂²×C₂²⋊C₄	C₄×C₃₁	semidirect
173. C₂²×C₄²	C₂²×C₃₁	semidirect
174. #388	C₂²×C₃₁	semidirect
175. #380	C₂²×C₃₁	semidirect
177. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
178. C₂×#95	C₂²×C₃₁	semidirect
179. C₂×#95	C₂²×C₃₁	semidirect
182. C₂×C₃₁	#2312	direct (N × H)
204. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
209. C₂×C₂²⋊C₄	C₂×C₄×C₃₁	semidirect
215. C₂×C₄²	C₂³×C₃₁	semidirect
216. #95	C₂³×C₃₁	semidirect
217. #95	C₂³×C₃₁	semidirect
218. C₃₁	C₂×#2312	direct (N × H)
322. C₂	C₃₁×#2312	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₂²⋊C₄×C₃₁	2
C₃₁×#2312	2
C₂×C₃₁×#388	2
C₂×C₃₁×#380	2
C₂×C₃₁×#379	2
C₂×C₄×C₂²⋊C₄×C₃₁	2
C₂×#2312	31

Subgroups — C2×C31×#2312 #21490804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#2312 #21490804