Subgroups — C₃₁×#19964 #21476723

Order 7936.

568 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3398	C₂	1	2	yes	maximal
2	C₃₁×#3383	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3342	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1713	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1690	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1674	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1673	C₂	1	1	yes	maximal, characteristic
8	C₃₁×#1650	C₂	1	2	yes	maximal
9	C₃₁×#1648	C₂	1	2	yes	maximal, complemented
10	C₃₁×#1591	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
12	C₃₁×#557	C₂²	1	2	yes	—
13	C₃₁×#556	C₂²	1	2	yes	—
14	C₃₁×#500	C₂²	1	1	yes	characteristic
15	C₃₁×#500	C₂²	1	1	yes	characteristic
16	C₃₁×#500	C₂²	1	2	yes	—
17	C₃₁×#499	—	2	1	no	—
18	C₃₁×#497	—	2	2	no	—
19	C₃₁×#494	C₂²	1	2	yes	—
20	C₃₁×#485	—	2	2	no	—
21	C₃₁×#479	—	2	2	no	—
22	C₃₁×#475	C₂²	1	2	yes	—
23	C₃₁×#475	C₂²	1	2	yes	—
24	C₃₁×#467	—	2	1	no	—
25	C₃₁×#464	—	2	2	no	—
26	C₃₁×#462	—	2	2	no	—
27	C₃₁×#462	C₂²	1	2	yes	—
28	C₃₁×#461	C₂²	1	2	yes	—
29	C₃₁×#446	C₂²	1	2	yes	—
30	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
31	C₃₁×#441	—	2	2	no	—
32	C₄×Q₁₆×C₃₁	—	2	1	no	—
33	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
34	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
35	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
36	C₃₁×#427	—	2	1	no	—
37	C₃₁×#335	C₂²	1	1	yes	characteristic
38	C₃₁×#334	C₂²	1	1	yes	characteristic
39	C₃₁×#332	C₂²	1	2	yes	—
40	C₃₁×#332	C₂²	1	2	yes	—
41	C₃₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₃₁×Q₈⋊C₈	C₂²	1	2	yes	—
43	C₃₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₈²×C₃₁	C₂²	1	1	yes	characteristic
45	C₂×Q₁₆×C₃₁	—	2	2	no	—
46	C₂×Q₁₆×C₃₁	—	2	2	no	—
47	C₂×Q₁₆×C₃₁	—	2	2	no	—
48	C₂×Q₁₆×C₃₁	D₄	1	1	yes	characteristic
49	C₂×SD₁₆×C₃₁	—	2	2	no	—
50	C₂×SD₁₆×C₃₁	D₄	1	1	yes	characteristic
51	C₂²×C₈×C₃₁	—	2	1	no	—
52	C₃₁×C₄⋊Q₈	—	2	2	no	—
53	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
54	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
55	C₃₁×#126	—	4	2	no	—
56	C₃₁×#125	—	2	2	no	—
57	C₃₁×#125	—	4	2	no	—
58	C₃₁×#124	—	2	2	no	—
59	C₃₁×C₂²⋊Q₈	—	2	2	no	—
60	C₄×Q₈×C₃₁	—	2	2	no	—
61	C₄×Q₈×C₃₁	—	2	2	no	—
62	C₄×Q₈×C₃₁	—	2	2	no	—
63	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
64	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
65	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
66	C₃₁×#117	—	2	2	no	—
67	C₃₁×#107	—	2	1	no	—
68	C₃₁×#107	—	2	1	no	—
69	C₃₁×#107	—	2	1	no	—
70	C₃₁×#107	—	2	1	no	—
71	C₃₁×#107	—	4	2	no	—
72	C₃₁×#107	D₄	1	1	yes	characteristic
73	C₃₁×#106	—	2	2	no	—
74	C₃₁×#106	—	2	2	no	—
75	C₃₁×#106	D₄	1	1	yes	characteristic
76	C₃₁×C₄⋊C₈	—	2	1	no	—
77	C₃₁×C₄⋊C₈	—	2	2	no	—
78	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
79	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
80	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
81	C₃₁×#103	—	2	2	no	—
82	C₃₁×#103	—	2	2	no	—
83	C₃₁×#103	—	2	2	no	—
