Subgroups — C₃₁×#36614 #21493373

Order 7936.

7538 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#525	C₂	1	3	yes	maximal, complemented
3	C₃₁×#2849	C₂	1	6	yes	maximal, complemented
4	C₃₁×#2848	C₂	1	4	yes	maximal, complemented
5	C₃₁×#2847	C₂	1	4	yes	maximal, complemented
6	C₃₁×#2846	C₂	1	2	yes	maximal, complemented
7	C₄×C₃₁×#120	C₂	1	8	yes	maximal, complemented
8	C₃₁×#2280	C₂	1	3	yes	maximal, complemented
9	C₂⁶×C₃₁	C₂²	1	1	yes	characteristic
10	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
11	C₂⁴×C₄×C₃₁	—	2	24	no	—
12	C₂⁴×C₄×C₃₁	C₂²	1	4	yes	—
13	C₂⁴×C₄×C₃₁	C₂²	1	3	yes	—
14	C₂⁴×C₄×C₃₁	C₂²	1	4	yes	—
15	C₂⁴×C₄×C₃₁	C₂²	1	3	yes	—
16	C₃₁×#525	—	2	24	no	—
17	C₂×C₃₁×#123	C₂²	1	6	yes	complemented
18	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	6	yes	complemented
19	C₂×C₃₁×#121	C₂²	1	6	yes	complemented
20	C₂×C₃₁×#120	C₂²	1	8	yes	—
21	C₂×C₃₁×#120	C₂²	1	6	yes	—
22	C₂×C₄×D₄×C₃₁	C₂²	1	12	yes	complemented
23	C₂×C₃₁×#117	C₂²	1	3	yes	complemented
24	C₃₁×#386	C₂²	1	24	yes	complemented
25	C₃₁×#385	C₂²	1	24	yes	complemented
26	C₃₁×#381	C₂²	1	6	yes	complemented
27	C₃₁×#380	C₂²	1	12	yes	complemented
28	C₃₁×#379	C₂²	1	8	yes	—
29	C₃₁×#379	C₂²	1	6	yes	—
30	C₄×C₂²⋊C₄×C₃₁	C₂²	1	12	yes	complemented
31	C₂⁵×C₃₁	—	2	12	no	—
32	C₂⁵×C₃₁	—	2	16	no	—
33	C₂⁵×C₃₁	C₂³	1	3	yes	—
34	C₂⁵×C₃₁	C₂³	1	4	yes	—
35	C₂×#41×C₃₁	—	2	12	no	—
36	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic, complemented
37	C₂²×D₄×C₃₁	C₂³	1	12	yes	—
38	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
39	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic, complemented
40	C₂³×C₄×C₃₁	—	2	128	no	—
41	C₂³×C₄×C₃₁	—	2	12	no	—
42	C₂³×C₄×C₃₁	—	2	48	no	—
43	C₂³×C₄×C₃₁	—	2	48	no	—
44	C₂³×C₄×C₃₁	—	2	24	no	—
45	C₂³×C₄×C₃₁	—	2	24	no	—
46	C₂³×C₄×C₃₁	D₄	1	24	yes	complemented
47	C₂³×C₄×C₃₁	C₂³	1	12	yes	—
48	C₂³×C₄×C₃₁	C₂³	1	6	yes	—
49	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
50	C₂³×C₄×C₃₁	C₂³	1	6	yes	—
51	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₃₁	C₂³	1	2	yes	complemented
53	C₃₁×#123	—	2	24	no	—
54	C₃₁×C₂²⋊Q₈	—	2	24	no	—
55	C₃₁×#121	—	2	24	no	—
56	C₃₁×#120	—	2	24	no	—
57	C₃₁×#120	—	2	32	no	—
58	C₄×D₄×C₃₁	—	2	48	no	—
