Subgroups — C₃₁×#33719 #21490478

Order 7936.

834 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#510	C₂	1	2	yes	maximal, complemented
2	C₂×C₃₁×#509	C₂	1	2	yes	maximal, complemented
3	C₃₁×#3147	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₁×#495	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2251	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2250	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2249	C₂	1	4	yes	maximal, complemented
8	C₄×C₃₁×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃₁×#135	—	2	1	no	—
10	C₂×C₃₁×#135	C₂²	1	2	yes	—
11	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
12	C₂²×SD₁₆×C₃₁	—	2	1	no	—
13	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
14	C₃₁×#532	—	2	1	no	—
15	C₂×C₃₁×#124	—	2	1	no	—
16	C₃₁×#510	—	2	8	no	—
17	C₃₁×#509	—	2	8	no	—
18	C₂×C₃₁×Q₃₂	C₂²	1	4	yes	complemented
19	C₂×C₃₁×SD₃₂	C₂²	1	4	yes	—
20	C₂×C₃₁×SD₃₂	C₂²	1	4	yes	complemented
21	C₂×C₃₁×D₁₆	C₂²	1	4	yes	—
22	C₂×C₃₁×M₃₂	C₂²	1	2	yes	—
23	C₃₁×#495	—	2	1	no	—
24	C₃₁×#495	—	2	1	no	—
25	C₃₁×#495	—	2	1	no	—
26	C₃₁×#495	C₂²	1	2	yes	—
27	C₃₁×#495	C₂²	1	2	yes	—
28	C₃₁×#495	C₂²	1	2	yes	complemented
29	C₃₁×#494	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#493	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#492	—	2	1	no	—
32	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
33	C₃₁×#346	C₂²	1	2	yes	complemented
34	C₄×C₁₆×C₃₁	C₂²	1	2	yes	complemented
35	C₂×#41×C₃₁	—	2	2	no	—
36	C₂²×Q₈×C₃₁	—	2	1	no	—
37	C₂²×D₄×C₃₁	—	2	1	no	—
38	C₃₁×#135	—	2	4	no	—
39	C₃₁×#135	—	2	4	no	—
40	C₃₁×#135	—	4	4	no	—
41	C₂×Q₁₆×C₃₁	—	2	4	no	—
42	C₂×Q₁₆×C₃₁	—	2	1	no	—
43	C₂×Q₁₆×C₃₁	—	2	1	no	—
44	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
45	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
46	C₂×SD₁₆×C₃₁	—	2	2	no	—
47	C₂×SD₁₆×C₃₁	—	2	2	no	—
48	C₂×SD₁₆×C₃₁	—	2	2	no	—
49	C₂×SD₁₆×C₃₁	—	2	2	no	—
50	C₂×SD₁₆×C₃₁	—	4	4	no	—
51	C₂×D₈×C₃₁	—	2	4	no	—
52	C₂×D₈×C₃₁	—	2	1	no	—
53	C₂×D₈×C₃₁	—	2	1	no	—
54	C₂×D₈×C₃₁	C₂³	1	2	yes	—
55	C₂×D₈×C₃₁	C₂³	1	2	yes	—
56	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
57	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
58	C₃₁×C₄⋊Q₈	—	2	1	no	—
59	C₃₁×#127	—	2	1	no	—
60	C₃₁×#124	—	2	2	no	—
61	C₃₁×#124	—	2	2	no	—
62	C₃₁×#124	—	2	2	no	—
63	C₃₁×#124	—	4	2	no	—
64	C₃₁×#121	—	4	2	no	—
65	C₄×D₄×C₃₁	—	4	2	no	—
66	C₂×C₂²⋊C₄×C₃₁	—	4	2	no	—
67	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
68	C₃₁×Q₃₂	—	2	8	no	—