84	C₃₁×#103	—	2	2	no	—
85	C₃₁×#103	D₄	1	1	yes	characteristic
86	C₃₁×#103	D₄	1	2	yes	—
87	C₃₁×#102	D₄	1	1	yes	characteristic
88	C₃₁×C₂²⋊C₈	—	2	1	no	—
89	C₃₁×#97	—	2	2	no	—
90	C₄×C₈×C₃₁	—	2	1	no	—
91	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
94	C₂×Q₈×C₃₁	—	2	2	no	—
95	C₂×Q₈×C₃₁	—	2	2	no	—
96	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
97	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
98	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₃₁	—	2	1	no	—
100	Q₁₆×C₃₁	—	2	2	no	—
101	Q₁₆×C₃₁	—	4	4	no	—
102	Q₁₆×C₃₁	—	8	2	no	—
103	Q₁₆×C₃₁	—	8	2	no	—
104	SD₁₆×C₃₁	—	2	2	no	—
105	SD₁₆×C₃₁	—	8	2	no	—
106	C₂×C₈×C₃₁	—	2	1	no	—
107	C₂×C₈×C₃₁	—	2	1	no	—
108	C₂×C₈×C₃₁	—	2	2	no	—
109	C₂×C₈×C₃₁	—	2	1	no	—
110	C₂×C₈×C₃₁	—	4	2	no	—
111	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
115	C₄⋊C₄×C₃₁	—	2	1	no	—
116	C₄⋊C₄×C₃₁	—	2	2	no	—
117	C₄⋊C₄×C₃₁	—	2	2	no	—
118	C₄⋊C₄×C₃₁	—	2	2	no	—
119	C₄⋊C₄×C₃₁	—	2	2	no	—
120	C₄⋊C₄×C₃₁	—	2	2	no	—
121	C₄⋊C₄×C₃₁	—	4	2	no	—
122	C₄⋊C₄×C₃₁	—	4	2	no	—
123	C₄⋊C₄×C₃₁	—	4	2	no	—
124	C₄⋊C₄×C₃₁	—	4	2	no	—
125	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
126	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
127	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
128	C₂²⋊C₄×C₃₁	—	2	1	no	—
129	C₂²⋊C₄×C₃₁	—	4	2	no	—
130	C₂²⋊C₄×C₃₁	—	4	2	no	—
131	C₄²×C₃₁	—	2	1	no	—
132	C₄²×C₃₁	—	2	2	no	—
133	C₄²×C₃₁	—	4	2	no	—
134	C₄²×C₃₁	—	4	2	no	—
135	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
136	#19964	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₃₁	—	2	1	no	—
138	Q₈×C₃₁	—	2	1	no	—
139	Q₈×C₃₁	—	2	2	no	—
140	Q₈×C₃₁	—	2	1	no	—
141	Q₈×C₃₁	—	2	2	no	—
142	Q₈×C₃₁	—	4	2	no	—
143	Q₈×C₃₁	—	4	2	no	—
144	Q₈×C₃₁	—	4	2	no	—
145	Q₈×C₃₁	—	4	2	no	—
146	D₄×C₃₁	—	2	1	no	—
147	D₄×C₃₁	—	2	1	no	—
148	C₂×C₄×C₃₁	—	2	1	no	—
149	C₂×C₄×C₃₁	—	2	2	no	—
150	C₂×C₄×C₃₁	—	2	2	no	—
151	C₂×C₄×C₃₁	—	2	1	no	—
152	C₂×C₄×C₃₁	—	2	1	no	—
153	C₂×C₄×C₃₁	—	4	1	no	—
154	C₂×C₄×C₃₁	—	4	1	no	—
155	C₂×C₄×C₃₁	—	4	2	no	—
156	C₂×C₄×C₃₁	—	4	2	no	—
157	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
160	C₈×C₃₁	—	2	2	no	—
161	C₈×C₃₁	—	2	1	no	—
162	C₈×C₃₁	—	2	1	no	—
163	C₈×C₃₁	—	4	1	no	—
164	C₈×C₃₁	—	4	2	no	—
165	C₈×C₃₁	—	4	1	no	—
166	C₈×C₃₁	#135	1	2	yes	—
167	C₈×C₃₁	#137	1	2	yes	—
168	#3398	C₂×C₃₁	1	2	yes	—
169	#3383	C₂×C₃₁	1	1	yes	characteristic, complemented
170	#3342	C₂×C₃₁	1	1	yes	characteristic
171	#1713	C₂×C₃₁	1	1	yes	characteristic, complemented
172	#1690	C₂×C₃₁	1	2	yes	complemented
173	#1674	C₂×C₃₁	1	1	yes	characteristic, complemented
174	#1673	C₂×C₃₁	1	1	yes	characteristic
175	#1650	C₂×C₃₁	1	2	yes	—
176	#1648	C₂×C₃₁	1	2	yes	complemented
177	#1591	C₂×C₃₁	1	1	yes	characteristic, complemented
178	C₈×SD₁₆	C₂×C₃₁	1	1	yes	characteristic
179	C₂²×C₃₁	—	4	1	no	—
180	C₂²×C₃₁	—	4	1	no	—
181	C₂²×C₃₁	—	4	1	no	—
182	C₂²×C₃₁	D₄²	1	1	yes	characteristic
183	C₄×C₃₁	—	2	1	no	—
184	C₄×C₃₁	—	4	1	no	—
185	C₄×C₃₁	—	4	2	no	—
186	C₄×C₃₁	—	4	1	no	—
187	C₄×C₃₁	—	4	1	no	—
188	C₄×C₃₁	—	4	2	no	—