59	C₃₁×#117	—	2	12	no	—
60	C₂×C₄⋊C₄×C₃₁	C₂³	1	6	yes	complemented
61	C₂×C₄⋊C₄×C₃₁	C₂³	1	12	yes	complemented
62	C₂×C₂²⋊C₄×C₃₁	C₂³	1	6	yes	—
63	C₂×C₂²⋊C₄×C₃₁	C₂³	1	12	yes	—
64	C₂×C₂²⋊C₄×C₃₁	C₂³	1	24	yes	—
65	C₂×C₂²⋊C₄×C₃₁	C₂³	1	12	yes	complemented
66	C₂×C₄²×C₃₁	C₂³	1	6	yes	complemented
67	C₃₁×#95	C₂³	1	24	yes	complemented
68	C₂⁴×C₃₁	—	2	32	no	—
69	C₂⁴×C₃₁	—	2	192	no	—
70	C₂⁴×C₃₁	—	2	24	no	—
71	C₂⁴×C₃₁	—	2	12	no	—
72	C₂⁴×C₃₁	—	2	24	no	—
73	C₂⁴×C₃₁	—	2	24	no	—
74	C₂⁴×C₃₁	C₂×D₄	1	12	yes	—
75	C₂⁴×C₃₁	#41	1	16	yes	complemented
76	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
77	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
78	C₂⁴×C₃₁	C₂⁴	1	6	yes	—
79	#41×C₃₁	—	4	16	no	—
80	C₂×Q₈×C₃₁	—	2	6	no	—
81	C₂×D₄×C₃₁	—	2	24	no	—
82	C₂×D₄×C₃₁	—	2	12	no	—
83	C₂×D₄×C₃₁	—	2	48	no	—
84	C₂×D₄×C₃₁	—	2	6	no	—
85	C₂²×C₄×C₃₁	—	2	96	no	—
86	C₂²×C₄×C₃₁	—	2	128	no	—
87	C₂²×C₄×C₃₁	—	2	128	no	—
88	C₂²×C₄×C₃₁	—	2	24	no	—
89	C₂²×C₄×C₃₁	—	2	12	no	—
90	C₂²×C₄×C₃₁	—	2	96	no	—
91	C₂²×C₄×C₃₁	—	2	48	no	—
92	C₂²×C₄×C₃₁	—	2	24	no	—
93	C₂²×C₄×C₃₁	—	2	24	no	—
94	C₂²×C₄×C₃₁	—	2	12	no	—
95	C₂²×C₄×C₃₁	C₂×D₄	1	24	yes	—
96	C₂²×C₄×C₃₁	C₂×D₄	1	24	yes	—
97	C₂²×C₄×C₃₁	C₂×D₄	1	12	yes	—
98	C₂²×C₄×C₃₁	C₂×D₄	1	12	yes	—
99	C₂²×C₄×C₃₁	C₂⁴	1	12	yes	—
100	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
101	C₂²×C₄×C₃₁	C₂⁴	1	6	yes	—
102	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
103	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
104	C₄⋊C₄×C₃₁	—	2	12	no	—
105	C₄⋊C₄×C₃₁	—	2	24	no	—
106	C₂²⋊C₄×C₃₁	—	2	12	no	—
107	C₂²⋊C₄×C₃₁	—	2	24	no	—
108	C₂²⋊C₄×C₃₁	—	2	48	no	—
109	C₂²⋊C₄×C₃₁	—	2	24	no	—
110	C₄²×C₃₁	—	2	12	no	—
111	#36614	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂³×C₃₁	—	2	32	no	—
113	C₂³×C₃₁	—	2	256	no	—
114	C₂³×C₃₁	—	2	96	no	—
115	C₂³×C₃₁	—	2	96	no	—
116	C₂³×C₃₁	—	2	24	no	—
117	C₂³×C₃₁	—	2	48	no	—
118	C₂³×C₃₁	—	2	96	no	—
119	C₂³×C₃₁	—	2	12	no	—
120	C₂³×C₃₁	—	2	4	no	—
121	C₂³×C₃₁	—	2	12	no	—
122	C₂³×C₃₁	—	2	6	no	—
123	C₂³×C₃₁	—	2	8	no	—
124	C₂³×C₃₁	C₂²×D₄	1	6	yes	—
125	C₂³×C₃₁	C₂²×D₄	1	12	yes	—
126	C₂³×C₃₁	C₂×#41	1	24	yes	—
127	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
128	Q₈×C₃₁	—	4	4	no	—
