Subgroups — C₃₁×#17520 #21474279

Order 7936.

1074 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3483	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2991	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₃₁×#131	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#1492	C₂	1	3	yes	maximal, complemented
5	C₃₁×#1489	C₂	1	3	yes	maximal, complemented
6	C₃₁×#1484	C₂	1	3	yes	maximal, complemented
7	C₃₁×#1476	C₂	1	3	yes	maximal, complemented
8	C₂×C₃₁×#131	—	2	1	no	—
9	Q₈²×C₃₁	C₄	1	1	yes	characteristic
10	C₃₁×#555	—	2	3	no	—
11	C₃₁×#555	C₄	1	3	yes	—
12	C₃₁×#550	—	2	1	no	—
13	C₃₁×#550	C₄	1	3	yes	—
14	C₃₁×#550	C₄	1	1	yes	characteristic
15	C₃₁×#532	—	2	3	no	—
16	C₃₁×#532	C₂²	1	3	yes	—
17	C₄×#41×C₃₁	—	2	1	no	—
18	C₄×#41×C₃₁	C₂²	1	3	yes	—
19	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
20	C₈×Q₈×C₃₁	—	2	1	no	—
21	C₃₁×#436	—	2	3	no	—
22	C₃₁×#431	C₂²	1	3	yes	—
23	C₃₁×#423	C₂²	1	3	yes	—
24	C₃₁×#405	—	2	3	no	—
25	C₄×M₁₆×C₃₁	C₂²	1	3	yes	—
26	C₂×C₄×C₈×C₃₁	C₂²	1	3	yes	—
27	C₃₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
28	C₃₁×Q₈⋊C₈	C₂²	1	3	yes	—
29	C₃₁×D₄⋊C₈	C₂²	1	3	yes	—
30	C₃₁×D₄⋊C₈	C₂²	1	3	yes	—
31	C₃₁×D₄⋊C₈	C₂²	1	6	yes	—
32	C₂×#41×C₃₁	—	2	1	no	—
33	C₂×#41×C₃₁	—	2	3	no	—
34	C₂×#41×C₃₁	C₂×C₄	1	3	yes	—
35	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
36	C₃₁×#131	—	2	8	no	—
37	C₂×M₁₆×C₃₁	—	2	3	no	—
38	C₂×M₁₆×C₃₁	—	2	3	no	—
39	C₂²×C₈×C₃₁	—	2	3	no	—
40	C₃₁×C₄⋊Q₈	—	2	3	no	—
41	C₃₁×C₄⋊Q₈	C₂×C₄	1	3	yes	—
42	C₃₁×#127	—	2	3	no	—
43	C₃₁×#127	C₂×C₄	1	3	yes	—
44	C₃₁×#124	—	2	6	no	—
45	C₃₁×#124	—	2	3	no	—
46	C₃₁×#121	—	2	3	no	—
47	C₃₁×#121	—	2	3	no	—
48	C₃₁×#121	—	2	3	no	—
49	C₃₁×#121	—	2	6	no	—
50	C₃₁×#121	C₂×C₄	1	6	yes	—
51	C₄×Q₈×C₃₁	—	2	1	no	—
52	C₄×Q₈×C₃₁	C₂×C₄	1	3	yes	—
53	C₄×Q₈×C₃₁	C₂×C₄	1	1	yes	characteristic
54	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
55	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
56	C₄×D₄×C₃₁	—	2	3	no	—
57	C₄×D₄×C₃₁	—	2	3	no	—
58	C₄×D₄×C₃₁	—	2	3	no	—
59	C₄×D₄×C₃₁	—	2	3	no	—
60	C₄×D₄×C₃₁	C₂×C₄	1	3	yes	—
61	C₄×D₄×C₃₁	C₂×C₄	1	3	yes	—
62	C₄×D₄×C₃₁	D₄	1	3	yes	—
63	C₄×D₄×C₃₁	C₂³	1	3	yes	—
64	C₃₁×#117	—	2	3	no	—
65	C₃₁×#117	—	2	3	no	—
66	C₃₁×#117	C₂×C₄	1	3	yes	—
67	C₃₁×#117	D₄	1	3	yes	—
68	C₂×C₄²×C₃₁	—	2	3	no	—
69	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
70	C₃₁×C₄⋊C₈	—	2	3	no	—
71	C₃₁×C₄⋊C₈	C₂³	1	3	yes	—
72	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
73	C₃₁×C₂²⋊C₈	—	2	3	no	—