189	C₄×C₃₁	—	8	2	no	—
190	C₄×C₃₁	—	8	2	no	—
191	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
192	C₄×C₃₁	C₂×#137	1	1	yes	characteristic
193	C₄×C₃₁	#576	1	1	yes	characteristic
194	C₄×C₃₁	#578	1	1	yes	characteristic
195	#557	C₂²×C₃₁	1	2	yes	—
196	#556	C₂²×C₃₁	1	2	yes	—
197	#500	C₂²×C₃₁	1	1	yes	characteristic
198	#500	C₂²×C₃₁	1	1	yes	characteristic
199	#500	C₂²×C₃₁	1	2	yes	—
200	#499	—	2	1	no	—
201	#497	—	2	2	no	—
202	#494	C₂²×C₃₁	1	2	yes	—
203	#485	—	2	2	no	—
204	#479	—	2	2	no	—
205	#475	C₂²×C₃₁	1	2	yes	—
206	#475	C₂²×C₃₁	1	2	yes	—
207	#467	—	2	1	no	—
208	#464	—	2	2	no	—
209	#462	—	2	2	no	—
210	#462	C₂²×C₃₁	1	2	yes	—
211	#461	C₂²×C₃₁	1	2	yes	—
212	#446	C₂²×C₃₁	1	2	yes	—
213	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
214	#441	—	2	2	no	—
215	C₄×Q₁₆	—	2	1	no	—
216	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
217	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
218	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
219	#427	—	2	1	no	—
220	#335	C₂²×C₃₁	1	1	yes	characteristic
221	#334	C₂²×C₃₁	1	1	yes	characteristic
222	#332	C₂²×C₃₁	1	2	yes	—
223	#332	C₂²×C₃₁	1	2	yes	—
224	Q₈⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
225	Q₈⋊C₈	C₂²×C₃₁	1	2	yes	—
226	D₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
227	C₈²	C₂²×C₃₁	1	1	yes	characteristic
228	C₂×C₃₁	—	8	1	no	—
229	C₂×C₃₁	#3276	1	1	yes	characteristic
230	C₂×C₃₁	#3287	1	1	yes	characteristic
231	C₂×C₃₁	#3293	1	1	yes	characteristic
232	C₂×Q₁₆	—	2	2	no	—
233	C₂×Q₁₆	—	2	2	no	—
234	C₂×Q₁₆	—	2	2	no	—
235	C₂×Q₁₆	D₄×C₃₁	1	1	yes	characteristic
236	C₂×SD₁₆	—	2	2	no	—
237	C₂×SD₁₆	D₄×C₃₁	1	1	yes	characteristic
238	C₂²×C₈	—	2	1	no	—
239	C₄⋊Q₈	—	2	2	no	—
240	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
241	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
242	#126	—	4	2	no	—
243	#125	—	2	2	no	—
244	#125	—	4	2	no	—
245	#124	—	2	2	no	—
246	C₂²⋊Q₈	—	2	2	no	—
247	C₄×Q₈	—	2	2	no	—
248	C₄×Q₈	—	2	2	no	—
249	C₄×Q₈	—	2	2	no	—
250	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
251	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
252	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
253	#117	—	2	2	no	—
254	#107	—	2	1	no	—
255	#107	—	2	1	no	—
256	#107	—	2	1	no	—
257	#107	—	2	1	no	—
258	#107	—	4	2	no	—
259	#107	D₄×C₃₁	1	1	yes	characteristic
260	#106	—	2	2	no	—
261	#106	—	2	2	no	—
262	#106	D₄×C₃₁	1	1	yes	characteristic
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	2	2	no	—
265	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
266	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
267	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
268	#103	—	2	2	no	—
269	#103	—	2	2	no	—
270	#103	—	2	2	no	—
271	#103	—	2	2	no	—
272	#103	D₄×C₃₁	1	1	yes	characteristic
273	#103	D₄×C₃₁	1	2	yes	—
274	#102	D₄×C₃₁	1	1	yes	characteristic
275	C₂²⋊C₈	—	2	1	no	—
276	#97	—	2	2	no	—
277	C₄×C₈	—	2	1	no	—
278	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
279	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