129	D₄×C₃₁	—	4	8	no	—
130	D₄×C₃₁	—	4	48	no	—
131	D₄×C₃₁	—	4	4	no	—
132	C₂×C₄×C₃₁	—	2	96	no	—
133	C₂×C₄×C₃₁	—	2	24	no	—
134	C₂×C₄×C₃₁	—	2	12	no	—
135	C₂×C₄×C₃₁	—	2	48	no	—
136	C₂×C₄×C₃₁	—	2	48	no	—
137	C₂×C₄×C₃₁	—	2	12	no	—
138	C₂×C₄×C₃₁	—	2	6	no	—
139	C₂×C₄×C₃₁	—	2	24	no	—
140	C₂×C₄×C₃₁	—	4	8	no	—
141	C₂×C₄×C₃₁	#120	1	16	yes	complemented
142	C₂×C₄×C₃₁	C₂²×D₄	1	12	yes	—
143	C₂×C₄×C₃₁	C₂²×D₄	1	6	yes	—
144	C₂×C₄×C₃₁	C₂²×D₄	1	6	yes	—
145	C₂⁵×C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
146	C₂×#525	C₂×C₃₁	1	3	yes	complemented
147	#2849	C₂×C₃₁	1	6	yes	complemented
148	#2848	C₂×C₃₁	1	4	yes	complemented
149	#2847	C₂×C₃₁	1	4	yes	complemented
150	#2846	C₂×C₃₁	1	2	yes	complemented
151	C₄×#120	C₂×C₃₁	1	8	yes	complemented
152	#2280	C₂×C₃₁	1	3	yes	complemented
153	C₂²×C₃₁	—	2	96	no	—
154	C₂²×C₃₁	—	2	128	no	—
155	C₂²×C₃₁	—	2	12	no	—
156	C₂²×C₃₁	—	2	12	no	—
157	C₂²×C₃₁	—	2	12	no	—
158	C₂²×C₃₁	—	2	48	no	—
159	C₂²×C₃₁	—	4	2	no	—
160	C₂²×C₃₁	—	4	12	no	—
161	C₂²×C₃₁	C₂×#120	1	4	yes	—
162	C₂²×C₃₁	#525	1	24	yes	complemented
163	C₂²×C₃₁	C₂³×D₄	1	3	yes	—
164	C₂²×C₃₁	C₂²×#41	1	4	yes	—
165	C₄×C₃₁	—	2	12	no	—
166	C₄×C₃₁	—	4	2	no	—
167	C₄×C₃₁	—	4	12	no	—
168	C₄×C₃₁	C₂×#120	1	4	yes	—
169	C₄×C₃₁	C₂×#120	1	4	yes	—
170	C₂⁶	C₂²×C₃₁	1	1	yes	characteristic
171	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
172	C₂⁴×C₄	—	2	24	no	—
173	C₂⁴×C₄	C₂²×C₃₁	1	4	yes	—
174	C₂⁴×C₄	C₂²×C₃₁	1	3	yes	—
175	C₂⁴×C₄	C₂²×C₃₁	1	4	yes	—
176	C₂⁴×C₄	C₂²×C₃₁	1	3	yes	—
177	#525	—	2	24	no	—
178	C₂×#123	C₂²×C₃₁	1	6	yes	complemented
179	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	6	yes	complemented
180	C₂×#121	C₂²×C₃₁	1	6	yes	complemented
181	C₂×#120	C₂²×C₃₁	1	8	yes	—
182	C₂×#120	C₂²×C₃₁	1	6	yes	—
183	C₂×C₄×D₄	C₂²×C₃₁	1	12	yes	complemented
184	C₂×#117	C₂²×C₃₁	1	3	yes	complemented
185	#386	C₂²×C₃₁	1	24	yes	complemented
186	#385	C₂²×C₃₁	1	24	yes	complemented
187	#381	C₂²×C₃₁	1	6	yes	complemented
188	#380	C₂²×C₃₁	1	12	yes	complemented
189	#379	C₂²×C₃₁	1	8	yes	—
190	#379	C₂²×C₃₁	1	6	yes	—
191	C₄×C₂²⋊C₄	C₂²×C₃₁	1	12	yes	complemented
192	C₂×C₃₁	—	2	4	no	—
193	C₂×C₃₁	—	2	24	no	—
194	C₂×C₃₁	—	8	2	no	—
195	C₂×C₃₁	C₂²×#120	1	1	yes	characteristic