74	C₃₁×#97	—	2	3	no	—
75	C₄×C₈×C₃₁	—	2	3	no	—
76	C₄×C₈×C₃₁	—	2	3	no	—
77	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
78	C₄×C₈×C₃₁	C₂³	1	3	yes	—
79	#41×C₃₁	—	2	4	no	—
80	#41×C₃₁	—	2	6	no	—
81	#41×C₃₁	—	4	3	no	—
82	#41×C₃₁	—	4	4	no	—
83	#41×C₃₁	—	8	3	no	—
84	#41×C₃₁	—	8	3	no	—
85	C₂×Q₈×C₃₁	—	2	3	no	—
86	C₂×Q₈×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
87	C₂×Q₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
88	C₂×D₄×C₃₁	—	2	3	no	—
89	C₂×D₄×C₃₁	—	2	6	no	—
90	C₂×D₄×C₃₁	—	2	3	no	—
91	C₂×D₄×C₃₁	—	2	3	no	—
92	C₂×D₄×C₃₁	C₂²⋊C₄	1	3	yes	—
93	C₂×D₄×C₃₁	C₂²×C₄	1	3	yes	—
94	C₂²×C₄×C₃₁	—	2	3	no	—
95	C₂²×C₄×C₃₁	—	2	3	no	—
96	C₂²×C₄×C₃₁	—	2	3	no	—
97	C₂²×C₄×C₃₁	C₂²×C₄	1	3	yes	—
98	C₂²×C₄×C₃₁	C₂×D₄	1	3	yes	—
99	C₂²×C₄×C₃₁	C₂×D₄	1	3	yes	—
100	M₁₆×C₃₁	—	2	12	no	—
101	M₁₆×C₃₁	—	8	3	no	—
102	C₂×C₈×C₃₁	—	2	12	no	—
103	C₂×C₈×C₃₁	—	2	1	no	—
104	C₂×C₈×C₃₁	—	2	3	no	—
105	C₂×C₈×C₃₁	—	2	1	no	—
106	C₂×C₈×C₃₁	—	2	3	no	—
107	C₄⋊C₄×C₃₁	—	2	3	no	—
108	C₄⋊C₄×C₃₁	—	2	3	no	—
109	C₄⋊C₄×C₃₁	—	2	1	no	—
110	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	3	yes	—
111	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	3	yes	—
112	C₄⋊C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
113	C₄⋊C₄×C₃₁	C₂²×C₄	1	3	yes	—
114	C₂²⋊C₄×C₃₁	—	2	3	no	—
115	C₂²⋊C₄×C₃₁	—	2	6	no	—
116	C₂²⋊C₄×C₃₁	—	2	3	no	—
117	C₂²⋊C₄×C₃₁	—	2	3	no	—
118	C₂²⋊C₄×C₃₁	C₂²⋊C₄	1	6	yes	—
119	C₄²×C₃₁	—	2	3	no	—
120	C₄²×C₃₁	—	2	3	no	—
121	C₄²×C₃₁	—	2	1	no	—
122	C₄²×C₃₁	C₂²×C₄	1	3	yes	—
123	C₄²×C₃₁	C₂×D₄	1	3	yes	—
124	C₄²×C₃₁	C₂×D₄	1	3	yes	—
125	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
126	#17520	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂³×C₃₁	—	2	3	no	—
128	C₂³×C₃₁	C₂×C₂²⋊C₄	1	3	yes	—
129	Q₈×C₃₁	—	2	1	no	—
130	Q₈×C₃₁	—	8	3	no	—
131	Q₈×C₃₁	#104	1	4	yes	—
132	Q₈×C₃₁	#131	1	2	yes	complemented
133	D₄×C₃₁	—	2	3	no	—
134	D₄×C₃₁	—	2	3	no	—
135	D₄×C₃₁	—	2	6	no	—
136	D₄×C₃₁	—	4	6	no	—
137	D₄×C₃₁	—	4	6	no	—
138	D₄×C₃₁	—	8	3	no	—
139	D₄×C₃₁	—	8	6	no	—
140	C₂×C₄×C₃₁	—	2	1	no	—
141	C₂×C₄×C₃₁	—	2	3	no	—
142	C₂×C₄×C₃₁	—	2	3	no	—
143	C₂×C₄×C₃₁	—	2	3	no	—
144	C₂×C₄×C₃₁	—	2	3	no	—
145	C₂×C₄×C₃₁	—	2	6	no	—
146	C₂×C₄×C₃₁	—	2	1	no	—
147	C₂×C₄×C₃₁	—	2	3	no	—
148	C₂×C₄×C₃₁	—	4	6	no	—
149	C₂×C₄×C₃₁	—	4	3	no	—
150	C₂×C₄×C₃₁	—	4	3	no	—
151	C₂×C₄×C₃₁	—	4	6	no	—
152	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	3	yes	—
153	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	3	yes	—
