Subgroups — C₃₁×#12787 #21469546

Order 7936.

450 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₃₁×#131	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2150	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₁×#350	C₂	1	2	yes	maximal
5	C₃₁×#1379	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#131	C₄	1	1	yes	characteristic
7	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
8	C₄×#41×C₃₁	C₄	1	1	yes	characteristic
9	C₂×C₃₁×M₃₂	C₂²	1	2	yes	—
10	C₂²×C₁₆×C₃₁	C₂²	1	2	yes	—
11	C₃₁×#405	—	2	1	no	—
12	C₃₁×#405	—	2	1	no	—
13	C₃₁×#405	C₄	1	1	yes	characteristic
14	C₃₁×#405	C₂²	1	1	yes	characteristic
15	C₄×M₁₆×C₃₁	—	2	1	no	—
16	C₄×M₁₆×C₃₁	C₄	1	1	yes	characteristic
17	C₂×C₄×C₈×C₃₁	—	2	1	no	—
18	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
19	C₃₁×C₄⋊C₁₆	—	2	1	no	—
20	C₃₁×C₄⋊C₁₆	—	2	1	no	—
21	C₃₁×C₄⋊C₁₆	—	2	1	no	—
22	C₃₁×C₄⋊C₁₆	—	2	1	no	—
23	C₃₁×#350	—	2	4	no	—
24	C₂×#41×C₃₁	C₂×C₄	1	1	yes	characteristic
25	C₃₁×#131	—	2	2	no	—
26	C₃₁×#131	—	2	2	no	—
27	C₃₁×#131	—	2	1	no	—
28	C₃₁×#131	—	2	1	no	—
29	C₃₁×#131	D₄	1	2	yes	—
30	C₃₁×#131	Q₈	1	2	yes	—
31	C₂×M₁₆×C₃₁	—	2	1	no	—
32	C₂×M₁₆×C₃₁	—	2	1	no	—
33	C₂×M₁₆×C₃₁	C₂×C₄	1	1	yes	characteristic
34	C₂×M₁₆×C₃₁	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₈×C₃₁	—	2	1	no	—
36	C₂²×C₈×C₃₁	—	2	1	no	—
37	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
39	C₄×Q₈×C₃₁	C₈	1	1	yes	characteristic
40	C₄×Q₈×C₃₁	C₈	1	1	yes	characteristic
41	C₄×D₄×C₃₁	—	2	1	no	—
42	C₄×D₄×C₃₁	—	2	1	no	—
43	C₄×D₄×C₃₁	C₈	1	1	yes	characteristic
44	C₄×D₄×C₃₁	C₈	1	1	yes	characteristic
45	C₃₁×#117	—	2	1	no	—
46	C₃₁×#117	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₃₁	—	2	1	no	—
48	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
49	C₃₁×M₃₂	—	2	2	no	—
50	C₃₁×M₃₂	—	2	2	no	—
51	C₂×C₁₆×C₃₁	—	2	2	no	—
52	C₂×C₁₆×C₃₁	—	2	2	no	—
53	C₂×C₁₆×C₃₁	—	2	2	no	—
54	C₂×C₁₆×C₃₁	—	2	2	no	—
55	C₃₁×#97	—	2	1	no	—
56	C₃₁×#97	—	2	1	no	—
57	C₃₁×#97	—	2	1	no	—
58	C₄×C₈×C₃₁	—	2	1	no	—
59	C₄×C₈×C₃₁	—	2	1	no	—
60	C₄×C₈×C₃₁	—	2	1	no	—
61	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
62	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
63	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
64	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
65	#41×C₃₁	—	2	1	no	—
66	#41×C₃₁	—	2	1	no	—
67	#41×C₃₁	C₄⋊C₄	1	2	yes	—
68	#41×C₃₁	M₁₆	1	2	yes	—
69	C₂×Q₈×C₃₁	C₂×C₈	1	1	yes	characteristic
70	C₂×D₄×C₃₁	—	2	1	no	—
71	C₂×D₄×C₃₁	C₂×C₈	1	1	yes	characteristic