196	C₂×C₃₁	C₂×#525	1	6	yes	—
197	C₂⁵	—	2	12	no	—
198	C₂⁵	—	2	16	no	—
199	C₂⁵	C₂³×C₃₁	1	3	yes	—
200	C₂⁵	C₂³×C₃₁	1	4	yes	—
201	C₂×#41	—	2	12	no	—
202	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic, complemented
203	C₂²×D₄	C₂³×C₃₁	1	12	yes	—
204	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
205	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic, complemented
206	C₂³×C₄	—	2	128	no	—
207	C₂³×C₄	—	2	12	no	—
208	C₂³×C₄	—	2	48	no	—
209	C₂³×C₄	—	2	48	no	—
210	C₂³×C₄	—	2	24	no	—
211	C₂³×C₄	—	2	24	no	—
212	C₂³×C₄	D₄×C₃₁	1	24	yes	complemented
213	C₂³×C₄	C₂³×C₃₁	1	12	yes	—
214	C₂³×C₄	C₂³×C₃₁	1	6	yes	—
215	C₂³×C₄	C₂³×C₃₁	1	6	yes	—
216	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
217	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
218	C₂³×C₄	C₂³×C₃₁	1	2	yes	complemented
219	#123	—	2	24	no	—
220	C₂²⋊Q₈	—	2	24	no	—
221	#121	—	2	24	no	—
222	#120	—	2	24	no	—
223	#120	—	2	32	no	—
224	C₄×D₄	—	2	48	no	—
225	#117	—	2	12	no	—
226	C₂×C₄⋊C₄	C₂³×C₃₁	1	6	yes	complemented
227	C₂×C₄⋊C₄	C₂³×C₃₁	1	12	yes	complemented
228	C₂×C₂²⋊C₄	C₂³×C₃₁	1	6	yes	—
229	C₂×C₂²⋊C₄	C₂³×C₃₁	1	12	yes	—
230	C₂×C₂²⋊C₄	C₂³×C₃₁	1	24	yes	—
231	C₂×C₂²⋊C₄	C₂³×C₃₁	1	12	yes	complemented
232	C₂×C₄²	C₂³×C₃₁	1	6	yes	complemented
233	#95	C₂³×C₃₁	1	24	yes	complemented
234	C₃₁	#36614	1	1	yes	characteristic, direct product factor, Sylow
235	C₂⁴	—	2	32	no	—
236	C₂⁴	—	2	192	no	—
237	C₂⁴	—	2	24	no	—
238	C₂⁴	—	2	12	no	—
239	C₂⁴	—	2	24	no	—
240	C₂⁴	—	2	24	no	—
241	C₂⁴	C₂×D₄×C₃₁	1	12	yes	—
242	C₂⁴	#41×C₃₁	1	16	yes	complemented
243	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
244	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
245	C₂⁴	C₂⁴×C₃₁	1	6	yes	—
246	#41	—	4	16	no	—
247	C₂×Q₈	—	2	6	no	—
248	C₂×D₄	—	2	24	no	—
249	C₂×D₄	—	2	12	no	—
250	C₂×D₄	—	2	48	no	—
251	C₂×D₄	—	2	6	no	—
252	C₂²×C₄	—	2	96	no	—
253	C₂²×C₄	—	2	128	no	—
254	C₂²×C₄	—	2	128	no	—
255	C₂²×C₄	—	2	24	no	—
256	C₂²×C₄	—	2	12	no	—
257	C₂²×C₄	—	2	96	no	—
258	C₂²×C₄	—	2	48	no	—
259	C₂²×C₄	—	2	24	no	—
260	C₂²×C₄	—	2	24	no	—
261	C₂²×C₄	—	2	12	no	—
262	C₂²×C₄	C₂×D₄×C₃₁	1	24	yes	—
263	C₂²×C₄	C₂×D₄×C₃₁	1	24	yes	—
264	C₂²×C₄	C₂×D₄×C₃₁	1	12	yes	—