154	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	3	yes	—
155	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
158	C₈×C₃₁	—	2	2	no	—
159	C₈×C₃₁	—	2	6	no	—
160	C₈×C₃₁	—	4	3	no	—
161	C₈×C₃₁	—	4	1	no	—
162	#3483	C₂×C₃₁	1	1	yes	characteristic
163	#2991	C₂×C₃₁	1	1	yes	characteristic, complemented
164	C₄×#131	C₂×C₃₁	1	1	yes	characteristic, complemented
165	#1492	C₂×C₃₁	1	3	yes	complemented
166	#1489	C₂×C₃₁	1	3	yes	complemented
167	#1484	C₂×C₃₁	1	3	yes	complemented
168	#1476	C₂×C₃₁	1	3	yes	complemented
169	C₂²×C₃₁	—	2	3	no	—
170	C₂²×C₃₁	—	2	3	no	—
171	C₂²×C₃₁	—	2	3	no	—
172	C₂²×C₃₁	—	4	3	no	—
173	C₂²×C₃₁	—	4	3	no	—
174	C₂²×C₃₁	—	4	3	no	—
175	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
176	C₄×C₃₁	—	2	3	no	—
177	C₄×C₃₁	—	2	2	no	—
178	C₄×C₃₁	—	2	3	no	—
179	C₄×C₃₁	—	2	1	no	—
180	C₄×C₃₁	—	4	3	no	—
181	C₄×C₃₁	—	4	1	no	—
182	C₄×C₃₁	C₂×#104	1	6	yes	—
183	C₄×C₃₁	C₂×#131	1	1	yes	characteristic
184	C₄×C₃₁	#568	1	1	yes	characteristic
185	C₄×C₃₁	#576	1	1	yes	characteristic
186	C₄×C₃₁	#577	1	1	yes	characteristic
187	C₂×#131	—	2	1	no	—
188	Q₈²	C₄×C₃₁	1	1	yes	characteristic
189	#555	—	2	3	no	—
190	#555	C₄×C₃₁	1	3	yes	—
191	#550	—	2	1	no	—
192	#550	C₄×C₃₁	1	3	yes	—
193	#550	C₄×C₃₁	1	1	yes	characteristic
194	#532	—	2	3	no	—
195	#532	C₂²×C₃₁	1	3	yes	—
196	C₄×#41	—	2	1	no	—
197	C₄×#41	C₂²×C₃₁	1	3	yes	—
198	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
199	C₈×Q₈	—	2	1	no	—
200	#436	—	2	3	no	—
201	#431	C₂²×C₃₁	1	3	yes	—
202	#423	C₂²×C₃₁	1	3	yes	—
203	#405	—	2	3	no	—
204	C₄×M₁₆	C₂²×C₃₁	1	3	yes	—
205	C₂×C₄×C₈	C₂²×C₃₁	1	3	yes	—
206	Q₈⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
207	Q₈⋊C₈	C₂²×C₃₁	1	3	yes	—
208	D₄⋊C₈	C₂²×C₃₁	1	3	yes	—
209	D₄⋊C₈	C₂²×C₃₁	1	3	yes	—
210	D₄⋊C₈	C₂²×C₃₁	1	6	yes	—
211	C₂×C₃₁	—	4	3	no	—
212	C₂×C₃₁	—	8	3	no	—
213	C₂×C₃₁	#2880	1	1	yes	characteristic
214	C₂×C₃₁	#2897	1	1	yes	characteristic
215	C₂×C₃₁	C₂²×#104	1	1	yes	characteristic
216	C₂×#41	—	2	1	no	—
217	C₂×#41	—	2	3	no	—
218	C₂×#41	C₂×C₄×C₃₁	1	3	yes	—
219	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
220	#131	—	2	8	no	—
221	C₂×M₁₆	—	2	3	no	—
222	C₂×M₁₆	—	2	3	no	—
223	C₂²×C₈	—	2	3	no	—
224	C₄⋊Q₈	—	2	3	no	—
225	C₄⋊Q₈	C₂×C₄×C₃₁	1	3	yes	—
226	#127	—	2	3	no	—
227	#127	C₂×C₄×C₃₁	1	3	yes	—
228	#124	—	2	6	no	—
229	#124	—	2	3	no	—
230	#121	—	2	3	no	—
231	#121	—	2	3	no	—
232	#121	—	2	3	no	—
233	#121	—	2	6	no	—
234	#121	C₂×C₄×C₃₁	1	6	yes	—
235	C₄×Q₈	—	2	1	no	—