69	C₃₁×SD₃₂	—	2	8	no	—
70	C₃₁×SD₃₂	—	2	8	no	—
71	C₃₁×D₁₆	—	2	8	no	—
72	C₃₁×M₃₂	D₄	1	8	yes	complemented
73	C₂×C₁₆×C₃₁	C₂³	1	4	yes	—
74	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
75	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
76	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
77	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
78	C₂⁴×C₃₁	—	4	1	no	—
79	#41×C₃₁	—	4	4	no	—
80	#41×C₃₁	—	4	4	no	—
81	C₂×Q₈×C₃₁	—	2	2	no	—
82	C₂×Q₈×C₃₁	—	2	2	no	—
83	C₂×Q₈×C₃₁	—	4	1	no	—
84	C₂×Q₈×C₃₁	—	4	2	no	—
85	C₂×Q₈×C₃₁	—	4	2	no	—
86	C₂×D₄×C₃₁	—	2	2	no	—
87	C₂×D₄×C₃₁	—	2	2	no	—
88	C₂×D₄×C₃₁	—	4	2	no	—
89	C₂×D₄×C₃₁	—	4	2	no	—
90	C₂×D₄×C₃₁	—	4	2	no	—
91	C₂×D₄×C₃₁	—	4	2	no	—
92	C₂×D₄×C₃₁	—	4	1	no	—
93	C₂²×C₄×C₃₁	—	4	1	no	—
94	C₂²×C₄×C₃₁	—	4	2	no	—
95	C₂²×C₄×C₃₁	D₈	1	2	yes	—
96	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
97	Q₁₆×C₃₁	—	2	2	no	—
98	Q₁₆×C₃₁	—	2	4	no	—
99	Q₁₆×C₃₁	—	2	2	no	—
100	Q₁₆×C₃₁	—	4	2	no	—
101	Q₁₆×C₃₁	—	4	2	no	—
102	SD₁₆×C₃₁	—	4	4	no	—
103	SD₁₆×C₃₁	—	4	4	no	—
104	SD₁₆×C₃₁	—	4	4	no	—
105	SD₁₆×C₃₁	—	4	4	no	—
106	D₈×C₃₁	—	2	2	no	—
107	D₈×C₃₁	—	2	4	no	—
108	D₈×C₃₁	—	2	2	no	—
109	D₈×C₃₁	—	4	2	no	—
110	D₈×C₃₁	—	4	2	no	—
111	C₂×C₈×C₃₁	D₈	1	4	yes	—
112	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
114	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
117	C₄⋊C₄×C₃₁	—	4	2	no	—
118	C₂²⋊C₄×C₃₁	—	4	4	no	—
119	C₂²⋊C₄×C₃₁	—	4	4	no	—
120	C₂²⋊C₄×C₃₁	—	4	4	no	—
121	C₄²×C₃₁	D₈	1	2	yes	—
122	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
124	C₁₆×C₃₁	C₂×D₄	1	8	yes	—
125	#33719	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂³×C₃₁	—	4	2	no	—
127	C₂³×C₃₁	—	4	2	no	—
128	C₂³×C₃₁	—	8	4	no	—
129	C₂³×C₃₁	—	8	2	no	—
130	C₂³×C₃₁	C₂×D₈	1	1	yes	characteristic
131	Q₈×C₃₁	—	4	2	no	—
132	Q₈×C₃₁	—	4	2	no	—
133	Q₈×C₃₁	—	4	2	no	—
134	Q₈×C₃₁	—	4	2	no	—
135	Q₈×C₃₁	—	8	2	no	—
136	D₄×C₃₁	—	4	2	no	—
137	D₄×C₃₁	—	4	2	no	—
138	D₄×C₃₁	—	4	2	no	—
139	D₄×C₃₁	—	4	2	no	—
140	D₄×C₃₁	—	8	4	no	—
141	D₄×C₃₁	—	8	4	no	—
142	D₄×C₃₁	—	8	2	no	—
143	C₂×C₄×C₃₁	—	4	2	no	—
144	C₂×C₄×C₃₁	—	4	2	no	—
145	C₂×C₄×C₃₁	—	4	2	no	—
146	C₂×C₄×C₃₁	—	8	2	no	—
147	C₂×C₄×C₃₁	—	8	4	no	—
148	C₂×C₄×C₃₁	#127	1	2	yes	—
149	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
150	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
151	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
152	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