265	C₂²×C₄	C₂×D₄×C₃₁	1	12	yes	—
266	C₂²×C₄	C₂⁴×C₃₁	1	12	yes	—
267	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
268	C₂²×C₄	C₂⁴×C₃₁	1	6	yes	—
269	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
270	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
271	C₄⋊C₄	—	2	12	no	—
272	C₄⋊C₄	—	2	24	no	—
273	C₂²⋊C₄	—	2	12	no	—
274	C₂²⋊C₄	—	2	24	no	—
275	C₂²⋊C₄	—	2	48	no	—
276	C₂²⋊C₄	—	2	24	no	—
277	C₄²	—	2	12	no	—
278	C₂³	—	2	32	no	—
279	C₂³	—	2	256	no	—
280	C₂³	—	2	96	no	—
281	C₂³	—	2	96	no	—
282	C₂³	—	2	24	no	—
283	C₂³	—	2	48	no	—
284	C₂³	—	2	96	no	—
285	C₂³	—	2	12	no	—
286	C₂³	—	2	4	no	—
287	C₂³	—	2	12	no	—
288	C₂³	—	2	6	no	—
289	C₂³	—	2	8	no	—
290	C₂³	C₂²×D₄×C₃₁	1	6	yes	—
291	C₂³	C₂²×D₄×C₃₁	1	12	yes	—
292	C₂³	C₂×#41×C₃₁	1	24	yes	—
293	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
294	Q₈	—	4	4	no	—
295	D₄	—	4	8	no	—
296	D₄	—	4	48	no	—
297	D₄	—	4	4	no	—
298	C₂×C₄	—	2	96	no	—
299	C₂×C₄	—	2	24	no	—
300	C₂×C₄	—	2	12	no	—
301	C₂×C₄	—	2	48	no	—
302	C₂×C₄	—	2	48	no	—
303	C₂×C₄	—	2	12	no	—
304	C₂×C₄	—	2	6	no	—
305	C₂×C₄	—	2	24	no	—
306	C₂×C₄	—	4	8	no	—
307	C₂×C₄	C₃₁×#120	1	16	yes	complemented
308	C₂×C₄	C₂²×D₄×C₃₁	1	12	yes	—
309	C₂×C₄	C₂²×D₄×C₃₁	1	6	yes	—
310	C₂×C₄	C₂²×D₄×C₃₁	1	6	yes	—
311	C₂²	—	2	96	no	—
312	C₂²	—	2	128	no	—
313	C₂²	—	2	12	no	—
314	C₂²	—	2	12	no	—
315	C₂²	—	2	12	no	—
316	C₂²	—	2	48	no	—
317	C₂²	—	4	2	no	—
318	C₂²	—	4	12	no	—
319	C₂²	C₂×C₃₁×#120	1	4	yes	—
320	C₂²	C₃₁×#525	1	24	yes	complemented
321	C₂²	C₂³×D₄×C₃₁	1	3	yes	—
322	C₂²	C₂²×#41×C₃₁	1	4	yes	—
323	C₄	—	2	12	no	—
324	C₄	—	4	2	no	—
325	C₄	—	4	12	no	—
326	C₄	C₂×C₃₁×#120	1	4	yes	—
327	C₄	C₂×C₃₁×#120	1	4	yes	—
328	C₂	—	2	4	no	—
329	C₂	—	2	24	no	—
330	C₂	—	8	2	no	—
331	C₂	C₂²×C₃₁×#120	1	1	yes	characteristic
332	C₂	C₂×C₃₁×#525	1	6	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂⁵×C₄×C₃₁	C₂	semidirect
2. C₂×C₃₁×#525	C₂	semidirect
3. C₃₁×#2849	C₂	semidirect
4. C₃₁×#2848	C₂	semidirect
5. C₃₁×#2847	C₂	semidirect
6. C₃₁×#2846	C₂	semidirect
7. C₄×C₃₁×#120	C₂	semidirect
8. C₃₁×#2280	C₂	semidirect
10. C₂²×#41×C₃₁	C₂²	semidirect
17. C₂×C₃₁×#123	C₂²	semidirect
18. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