236	C₄×Q₈	C₂×C₄×C₃₁	1	3	yes	—
237	C₄×Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic
238	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
239	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
240	C₄×D₄	—	2	3	no	—
241	C₄×D₄	—	2	3	no	—
242	C₄×D₄	—	2	3	no	—
243	C₄×D₄	—	2	3	no	—
244	C₄×D₄	C₂×C₄×C₃₁	1	3	yes	—
245	C₄×D₄	C₂×C₄×C₃₁	1	3	yes	—
246	C₄×D₄	D₄×C₃₁	1	3	yes	—
247	C₄×D₄	C₂³×C₃₁	1	3	yes	—
248	#117	—	2	3	no	—
249	#117	—	2	3	no	—
250	#117	C₂×C₄×C₃₁	1	3	yes	—
251	#117	D₄×C₃₁	1	3	yes	—
252	C₂×C₄²	—	2	3	no	—
253	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
254	C₄⋊C₈	—	2	3	no	—
255	C₄⋊C₈	C₂³×C₃₁	1	3	yes	—
256	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
257	C₂²⋊C₈	—	2	3	no	—
258	#97	—	2	3	no	—
259	C₄×C₈	—	2	3	no	—
260	C₄×C₈	—	2	3	no	—
261	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
262	C₄×C₈	C₂³×C₃₁	1	3	yes	—
263	C₃₁	#17520	1	1	yes	characteristic, direct product factor, Sylow
264	#41	—	2	4	no	—
265	#41	—	2	6	no	—
266	#41	—	4	3	no	—
267	#41	—	4	4	no	—
268	#41	—	8	3	no	—
269	#41	—	8	3	no	—
270	C₂×Q₈	—	2	3	no	—
271	C₂×Q₈	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
272	C₂×Q₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
273	C₂×D₄	—	2	3	no	—
274	C₂×D₄	—	2	6	no	—
275	C₂×D₄	—	2	3	no	—
276	C₂×D₄	—	2	3	no	—
277	C₂×D₄	C₂²⋊C₄×C₃₁	1	3	yes	—
278	C₂×D₄	C₂²×C₄×C₃₁	1	3	yes	—
279	C₂²×C₄	—	2	3	no	—
280	C₂²×C₄	—	2	3	no	—
281	C₂²×C₄	—	2	3	no	—
282	C₂²×C₄	C₂²×C₄×C₃₁	1	3	yes	—
283	C₂²×C₄	C₂×D₄×C₃₁	1	3	yes	—
284	C₂²×C₄	C₂×D₄×C₃₁	1	3	yes	—
285	M₁₆	—	2	12	no	—
286	M₁₆	—	8	3	no	—
287	C₂×C₈	—	2	12	no	—
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	2	3	no	—
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	—	2	3	no	—
292	C₄⋊C₄	—	2	3	no	—
293	C₄⋊C₄	—	2	3	no	—
294	C₄⋊C₄	—	2	1	no	—
295	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	3	yes	—
296	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	3	yes	—
297	C₄⋊C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
298	C₄⋊C₄	C₂²×C₄×C₃₁	1	3	yes	—
299	C₂²⋊C₄	—	2	3	no	—
300	C₂²⋊C₄	—	2	6	no	—
301	C₂²⋊C₄	—	2	3	no	—
302	C₂²⋊C₄	—	2	3	no	—
303	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	6	yes	—
304	C₄²	—	2	3	no	—
305	C₄²	—	2	3	no	—
306	C₄²	—	2	1	no	—
307	C₄²	C₂²×C₄×C₃₁	1	3	yes	—
308	C₄²	C₂×D₄×C₃₁	1	3	yes	—
309	C₄²	C₂×D₄×C₃₁	1	3	yes	—
310	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
311	C₂³	—	2	3	no	—
312	C₂³	C₂×C₂²⋊C₄×C₃₁	1	3	yes	—
313	Q₈	—	2	1	no	—
