Subgroups — C₃₁×#20494 #21477253

Order 7936.

1234 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#436	C₂	1	2	yes	maximal
2	C₂×C₄×M₁₆×C₃₁	C₂	1	2	yes	maximal, complemented
3	C₄²×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₈×C₄⋊C₄×C₃₁	C₂	1	2	yes	maximal, complemented
5	C₃₁×#1767	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1753	C₂	1	4	yes	maximal, complemented
7	C₃₁×#1749	C₂	1	2	yes	maximal, complemented
8	C₄×C₃₁×#97	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×M₁₆×C₃₁	C₂²	1	4	yes	—
10	C₂×C₄×D₄×C₃₁	C₄	1	2	yes	—
11	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
13	C₃₁×#436	C₄	1	16	yes	complemented
14	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₃₁×C₂²⋊C₈	C₂²	1	4	yes	—
16	C₄×M₁₆×C₃₁	—	2	8	no	—
17	C₂×C₃₁×#97	C₂²	1	2	yes	—
18	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×#97	C₂²	1	2	yes	—
20	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₃₁	C₂²	1	4	yes	—
22	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
23	C₄×C₄⋊C₄×C₃₁	C₄	1	2	yes	—
24	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
25	C₄×C₂²⋊C₄×C₃₁	C₄	1	4	yes	—
26	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
27	C₄³×C₃₁	C₂²	1	1	yes	characteristic
28	C₃₁×#336	C₂²	1	4	yes	—
29	C₃₁×#336	C₂²	1	2	yes	—
30	C₂²×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₃₁	C₂×C₄	1	4	yes	—
32	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
33	C₂×M₁₆×C₃₁	—	2	8	no	—
34	C₂×M₁₆×C₃₁	—	2	8	no	—
35	C₂×M₁₆×C₃₁	C₂×C₄	1	16	yes	complemented
36	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
37	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
38	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
39	C₄×D₄×C₃₁	—	2	8	no	—
40	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	—
41	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
43	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
44	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₃₁	—	2	4	no	—
46	C₂×C₄²×C₃₁	—	2	4	no	—
47	C₂×C₄²×C₃₁	C₂×C₄	1	4	yes	—
48	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
51	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
54	C₃₁×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
55	C₃₁×C₂²⋊C₈	C₂×C₄	1	16	yes	complemented
56	C₃₁×#97	—	2	4	no	—
57	C₃₁×#97	—	2	4	no	—
58	C₃₁×#97	—	2	2	no	—
59	C₃₁×#97	D₄	1	4	yes	complemented
60	C₄×C₈×C₃₁	—	2	8	no	—
61	C₄×C₈×C₃₁	C₂×C₄	1	8	yes	complemented
62	C₃₁×#95	C₂×C₄	1	2	yes	—
63	C₃₁×#95	C₂×C₄	1	4	yes	—
64	C₂⁴×C₃₁	C₂²×C₄	1	2	yes	—
65	C₂×D₄×C₃₁	—	2	4	no	—
66	C₂×D₄×C₃₁	C₄²	1	4	yes	—
67	C₂²×C₄×C₃₁	—	2	2	no	—
68	C₂²×C₄×C₃₁	—	2	2	no	—
69	C₂²×C₄×C₃₁	—	2	4	no	—
70	C₂²×C₄×C₃₁	—	2	8	no	—
71	C₂²×C₄×C₃₁	—	2	8	no	—
72	C₂²×C₄×C₃₁	—	4	4	no	—
73	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
74	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
76	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
77	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
78	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
79	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
81	M₁₆×C₃₁	—	2	32	no	—
82	C₂×C₈×C₃₁	—	2	4	no	—
83	C₂×C₈×C₃₁	—	2	2	no	—
84	C₂×C₈×C₃₁	—	2	2	no	—
85	C₂×C₈×C₃₁	—	2	4	no	—
86	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
87	C₂×C₈×C₃₁	C₂²×C₄	1	8	yes	—