153	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
154	C₈×C₃₁	#127	1	2	yes	—
155	C₈×C₃₁	C₂×D₈	1	2	yes	—
156	C₈×C₃₁	C₂×D₈	1	2	yes	—
157	C₈×C₃₁	C₂²×D₄	1	2	yes	—
158	C₂×#510	C₂×C₃₁	1	2	yes	complemented
159	C₂×#509	C₂×C₃₁	1	2	yes	complemented
160	#3147	C₂×C₃₁	1	1	yes	characteristic, complemented
161	C₂×#495	C₂×C₃₁	1	1	yes	characteristic, complemented
162	#2251	C₂×C₃₁	1	2	yes	complemented
163	#2250	C₂×C₃₁	1	2	yes	complemented
164	#2249	C₂×C₃₁	1	4	yes	complemented
165	C₄×M₃₂	C₂×C₃₁	1	1	yes	characteristic, complemented
166	C₂²×C₃₁	—	2	2	no	—
167	C₂²×C₃₁	—	8	2	no	—
168	C₂²×C₃₁	—	8	2	no	—
169	C₂²×C₃₁	—	8	4	no	—
170	C₂²×C₃₁	—	8	4	no	—
171	C₂²×C₃₁	—	16	4	no	—
172	C₂²×C₃₁	#493	1	2	yes	—
173	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
174	C₄×C₃₁	—	2	2	no	—
175	C₄×C₃₁	—	2	2	no	—
176	C₄×C₃₁	—	8	2	no	—
177	C₄×C₃₁	—	8	2	no	—
178	C₄×C₃₁	#493	1	2	yes	—
179	C₄×C₃₁	C₂×#127	1	1	yes	characteristic
180	C₄×C₃₁	C₂²×D₈	1	1	yes	characteristic
181	C₂×#135	—	2	1	no	—
182	C₂×#135	C₂²×C₃₁	1	2	yes	—
183	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
184	C₂²×SD₁₆	—	2	1	no	—
185	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
186	#532	—	2	1	no	—
187	C₂×#124	—	2	1	no	—
188	#510	—	2	8	no	—
189	#509	—	2	8	no	—
190	C₂×Q₃₂	C₂²×C₃₁	1	4	yes	complemented
191	C₂×SD₃₂	C₂²×C₃₁	1	4	yes	—
192	C₂×SD₃₂	C₂²×C₃₁	1	4	yes	complemented
193	C₂×D₁₆	C₂²×C₃₁	1	4	yes	—
194	C₂×M₃₂	C₂²×C₃₁	1	2	yes	—
195	#495	—	2	1	no	—
196	#495	—	2	1	no	—
197	#495	—	2	1	no	—
198	#495	C₂²×C₃₁	1	2	yes	—
199	#495	C₂²×C₃₁	1	2	yes	—
200	#495	C₂²×C₃₁	1	2	yes	complemented
201	#494	C₂²×C₃₁	1	1	yes	characteristic, complemented
202	#493	C₂²×C₃₁	1	1	yes	characteristic, complemented
203	#492	—	2	1	no	—
204	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
205	#346	C₂²×C₃₁	1	2	yes	complemented
206	C₄×C₁₆	C₂²×C₃₁	1	2	yes	complemented
207	C₂×C₃₁	—	2	2	no	—
208	C₂×C₃₁	—	16	2	no	—
209	C₂×C₃₁	—	16	2	no	—
210	C₂×C₃₁	C₂×#493	1	1	yes	characteristic
211	C₂×C₃₁	#3414	1	2	yes	—
212	C₂×#41	—	2	2	no	—
213	C₂²×Q₈	—	2	1	no	—
214	C₂²×D₄	—	2	1	no	—
215	#135	—	2	4	no	—
216	#135	—	2	4	no	—
217	#135	—	4	4	no	—
218	C₂×Q₁₆	—	2	4	no	—
219	C₂×Q₁₆	—	2	1	no	—
220	C₂×Q₁₆	—	2	1	no	—
221	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
222	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
223	C₂×SD₁₆	—	2	2	no	—
224	C₂×SD₁₆	—	2	2	no	—
225	C₂×SD₁₆	—	2	2	no	—
226	C₂×SD₁₆	—	2	2	no	—
227	C₂×SD₁₆	—	4	4	no	—
228	C₂×D₈	—	2	4	no	—
229	C₂×D₈	—	2	1	no	—
230	C₂×D₈	—	2	1	no	—