72	C₂²×C₄×C₃₁	—	2	1	no	—
73	C₂²×C₄×C₃₁	—	2	1	no	—
74	C₂²×C₄×C₃₁	—	2	1	no	—
75	C₂²×C₄×C₃₁	M₁₆	1	1	yes	characteristic
76	C₂²×C₄×C₃₁	M₁₆	1	1	yes	characteristic
77	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
78	M₁₆×C₃₁	—	2	4	no	—
79	M₁₆×C₃₁	—	2	1	no	—
80	M₁₆×C₃₁	—	2	1	no	—
81	M₁₆×C₃₁	—	2	2	no	—
82	M₁₆×C₃₁	—	2	2	no	—
83	M₁₆×C₃₁	C₄⋊C₄	1	2	yes	—
84	M₁₆×C₃₁	M₁₆	1	2	yes	—
85	C₂×C₈×C₃₁	—	2	4	no	—
86	C₂×C₈×C₃₁	—	2	1	no	—
87	C₂×C₈×C₃₁	—	2	1	no	—
88	C₂×C₈×C₃₁	—	2	1	no	—
89	C₂×C₈×C₃₁	—	2	1	no	—
90	C₂×C₈×C₃₁	—	2	2	no	—
91	C₂×C₈×C₃₁	—	2	2	no	—
92	C₂×C₈×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₈×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
95	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
96	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
97	C₂×C₈×C₃₁	C₂×Q₈	1	1	yes	characteristic
98	C₂×C₈×C₃₁	#41	1	1	yes	characteristic
99	C₂×C₈×C₃₁	#41	1	1	yes	characteristic
100	C₄⋊C₄×C₃₁	—	2	1	no	—
101	C₄⋊C₄×C₃₁	—	2	1	no	—
102	C₄⋊C₄×C₃₁	C₂×C₈	1	1	yes	characteristic
103	C₄⋊C₄×C₃₁	C₂×C₈	1	1	yes	characteristic
104	C₂²⋊C₄×C₃₁	—	2	1	no	—
105	C₂²⋊C₄×C₃₁	—	2	1	no	—
106	C₂²⋊C₄×C₃₁	—	2	1	no	—
107	C₄²×C₃₁	—	2	1	no	—
108	C₄²×C₃₁	—	2	1	no	—
109	C₄²×C₃₁	—	2	1	no	—
110	C₄²×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
111	C₄²×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
112	C₄²×C₃₁	C₂×C₈	1	1	yes	characteristic
113	C₄²×C₃₁	C₂×C₈	1	1	yes	characteristic
114	C₁₆×C₃₁	—	4	2	no	—
115	C₁₆×C₃₁	—	4	2	no	—
116	#12787	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂³×C₃₁	—	2	1	no	—
118	C₂³×C₃₁	C₂×M₁₆	1	1	yes	characteristic
119	Q₈×C₃₁	—	2	1	no	—
120	Q₈×C₃₁	C₄⋊C₈	1	2	yes	—
121	D₄×C₃₁	—	2	2	no	—
122	D₄×C₃₁	—	2	2	no	—
123	D₄×C₃₁	—	2	1	no	—
124	D₄×C₃₁	C₄⋊C₈	1	2	yes	—
125	C₂×C₄×C₃₁	—	2	1	no	—
126	C₂×C₄×C₃₁	—	2	2	no	—
127	C₂×C₄×C₃₁	—	2	2	no	—
128	C₂×C₄×C₃₁	—	2	2	no	—
129	C₂×C₄×C₃₁	—	2	1	no	—
130	C₂×C₄×C₃₁	—	2	1	no	—
131	C₂×C₄×C₃₁	—	4	1	no	—
132	C₂×C₄×C₃₁	—	4	2	no	—
133	C₂×C₄×C₃₁	—	4	2	no	—
134	C₂×C₄×C₃₁	C₂²⋊C₈	1	1	yes	characteristic
135	C₂×C₄×C₃₁	C₂²⋊C₈	1	1	yes	characteristic
136	C₂×C₄×C₃₁	C₂²⋊C₈	1	1	yes	characteristic
137	C₂×C₄×C₃₁	C₂²⋊C₈	1	1	yes	characteristic
138	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₃₁	#117	1	1	yes	characteristic
141	C₂×C₄×C₃₁	C₂²×C₈	1	1	yes	characteristic
142	C₂×C₄×C₃₁	C₂×M₁₆	1	1	yes	characteristic
143	C₂×C₄×C₃₁	C₂×M₁₆	1	1	yes	characteristic
144	C₈×C₃₁	—	2	2	no	—
145	C₈×C₃₁	—	2	1	no	—
146	C₈×C₃₁	—	2	2	no	—
147	C₈×C₃₁	—	2	1	no	—