88	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
89	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
90	C₂×C₈×C₃₁	#41	1	4	yes	—
91	C₄⋊C₄×C₃₁	C₄²	1	4	yes	—
92	C₄⋊C₄×C₃₁	M₁₆	1	8	yes	complemented
93	C₂²⋊C₄×C₃₁	—	2	8	no	—
94	C₂²⋊C₄×C₃₁	C₄²	1	8	yes	—
95	C₄²×C₃₁	—	2	8	no	—
96	C₄²×C₃₁	—	2	4	no	—
97	C₄²×C₃₁	—	2	2	no	—
98	C₄²×C₃₁	—	2	2	no	—
99	C₄²×C₃₁	—	2	2	no	—
100	C₄²×C₃₁	—	4	2	no	—
101	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
102	C₄²×C₃₁	C₂×D₄	1	2	yes	—
103	C₄²×C₃₁	#41	1	2	yes	—
104	#20494	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
105	C₂³×C₃₁	—	2	2	no	—
106	C₂³×C₃₁	—	2	2	no	—
107	C₂³×C₃₁	—	2	4	no	—
108	C₂³×C₃₁	—	2	4	no	—
109	C₂³×C₃₁	C₂×C₄²	1	4	yes	—
110	C₂³×C₃₁	C₂³×C₄	1	1	yes	characteristic
111	D₄×C₃₁	—	2	8	no	—
112	C₂×C₄×C₃₁	—	2	4	no	—
113	C₂×C₄×C₃₁	—	2	2	no	—
114	C₂×C₄×C₃₁	—	2	2	no	—
115	C₂×C₄×C₃₁	—	2	2	no	—
116	C₂×C₄×C₃₁	—	2	2	no	—
117	C₂×C₄×C₃₁	—	2	2	no	—
118	C₂×C₄×C₃₁	—	2	4	no	—
119	C₂×C₄×C₃₁	—	2	8	no	—
120	C₂×C₄×C₃₁	—	2	8	no	—
121	C₂×C₄×C₃₁	—	2	2	no	—
122	C₂×C₄×C₃₁	—	2	2	no	—
123	C₂×C₄×C₃₁	—	2	2	no	—
124	C₂×C₄×C₃₁	—	4	16	no	—
125	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
126	C₂×C₄×C₃₁	C₂×C₄²	1	4	yes	—
127	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
128	C₂×C₄×C₃₁	C₄×D₄	1	4	yes	—
129	C₂×C₄×C₃₁	C₂×M₁₆	1	8	yes	—
130	C₂×C₄×C₃₁	C₂×M₁₆	1	4	yes	—
131	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
132	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
133	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
134	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
135	C₈×C₃₁	—	2	8	no	—
136	C₈×C₃₁	—	2	4	no	—
137	C₈×C₃₁	C₄×D₄	1	8	yes	complemented
138	C₂×#436	C₂×C₃₁	1	2	yes	—
139	C₂×C₄×M₁₆	C₂×C₃₁	1	2	yes	complemented
140	C₄²×D₄	C₂×C₃₁	1	1	yes	characteristic
141	C₈×C₄⋊C₄	C₂×C₃₁	1	2	yes	complemented
142	#1767	C₂×C₃₁	1	1	yes	characteristic, complemented
143	#1753	C₂×C₃₁	1	4	yes	complemented
144	#1749	C₂×C₃₁	1	2	yes	complemented
145	C₄×#97	C₂×C₃₁	1	1	yes	characteristic, complemented
146	C₂²×C₃₁	—	2	4	no	—
147	C₂²×C₃₁	—	2	4	no	—
148	C₂²×C₃₁	—	2	4	no	—
149	C₂²×C₃₁	—	4	4	no	—
150	C₂²×C₃₁	—	4	4	no	—
151	C₂²×C₃₁	C₂²×C₄²	1	1	yes	characteristic
152	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
153	C₂²×C₃₁	C₄×#41	1	1	yes	characteristic
154	C₂²×C₃₁	C₂²×M₁₆	1	2	yes	—
155	C₂²×C₃₁	#568	1	2	yes	—
156	C₄×C₃₁	—	2	2	no	—
157	C₄×C₃₁	—	2	4	no	—
158	C₄×C₃₁	—	2	8	no	—
159	C₄×C₃₁	—	2	4	no	—
160	C₄×C₃₁	—	4	2	no	—
161	C₄×C₃₁	C₄×M₁₆	1	4	yes	complemented
162	C₄×C₃₁	C₂×C₄×D₄	1	2	yes	—
163	C₄×C₃₁	C₄×#41	1	2	yes	—
164	C₂²×M₁₆	C₂²×C₃₁	1	4	yes	—
165	C₂×C₄×D₄	C₄×C₃₁	1	2	yes	—
166	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
167	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
168	#436	C₄×C₃₁	1	16	yes	complemented
169	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
170	C₂×C₂²⋊C₈	C₂²×C₃₁	1	4	yes	—
171	C₄×M₁₆	—	2	8	no	—
172	C₂×#97	C₂²×C₃₁	1	2	yes	—
173	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
174	C₂×#97	C₂²×C₃₁	1	2	yes	—
175	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
176	C₂×C₄×C₈	C₂²×C₃₁	1	4	yes	—
177	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
178	C₄×C₄⋊C₄	C₄×C₃₁	1	2	yes	—
179	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