231	C₂×D₈	C₂³×C₃₁	1	2	yes	—
232	C₂×D₈	C₂³×C₃₁	1	2	yes	—
233	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
235	C₄⋊Q₈	—	2	1	no	—
236	#127	—	2	1	no	—
237	#124	—	2	2	no	—
238	#124	—	2	2	no	—
239	#124	—	2	2	no	—
240	#124	—	4	2	no	—
241	#121	—	4	2	no	—
242	C₄×D₄	—	4	2	no	—
243	C₂×C₂²⋊C₄	—	4	2	no	—
244	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
245	Q₃₂	—	2	8	no	—
246	SD₃₂	—	2	8	no	—
247	SD₃₂	—	2	8	no	—
248	D₁₆	—	2	8	no	—
249	M₃₂	D₄×C₃₁	1	8	yes	complemented
250	C₂×C₁₆	C₂³×C₃₁	1	4	yes	—
251	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
252	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
253	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
254	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
255	C₃₁	#33719	1	1	yes	characteristic, direct product factor, Sylow
256	C₂⁴	—	4	1	no	—
257	#41	—	4	4	no	—
258	#41	—	4	4	no	—
259	C₂×Q₈	—	2	2	no	—
260	C₂×Q₈	—	2	2	no	—
261	C₂×Q₈	—	4	1	no	—
262	C₂×Q₈	—	4	2	no	—
263	C₂×Q₈	—	4	2	no	—
264	C₂×D₄	—	2	2	no	—
265	C₂×D₄	—	2	2	no	—
266	C₂×D₄	—	4	2	no	—
267	C₂×D₄	—	4	2	no	—
268	C₂×D₄	—	4	2	no	—
269	C₂×D₄	—	4	2	no	—
270	C₂×D₄	—	4	1	no	—
271	C₂²×C₄	—	4	1	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	D₈×C₃₁	1	2	yes	—
274	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
275	Q₁₆	—	2	2	no	—
276	Q₁₆	—	2	4	no	—
277	Q₁₆	—	2	2	no	—
278	Q₁₆	—	4	2	no	—
279	Q₁₆	—	4	2	no	—
280	SD₁₆	—	4	4	no	—
281	SD₁₆	—	4	4	no	—
282	SD₁₆	—	4	4	no	—
283	SD₁₆	—	4	4	no	—
284	D₈	—	2	2	no	—
285	D₈	—	2	4	no	—
286	D₈	—	2	2	no	—
287	D₈	—	4	2	no	—
288	D₈	—	4	2	no	—
289	C₂×C₈	D₈×C₃₁	1	4	yes	—
290	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
291	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
292	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
293	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
294	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
295	C₄⋊C₄	—	4	2	no	—
296	C₂²⋊C₄	—	4	4	no	—
297	C₂²⋊C₄	—	4	4	no	—
298	C₂²⋊C₄	—	4	4	no	—
299	C₄²	D₈×C₃₁	1	2	yes	—
300	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
301	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
302	C₁₆	C₂×D₄×C₃₁	1	8	yes	—
303	C₂³	—	4	2	no	—
304	C₂³	—	4	2	no	—
305	C₂³	—	8	4	no	—
306	C₂³	—	8	2	no	—
307	C₂³	C₂×D₈×C₃₁	1	1	yes	characteristic
308	Q₈	—	4	2	no	—
309	Q₈	—	4	2	no	—
310	Q₈	—	4	2	no	—
311	Q₈	—	4	2	no	—
312	Q₈	—	8	2	no	—
313	D₄	—	4	2	no	—
314	D₄	—	4	2	no	—
315	D₄	—	4	2	no	—
316	D₄	—	4	2	no	—
317	D₄	—	8	4	no	—