280	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
281	C₃₁	#19964	1	1	yes	characteristic, direct product factor, Sylow
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
285	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
286	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
287	C₂²×C₄	—	2	1	no	—
288	Q₁₆	—	2	2	no	—
289	Q₁₆	—	4	4	no	—
290	Q₁₆	—	8	2	no	—
291	Q₁₆	—	8	2	no	—
292	SD₁₆	—	2	2	no	—
293	SD₁₆	—	8	2	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	4	2	no	—
299	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
300	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
301	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
302	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
314	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
315	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
316	C₂²⋊C₄	—	2	1	no	—
317	C₂²⋊C₄	—	4	2	no	—
318	C₂²⋊C₄	—	4	2	no	—
319	C₄²	—	2	1	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	4	2	no	—
322	C₄²	—	4	2	no	—
323	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
324	C₂³	—	2	1	no	—
325	Q₈	—	2	1	no	—
326	Q₈	—	2	2	no	—
327	Q₈	—	2	1	no	—
328	Q₈	—	2	2	no	—
329	Q₈	—	4	2	no	—
330	Q₈	—	4	2	no	—
331	Q₈	—	4	2	no	—
332	Q₈	—	4	2	no	—
333	D₄	—	2	1	no	—
334	D₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
345	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
346	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
347	C₈	—	2	2	no	—
348	C₈	—	2	1	no	—
349	C₈	—	2	1	no	—
350	C₈	—	4	1	no	—
351	C₈	—	4	2	no	—
352	C₈	—	4	1	no	—
353	C₈	C₃₁×#135	1	2	yes	—
354	C₈	C₃₁×#137	1	2	yes	—
355	C₂²	—	4	1	no	—
356	C₂²	—	4	1	no	—
357	C₂²	—	4	1	no	—
358	C₂²	D₄²×C₃₁	1	1	yes	characteristic
359	C₄	—	2	1	no	—
360	C₄	—	4	1	no	—
361	C₄	—	4	2	no	—
362	C₄	—	4	1	no	—
363	C₄	—	4	1	no	—
364	C₄	—	4	2	no	—
365	C₄	—	8	2	no	—
366	C₄	—	8	2	no	—
367	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
368	C₄	C₂×C₃₁×#137	1	1	yes	characteristic
369	C₄	C₃₁×#576	1	1	yes	characteristic
370	C₄	C₃₁×#578	1	1	yes	characteristic
371	C₂	—	8	1	no	—
372	C₂	C₃₁×#3276	1	1	yes	characteristic
373	C₂	C₃₁×#3287	1	1	yes	characteristic
374	C₂	C₃₁×#3293	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₁
prime radical	C₂×D₄×C₃₁	C₂×D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#3383	C₂	semidirect
4. C₃₁×#1713	C₂	semidirect
5. C₃₁×#1690	C₂	semidirect
6. C₃₁×#1674	C₂	semidirect
9. C₃₁×#1648	C₂	semidirect
10. C₃₁×#1591	C₂	semidirect
136. #19964	C₃₁	direct (N × H)
169. #3383	C₂×C₃₁	semidirect
171. #1713	C₂×C₃₁	semidirect
172. #1690	C₂×C₃₁	semidirect
173. #1674	C₂×C₃₁	semidirect
176. #1648	C₂×C₃₁	semidirect
177. #1591	C₂×C₃₁	semidirect
281. C₃₁	#19964	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#3398	2
C₃₁×#3383	2
C₃₁×#3342	2
C₃₁×#1713	2
C₃₁×#1690	2
C₃₁×#1674	2
C₃₁×#1673	2
C₃₁×#1650	2
C₃₁×#1648	2
C₃₁×#1591	2
C₈×SD₁₆×C₃₁	2
#19964	31

Subgroups — C31×#19964 #21476723

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#19964 #21476723