180	C₄×C₂²⋊C₄	C₄×C₃₁	1	4	yes	—
181	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
182	C₄³	C₂²×C₃₁	1	1	yes	characteristic
183	#336	C₂²×C₃₁	1	4	yes	—
184	#336	C₂²×C₃₁	1	2	yes	—
185	C₂×C₃₁	—	4	4	no	—
186	C₂×C₃₁	C₄²×D₄	1	1	yes	characteristic
187	C₂×C₃₁	C₂×C₄×M₁₆	1	1	yes	characteristic
188	C₂×C₃₁	#2875	1	1	yes	characteristic
189	C₂×C₃₁	D₄×M₁₆	1	2	yes	—
190	C₂×C₃₁	#2971	1	2	yes	—
191	C₂²×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
192	C₂³×C₄	C₂×C₄×C₃₁	1	4	yes	—
193	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
194	C₂×M₁₆	—	2	8	no	—
195	C₂×M₁₆	—	2	8	no	—
196	C₂×M₁₆	C₂×C₄×C₃₁	1	16	yes	complemented
197	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
198	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
199	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
200	C₄×D₄	—	2	8	no	—
201	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	—
202	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
203	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
204	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
205	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
206	C₂×C₄²	—	2	4	no	—
207	C₂×C₄²	—	2	4	no	—
208	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
209	C₂×C₄²	C₂×C₄×C₃₁	1	4	yes	—
210	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
211	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
212	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
213	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
214	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
215	C₄⋊C₈	C₂×C₄×C₃₁	1	8	yes	complemented
216	C₂²⋊C₈	C₂×C₄×C₃₁	1	16	yes	complemented
217	#97	—	2	4	no	—
218	#97	—	2	4	no	—
219	#97	—	2	2	no	—
220	#97	D₄×C₃₁	1	4	yes	complemented
221	C₄×C₈	—	2	8	no	—
222	C₄×C₈	C₂×C₄×C₃₁	1	8	yes	complemented
223	#95	C₂×C₄×C₃₁	1	2	yes	—
224	#95	C₂×C₄×C₃₁	1	4	yes	—
225	C₃₁	#20494	1	1	yes	characteristic, direct product factor, Sylow
226	C₂⁴	C₂²×C₄×C₃₁	1	2	yes	—
227	C₂×D₄	—	2	4	no	—
228	C₂×D₄	C₄²×C₃₁	1	4	yes	—
229	C₂²×C₄	—	2	2	no	—
230	C₂²×C₄	—	2	2	no	—
231	C₂²×C₄	—	2	4	no	—
232	C₂²×C₄	—	2	8	no	—
233	C₂²×C₄	—	2	8	no	—
234	C₂²×C₄	—	4	4	no	—
235	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
236	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
237	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
238	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
239	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
240	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
241	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
242	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
243	M₁₆	—	2	32	no	—
244	C₂×C₈	—	2	4	no	—
245	C₂×C₈	—	2	2	no	—
246	C₂×C₈	—	2	2	no	—
247	C₂×C₈	—	2	4	no	—
248	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
249	C₂×C₈	C₂²×C₄×C₃₁	1	8	yes	—
250	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
251	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
252	C₂×C₈	#41×C₃₁	1	4	yes	—
253	C₄⋊C₄	C₄²×C₃₁	1	4	yes	—
254	C₄⋊C₄	M₁₆×C₃₁	1	8	yes	complemented
255	C₂²⋊C₄	—	2	8	no	—
256	C₂²⋊C₄	C₄²×C₃₁	1	8	yes	—
257	C₄²	—	2	8	no	—
258	C₄²	—	2	4	no	—
259	C₄²	—	2	2	no	—
260	C₄²	—	2	2	no	—
261	C₄²	—	2	2	no	—
262	C₄²	—	4	2	no	—