318	D₄	—	8	4	no	—
319	D₄	—	8	2	no	—
320	C₂×C₄	—	4	2	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	8	2	no	—
324	C₂×C₄	—	8	4	no	—
325	C₂×C₄	C₃₁×#127	1	2	yes	—
326	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
327	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
328	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
329	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
330	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
331	C₈	C₃₁×#127	1	2	yes	—
332	C₈	C₂×D₈×C₃₁	1	2	yes	—
333	C₈	C₂×D₈×C₃₁	1	2	yes	—
334	C₈	C₂²×D₄×C₃₁	1	2	yes	—
335	C₂²	—	2	2	no	—
336	C₂²	—	8	2	no	—
337	C₂²	—	8	2	no	—
338	C₂²	—	8	4	no	—
339	C₂²	—	8	4	no	—
340	C₂²	—	16	4	no	—
341	C₂²	C₃₁×#493	1	2	yes	—
342	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
343	C₄	—	2	2	no	—
344	C₄	—	2	2	no	—
345	C₄	—	8	2	no	—
346	C₄	—	8	2	no	—
347	C₄	C₃₁×#493	1	2	yes	—
348	C₄	C₂×C₃₁×#127	1	1	yes	characteristic
349	C₄	C₂²×D₈×C₃₁	1	1	yes	characteristic
350	C₂	—	2	2	no	—
351	C₂	—	16	2	no	—
352	C₂	—	16	2	no	—
353	C₂	C₂×C₃₁×#493	1	1	yes	characteristic
354	C₂	C₃₁×#3414	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ C₂×C₄×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#510	C₂	semidirect
2. C₂×C₃₁×#509	C₂	semidirect
3. C₃₁×#3147	C₂	semidirect
4. C₂×C₃₁×#495	C₂	semidirect
5. C₃₁×#2251	C₂	semidirect
6. C₃₁×#2250	C₂	semidirect
7. C₃₁×#2249	C₂	semidirect
8. C₄×C₃₁×M₃₂	C₂	semidirect
18. C₂×C₃₁×Q₃₂	C₂²	semidirect
20. C₂×C₃₁×SD₃₂	C₂²	semidirect
28. C₃₁×#495	C₂²	semidirect
29. C₃₁×#494	C₂²	semidirect
30. C₃₁×#493	C₂²	semidirect
33. C₃₁×#346	C₂²	semidirect
34. C₄×C₁₆×C₃₁	C₂²	semidirect
72. C₃₁×M₃₂	D₄	semidirect
125. #33719	C₃₁	direct (N × H)
158. C₂×#510	C₂×C₃₁	semidirect
159. C₂×#509	C₂×C₃₁	semidirect
160. #3147	C₂×C₃₁	semidirect
161. C₂×#495	C₂×C₃₁	semidirect
162. #2251	C₂×C₃₁	semidirect
163. #2250	C₂×C₃₁	semidirect
164. #2249	C₂×C₃₁	semidirect
165. C₄×M₃₂	C₂×C₃₁	semidirect
190. C₂×Q₃₂	C₂²×C₃₁	semidirect
192. C₂×SD₃₂	C₂²×C₃₁	semidirect
200. #495	C₂²×C₃₁	semidirect
201. #494	C₂²×C₃₁	semidirect
202. #493	C₂²×C₃₁	semidirect
205. #346	C₂²×C₃₁	semidirect
206. C₄×C₁₆	C₂²×C₃₁	semidirect
249. M₃₂	D₄×C₃₁	semidirect
255. C₃₁	#33719	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#510	2
C₂×C₃₁×#509	2
C₃₁×#3147	2
C₂×C₃₁×#495	2
C₃₁×#2251	2
C₃₁×#2250	2
C₃₁×#2249	2
C₄×C₃₁×M₃₂	2
#33719	31

Subgroups — C31×#33719 #21490478

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33719 #21490478