19. C₂×C₃₁×#121	C₂²	semidirect
22. C₂×C₄×D₄×C₃₁	C₂²	semidirect
23. C₂×C₃₁×#117	C₂²	semidirect
24. C₃₁×#386	C₂²	semidirect
25. C₃₁×#385	C₂²	semidirect
26. C₃₁×#381	C₂²	semidirect
27. C₃₁×#380	C₂²	semidirect
30. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
36. C₂²×Q₈×C₃₁	C₂³	semidirect
39. C₂²×D₄×C₃₁	C₂³	semidirect
46. C₂³×C₄×C₃₁	D₄	semidirect
52. C₂³×C₄×C₃₁	C₂³	semidirect
60. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
61. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
65. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
66. C₂×C₄²×C₃₁	C₂³	semidirect
67. C₃₁×#95	C₂³	semidirect
75. C₂⁴×C₃₁	#41	semidirect
111. #36614	C₃₁	direct (N × H)
141. C₂×C₄×C₃₁	#120	semidirect
145. C₂⁵×C₄	C₂×C₃₁	semidirect
146. C₂×#525	C₂×C₃₁	semidirect
147. #2849	C₂×C₃₁	semidirect
148. #2848	C₂×C₃₁	semidirect
149. #2847	C₂×C₃₁	semidirect
150. #2846	C₂×C₃₁	semidirect
151. C₄×#120	C₂×C₃₁	semidirect
152. #2280	C₂×C₃₁	semidirect
162. C₂²×C₃₁	#525	semidirect
171. C₂²×#41	C₂²×C₃₁	semidirect
178. C₂×#123	C₂²×C₃₁	semidirect
179. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
180. C₂×#121	C₂²×C₃₁	semidirect
183. C₂×C₄×D₄	C₂²×C₃₁	semidirect
184. C₂×#117	C₂²×C₃₁	semidirect
185. #386	C₂²×C₃₁	semidirect
186. #385	C₂²×C₃₁	semidirect
187. #381	C₂²×C₃₁	semidirect
188. #380	C₂²×C₃₁	semidirect
191. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
202. C₂²×Q₈	C₂³×C₃₁	semidirect
205. C₂²×D₄	C₂³×C₃₁	semidirect
212. C₂³×C₄	D₄×C₃₁	semidirect
218. C₂³×C₄	C₂³×C₃₁	semidirect
226. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
227. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
231. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
232. C₂×C₄²	C₂³×C₃₁	semidirect
233. #95	C₂³×C₃₁	semidirect
234. C₃₁	#36614	direct (N × H)
242. C₂⁴	#41×C₃₁	semidirect
307. C₂×C₄	C₃₁×#120	semidirect
320. C₂²	C₃₁×#525	semidirect

Maximal subgroups

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

subgroup	index
C₂⁵×C₄×C₃₁	2
C₂×C₃₁×#525	2
C₃₁×#2849	2
C₃₁×#2848	2
C₃₁×#2847	2
C₃₁×#2846	2
C₄×C₃₁×#120	2
C₃₁×#2280	2
#36614	31

Subgroups — C31×#36614 #21493373

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#36614 #21493373