263	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
264	C₄²	C₂×D₄×C₃₁	1	2	yes	—
265	C₄²	#41×C₃₁	1	2	yes	—
266	C₂³	—	2	2	no	—
267	C₂³	—	2	2	no	—
268	C₂³	—	2	4	no	—
269	C₂³	—	2	4	no	—
270	C₂³	C₂×C₄²×C₃₁	1	4	yes	—
271	C₂³	C₂³×C₄×C₃₁	1	1	yes	characteristic
272	D₄	—	2	8	no	—
273	C₂×C₄	—	2	4	no	—
274	C₂×C₄	—	2	2	no	—
275	C₂×C₄	—	2	2	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	2	2	no	—
279	C₂×C₄	—	2	4	no	—
280	C₂×C₄	—	2	8	no	—
281	C₂×C₄	—	2	8	no	—
282	C₂×C₄	—	2	2	no	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	4	16	no	—
286	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
287	C₂×C₄	C₂×C₄²×C₃₁	1	4	yes	—
288	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
289	C₂×C₄	C₄×D₄×C₃₁	1	4	yes	—
290	C₂×C₄	C₂×M₁₆×C₃₁	1	8	yes	—
291	C₂×C₄	C₂×M₁₆×C₃₁	1	4	yes	—
292	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
293	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
294	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
295	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
296	C₈	—	2	8	no	—
297	C₈	—	2	4	no	—
298	C₈	C₄×D₄×C₃₁	1	8	yes	complemented
299	C₂²	—	2	4	no	—
300	C₂²	—	2	4	no	—
301	C₂²	—	2	4	no	—
302	C₂²	—	4	4	no	—
303	C₂²	—	4	4	no	—
304	C₂²	C₂²×C₄²×C₃₁	1	1	yes	characteristic
305	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
306	C₂²	C₄×#41×C₃₁	1	1	yes	characteristic
307	C₂²	C₂²×M₁₆×C₃₁	1	2	yes	—
308	C₂²	C₃₁×#568	1	2	yes	—
309	C₄	—	2	2	no	—
310	C₄	—	2	4	no	—
311	C₄	—	2	8	no	—
312	C₄	—	2	4	no	—
313	C₄	—	4	2	no	—
314	C₄	C₄×M₁₆×C₃₁	1	4	yes	complemented
315	C₄	C₂×C₄×D₄×C₃₁	1	2	yes	—
316	C₄	C₄×#41×C₃₁	1	2	yes	—
317	C₂	—	4	4	no	—
318	C₂	C₄²×D₄×C₃₁	1	1	yes	characteristic
319	C₂	C₂×C₄×M₁₆×C₃₁	1	1	yes	characteristic
320	C₂	C₃₁×#2875	1	1	yes	characteristic
321	C₂	D₄×M₁₆×C₃₁	1	2	yes	—
322	C₂	C₃₁×#2971	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator	C₂²	C₂²×C₄²×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
socle	C₂³×C₃₁	C₂³×C₄
prime radical	C₂²×D₄×C₃₁	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×M₁₆×C₃₁	C₂	semidirect
4. C₈×C₄⋊C₄×C₃₁	C₂	semidirect
5. C₃₁×#1767	C₂	semidirect
6. C₃₁×#1753	C₂	semidirect
7. C₃₁×#1749	C₂	semidirect
8. C₄×C₃₁×#97	C₂	semidirect
13. C₃₁×#436	C₄	semidirect
35. C₂×M₁₆×C₃₁	C₂×C₄	semidirect
54. C₃₁×C₄⋊C₈	C₂×C₄	semidirect
55. C₃₁×C₂²⋊C₈	C₂×C₄	semidirect
59. C₃₁×#97	D₄	semidirect
61. C₄×C₈×C₃₁	C₂×C₄	semidirect
92. C₄⋊C₄×C₃₁	M₁₆	semidirect
104. #20494	C₃₁	direct (N × H)
137. C₈×C₃₁	C₄×D₄	semidirect
139. C₂×C₄×M₁₆	C₂×C₃₁	semidirect
141. C₈×C₄⋊C₄	C₂×C₃₁	semidirect
142. #1767	C₂×C₃₁	semidirect
143. #1753	C₂×C₃₁	semidirect
144. #1749	C₂×C₃₁	semidirect
145. C₄×#97	C₂×C₃₁	semidirect
161. C₄×C₃₁	C₄×M₁₆	semidirect
168. #436	C₄×C₃₁	semidirect
196. C₂×M₁₆	C₂×C₄×C₃₁	semidirect
215. C₄⋊C₈	C₂×C₄×C₃₁	semidirect
216. C₂²⋊C₈	C₂×C₄×C₃₁	semidirect
220. #97	D₄×C₃₁	semidirect
222. C₄×C₈	C₂×C₄×C₃₁	semidirect
225. C₃₁	#20494	direct (N × H)
254. C₄⋊C₄	M₁₆×C₃₁	semidirect
298. C₈	C₄×D₄×C₃₁	semidirect
314. C₄	C₄×M₁₆×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#436	2
C₂×C₄×M₁₆×C₃₁	2
C₄²×D₄×C₃₁	2
C₈×C₄⋊C₄×C₃₁	2
C₃₁×#1767	2
C₃₁×#1753	2
C₃₁×#1749	2
C₄×C₃₁×#97	2
#20494	31

Subgroups — C31×#20494 #21477253

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#20494 #21477253