148	C₈×C₃₁	#121	1	1	yes	characteristic
149	C₈×C₃₁	#121	1	1	yes	characteristic
150	C₈×C₃₁	C₂²⋊Q₈	1	1	yes	characteristic
151	C₈×C₃₁	C₂²⋊Q₈	1	1	yes	characteristic
152	C₄×#131	C₂×C₃₁	1	1	yes	characteristic
153	#2150	C₂×C₃₁	1	1	yes	characteristic, complemented
154	C₂×C₄⋊C₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
155	C₂×#350	C₂×C₃₁	1	2	yes	—
156	#1379	C₂×C₃₁	1	2	yes	complemented
157	C₂²×C₃₁	—	2	1	no	—
158	C₂²×C₃₁	—	2	1	no	—
159	C₂²×C₃₁	—	2	2	no	—
160	C₂²×C₃₁	—	4	1	no	—
161	C₂²×C₃₁	—	4	1	no	—
162	C₂²×C₃₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
163	C₂²×C₃₁	#423	1	1	yes	characteristic
164	C₂²×C₃₁	#432	1	1	yes	characteristic
165	C₄×C₃₁	—	2	2	no	—
166	C₄×C₃₁	—	2	1	no	—
167	C₄×C₃₁	—	2	1	no	—
168	C₄×C₃₁	—	2	1	no	—
169	C₄×C₃₁	—	4	1	no	—
170	C₄×C₃₁	—	4	1	no	—
171	C₄×C₃₁	#350	1	2	yes	complemented
172	C₄×C₃₁	#380	1	1	yes	characteristic
173	C₄×C₃₁	#407	1	1	yes	characteristic
174	C₄×C₃₁	C₂×C₄⋊C₈	1	1	yes	characteristic
175	C₄×C₃₁	#431	1	1	yes	characteristic
176	C₂×#131	C₄×C₃₁	1	1	yes	characteristic
177	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
178	C₄×#41	C₄×C₃₁	1	1	yes	characteristic
179	C₂×M₃₂	C₂²×C₃₁	1	2	yes	—
180	C₂²×C₁₆	C₂²×C₃₁	1	2	yes	—
181	#405	—	2	1	no	—
182	#405	—	2	1	no	—
183	#405	C₄×C₃₁	1	1	yes	characteristic
184	#405	C₂²×C₃₁	1	1	yes	characteristic
185	C₄×M₁₆	—	2	1	no	—
186	C₄×M₁₆	C₄×C₃₁	1	1	yes	characteristic
187	C₂×C₄×C₈	—	2	1	no	—
188	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
189	C₄⋊C₁₆	—	2	1	no	—
190	C₄⋊C₁₆	—	2	1	no	—
191	C₄⋊C₁₆	—	2	1	no	—
192	C₄⋊C₁₆	—	2	1	no	—
193	#350	—	2	4	no	—
194	C₂×C₃₁	—	2	1	no	—
195	C₂×C₃₁	—	2	1	no	—
196	C₂×C₃₁	—	4	2	no	—
197	C₂×C₃₁	#1797	1	1	yes	characteristic
198	C₂×C₃₁	C₂×#350	1	1	yes	characteristic
199	C₂×C₃₁	#2117	1	1	yes	characteristic
200	C₂×#41	C₂×C₄×C₃₁	1	1	yes	characteristic
201	#131	—	2	2	no	—
202	#131	—	2	2	no	—
203	#131	—	2	1	no	—
204	#131	—	2	1	no	—
205	#131	D₄×C₃₁	1	2	yes	—
206	#131	Q₈×C₃₁	1	2	yes	—
207	C₂×M₁₆	—	2	1	no	—
208	C₂×M₁₆	—	2	1	no	—
209	C₂×M₁₆	C₂×C₄×C₃₁	1	1	yes	characteristic
210	C₂×M₁₆	C₂×C₄×C₃₁	1	1	yes	characteristic
211	C₂²×C₈	—	2	1	no	—
212	C₂²×C₈	—	2	1	no	—
213	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
214	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
215	C₄×Q₈	C₈×C₃₁	1	1	yes	characteristic
216	C₄×Q₈	C₈×C₃₁	1	1	yes	characteristic
217	C₄×D₄	—	2	1	no	—
218	C₄×D₄	—	2	1	no	—
219	C₄×D₄	C₈×C₃₁	1	1	yes	characteristic
220	C₄×D₄	C₈×C₃₁	1	1	yes	characteristic