314	Q₈	—	8	3	no	—
315	Q₈	C₃₁×#104	1	4	yes	—
316	Q₈	C₃₁×#131	1	2	yes	complemented
317	D₄	—	2	6	no	—
318	D₄	—	2	3	no	—
319	D₄	—	2	3	no	—
320	D₄	—	4	6	no	—
321	D₄	—	4	6	no	—
322	D₄	—	8	3	no	—
323	D₄	—	8	6	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	6	no	—
326	C₂×C₄	—	2	3	no	—
327	C₂×C₄	—	2	3	no	—
328	C₂×C₄	—	2	3	no	—
329	C₂×C₄	—	2	3	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	3	no	—
332	C₂×C₄	—	4	6	no	—
333	C₂×C₄	—	4	6	no	—
334	C₂×C₄	—	4	3	no	—
335	C₂×C₄	—	4	3	no	—
336	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	3	yes	—
337	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	3	yes	—
338	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	3	yes	—
339	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
340	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
341	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
342	C₈	—	2	2	no	—
343	C₈	—	2	6	no	—
344	C₈	—	4	3	no	—
345	C₈	—	4	1	no	—
346	C₂²	—	2	3	no	—
347	C₂²	—	2	3	no	—
348	C₂²	—	2	3	no	—
349	C₂²	—	4	3	no	—
350	C₂²	—	4	3	no	—
351	C₂²	—	4	3	no	—
352	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
353	C₄	—	2	3	no	—
354	C₄	—	2	2	no	—
355	C₄	—	2	3	no	—
356	C₄	—	2	1	no	—
357	C₄	—	4	3	no	—
358	C₄	—	4	1	no	—
359	C₄	C₂×C₃₁×#104	1	6	yes	—
360	C₄	C₂×C₃₁×#131	1	1	yes	characteristic
361	C₄	C₃₁×#568	1	1	yes	characteristic
362	C₄	C₃₁×#576	1	1	yes	characteristic
363	C₄	C₃₁×#577	1	1	yes	characteristic
364	C₂	—	4	3	no	—
365	C₂	—	8	3	no	—
366	C₂	C₃₁×#2880	1	1	yes	characteristic
367	C₂	C₃₁×#2897	1	1	yes	characteristic
368	C₂	C₂²×C₃₁×#104	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₄²	C₂⁴×C₃₁
socle	C₂²×C₃₁	C₂²×C₂²⋊C₄
prime radical	C₃₁×#3483	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2991	C₂	semidirect
3. C₄×C₃₁×#131	C₂	semidirect
4. C₃₁×#1492	C₂	semidirect
5. C₃₁×#1489	C₂	semidirect
6. C₃₁×#1484	C₂	semidirect
7. C₃₁×#1476	C₂	semidirect
126. #17520	C₃₁	direct (N × H)
132. Q₈×C₃₁	#131	semidirect
163. #2991	C₂×C₃₁	semidirect
164. C₄×#131	C₂×C₃₁	semidirect
165. #1492	C₂×C₃₁	semidirect
166. #1489	C₂×C₃₁	semidirect
167. #1484	C₂×C₃₁	semidirect
168. #1476	C₂×C₃₁	semidirect
263. C₃₁	#17520	direct (N × H)
316. Q₈	C₃₁×#131	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3483	2
C₃₁×#2991	2
C₄×C₃₁×#131	2
C₃₁×#1492	2
C₃₁×#1489	2
C₃₁×#1484	2
C₃₁×#1476	2
#17520	31

Subgroups — C31×#17520 #21474279

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#17520 #21474279