221	#117	—	2	1	no	—
222	#117	C₂×C₄×C₃₁	1	1	yes	characteristic
223	C₂×C₄²	—	2	1	no	—
224	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
225	M₃₂	—	2	2	no	—
226	M₃₂	—	2	2	no	—
227	C₂×C₁₆	—	2	2	no	—
228	C₂×C₁₆	—	2	2	no	—
229	C₂×C₁₆	—	2	2	no	—
230	C₂×C₁₆	—	2	2	no	—
231	#97	—	2	1	no	—
232	#97	—	2	1	no	—
233	#97	—	2	1	no	—
234	C₄×C₈	—	2	1	no	—
235	C₄×C₈	—	2	1	no	—
236	C₄×C₈	—	2	1	no	—
237	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
238	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
239	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
240	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
241	C₃₁	#12787	1	1	yes	characteristic, direct product factor, Sylow
242	#41	—	2	1	no	—
243	#41	—	2	1	no	—
244	#41	C₄⋊C₄×C₃₁	1	2	yes	—
245	#41	M₁₆×C₃₁	1	2	yes	—
246	C₂×Q₈	C₂×C₈×C₃₁	1	1	yes	characteristic
247	C₂×D₄	—	2	1	no	—
248	C₂×D₄	C₂×C₈×C₃₁	1	1	yes	characteristic
249	C₂²×C₄	—	2	1	no	—
250	C₂²×C₄	—	2	1	no	—
251	C₂²×C₄	—	2	1	no	—
252	C₂²×C₄	M₁₆×C₃₁	1	1	yes	characteristic
253	C₂²×C₄	M₁₆×C₃₁	1	1	yes	characteristic
254	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
255	M₁₆	—	2	4	no	—
256	M₁₆	—	2	1	no	—
257	M₁₆	—	2	1	no	—
258	M₁₆	—	2	2	no	—
259	M₁₆	—	2	2	no	—
260	M₁₆	C₄⋊C₄×C₃₁	1	2	yes	—
261	M₁₆	M₁₆×C₃₁	1	2	yes	—
262	C₂×C₈	—	2	4	no	—
263	C₂×C₈	—	2	1	no	—
264	C₂×C₈	—	2	1	no	—
265	C₂×C₈	—	2	1	no	—
266	C₂×C₈	—	2	1	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
270	C₂×C₈	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
271	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
272	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
273	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
274	C₂×C₈	C₂×Q₈×C₃₁	1	1	yes	characteristic
275	C₂×C₈	#41×C₃₁	1	1	yes	characteristic
276	C₂×C₈	#41×C₃₁	1	1	yes	characteristic
277	C₄⋊C₄	—	2	1	no	—
278	C₄⋊C₄	—	2	1	no	—
279	C₄⋊C₄	C₂×C₈×C₃₁	1	1	yes	characteristic
280	C₄⋊C₄	C₂×C₈×C₃₁	1	1	yes	characteristic
281	C₂²⋊C₄	—	2	1	no	—
282	C₂²⋊C₄	—	2	1	no	—
283	C₂²⋊C₄	—	2	1	no	—
284	C₄²	—	2	1	no	—
285	C₄²	—	2	1	no	—
286	C₄²	—	2	1	no	—
287	C₄²	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
288	C₄²	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
289	C₄²	C₂×C₈×C₃₁	1	1	yes	characteristic
290	C₄²	C₂×C₈×C₃₁	1	1	yes	characteristic
291	C₁₆	—	4	2	no	—
292	C₁₆	—	4	2	no	—
293	C₂³	—	2	1	no	—
294	C₂³	C₂×M₁₆×C₃₁	1	1	yes	characteristic
295	Q₈	—	2	1	no	—
296	Q₈	C₃₁×C₄⋊C₈	1	2	yes	—
297	D₄	—	2	2	no	—
298	D₄	—	2	2	no	—
299	D₄	—	2	1	no	—
300	D₄	C₃₁×C₄⋊C₈	1	2	yes	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	4	1	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	4	2	no	—
310	C₂×C₄	C₃₁×C₂²⋊C₈	1	1	yes	characteristic
311	C₂×C₄	C₃₁×C₂²⋊C₈	1	1	yes	characteristic
312	C₂×C₄	C₃₁×C₂²⋊C₈	1	1	yes	characteristic
313	C₂×C₄	C₃₁×C₂²⋊C₈	1	1	yes	characteristic
314	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
315	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
316	C₂×C₄	C₃₁×#117	1	1	yes	characteristic
317	C₂×C₄	C₂²×C₈×C₃₁	1	1	yes	characteristic
318	C₂×C₄	C₂×M₁₆×C₃₁	1	1	yes	characteristic
319	C₂×C₄	C₂×M₁₆×C₃₁	1	1	yes	characteristic
320	C₈	—	2	1	no	—
321	C₈	—	2	2	no	—
322	C₈	—	2	1	no	—
323	C₈	—	2	2	no	—
324	C₈	C₃₁×#121	1	1	yes	characteristic
325	C₈	C₃₁×#121	1	1	yes	characteristic
326	C₈	C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
327	C₈	C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
328	C₂²	—	2	1	no	—
329	C₂²	—	2	1	no	—
330	C₂²	—	2	2	no	—
331	C₂²	—	4	1	no	—
332	C₂²	—	4	1	no	—
333	C₂²	C₂×C₃₁×C₂²⋊C₈	1	1	yes	characteristic
334	C₂²	C₃₁×#423	1	1	yes	characteristic
335	C₂²	C₃₁×#432	1	1	yes	characteristic
336	C₄	—	2	2	no	—
337	C₄	—	2	1	no	—
338	C₄	—	2	1	no	—
339	C₄	—	2	1	no	—
340	C₄	—	4	1	no	—
341	C₄	—	4	1	no	—
342	C₄	C₃₁×#350	1	2	yes	complemented
343	C₄	C₃₁×#380	1	1	yes	characteristic
344	C₄	C₃₁×#407	1	1	yes	characteristic
345	C₄	C₂×C₃₁×C₄⋊C₈	1	1	yes	characteristic
346	C₄	C₃₁×#431	1	1	yes	characteristic
347	C₂	—	2	1	no	—
348	C₂	—	2	1	no	—
349	C₂	—	4	2	no	—
350	C₂	C₃₁×#1797	1	1	yes	characteristic
351	C₂	C₂×C₃₁×#350	1	1	yes	characteristic
352	C₂	C₃₁×#2117	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₃₁	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₃₁
Frattini, cosocle	C₂²×C₈	C₂³×C₃₁
socle	C₂²×C₃₁	C₂×C₂²⋊C₈
prime radical	C₂×#41×C₃₁	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₃₁ ◁ C₂×C₄×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2150	C₂	semidirect
3. C₂×C₃₁×C₄⋊C₁₆	C₂	semidirect
5. C₃₁×#1379	C₂	semidirect
116. #12787	C₃₁	direct (N × H)
153. #2150	C₂×C₃₁	semidirect
154. C₂×C₄⋊C₁₆	C₂×C₃₁	semidirect
156. #1379	C₂×C₃₁	semidirect
171. C₄×C₃₁	#350	semidirect
241. C₃₁	#12787	direct (N × H)
342. C₄	C₃₁×#350	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₃₁×#131	2
C₃₁×#2150	2
C₂×C₃₁×C₄⋊C₁₆	2
C₂×C₃₁×#350	2
C₃₁×#1379	2
#12787	31

Subgroups — C31×#12787 #21469546

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#12787 #21469546