Subgroups — C₃₁×#33897 #21490656

Order 7936.

580 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×#3334	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3283	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2241	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2236	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2224	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2220	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2208	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2186	C₂	1	2	yes	maximal, complemented
9	C₄×C₃₁×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2169	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2139	C₂	1	2	yes	maximal, complemented
12	C₂×C₃₁×#135	C₂²	1	2	yes	—
13	C₃₁×#547	—	2	1	no	—
14	C₃₁×#547	—	2	1	no	—
15	C₂×C₃₁×SD₃₂	C₂²	1	2	yes	—
16	C₂×C₃₁×D₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₃₁×M₃₂	C₂²	1	2	yes	—
18	C₃₁×#500	C₂²	1	1	yes	characteristic
19	C₃₁×#494	C₂²	1	1	yes	characteristic
20	C₃₁×#480	—	2	2	no	—
21	C₃₁×#474	—	2	1	no	—
22	C₃₁×#467	C₂²	1	2	yes	—
23	C₃₁×#466	C₂²	1	2	yes	—
24	C₃₁×#461	—	2	1	no	—
25	C₃₁×#452	—	2	2	no	—
26	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
27	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
28	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×#107	C₂²	1	2	yes	—
30	C₃₁×#366	C₂²	1	1	yes	characteristic
31	C₃₁×#366	C₂²	1	2	yes	—
32	C₃₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
33	C₃₁×#358	C₂²	1	2	yes	—
34	C₃₁×#358	C₂²	1	2	yes	—
35	C₃₁×#358	C₂²	1	2	yes	—
36	C₃₁×#357	C₂²	1	1	yes	characteristic
37	C₃₁×#357	C₂²	1	2	yes	—
38	C₃₁×#357	C₂²	1	1	yes	characteristic
39	C₃₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
40	C₄×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
41	C₂×#41×C₃₁	—	2	2	no	—
42	C₂×#41×C₃₁	—	4	1	no	—
43	C₃₁×#135	—	2	4	no	—
44	C₃₁×#135	—	4	2	no	—
45	C₂×Q₁₆×C₃₁	—	2	1	no	—
46	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
47	C₂×SD₁₆×C₃₁	—	2	2	no	—
48	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
49	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
51	C₃₁×C₄⋊Q₈	—	2	1	no	—
52	C₃₁×C₄⋊Q₈	—	2	1	no	—
53	C₃₁×#123	—	4	2	no	—
54	C₃₁×#123	—	4	2	no	—
55	C₃₁×C₂²⋊Q₈	—	2	2	no	—
56	C₃₁×C₂²⋊Q₈	—	4	1	no	—
57	C₃₁×#121	—	2	2	no	—
58	C₃₁×#121	—	4	1	no	—
59	C₄×D₄×C₃₁	—	2	1	no	—
60	C₄×D₄×C₃₁	—	2	1	no	—
61	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₃₁	—	4	1	no	—
64	C₃₁×SD₃₂	—	4	2	no	—
65	C₃₁×D₁₆	—	2	2	no	—
66	C₃₁×M₃₂	—	4	2	no	—
67	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
68	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
69	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
70	C₃₁×#107	—	2	2	no	—
71	C₃₁×#107	—	2	1	no	—
72	C₃₁×#107	C₂³	1	1	yes	characteristic
73	C₃₁×#107	C₂³	1	2	yes	—
74	C₃₁×#107	C₂³	1	1	yes	characteristic
75	C₃₁×C₄⋊C₈	D₄	1	1	yes	characteristic
76	C₃₁×#103	—	2	2	no	—
77	C₃₁×#102	—	2	1	no	—
78	C₃₁×#102	—	2	1	no	—
79	C₃₁×#102	—	2	2	no	—
80	C₃₁×C₂²⋊C₈	D₄	1	2	yes	—
81	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
82	#41×C₃₁	—	4	4	no	—
83	#41×C₃₁	—	8	2	no	—
84	#41×C₃₁	—	8	4	no	—
85	C₂×Q₈×C₃₁	—	2	2	no	—
86	C₂×Q₈×C₃₁	—	4	1	no	—
87	C₂×D₄×C₃₁	—	2	1	no	—
88	C₂×D₄×C₃₁	—	2	1	no	—
89	C₂×D₄×C₃₁	—	4	2	no	—
90	C₂×D₄×C₃₁	—	4	2	no	—
91	C₂×D₄×C₃₁	D₈	1	1	yes	characteristic
92	C₂²×C₄×C₃₁	—	4	2	no	—
93	C₂²×C₄×C₃₁	—	4	1	no	—
94	C₂²×C₄×C₃₁	—	4	2	no	—
95	C₂²×C₄×C₃₁	—	4	1	no	—
96	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
97	Q₁₆×C₃₁	—	2	2	no	—
98	Q₁₆×C₃₁	—	2	2	no	—
99	Q₁₆×C₃₁	—	8	1	no	—
100	SD₁₆×C₃₁	—	4	4	no	—
101	D₈×C₃₁	—	2	1	no	—
102	D₈×C₃₁	—	2	1	no	—
103	D₈×C₃₁	—	2	1	no	—
104	D₈×C₃₁	#41	1	2	yes	complemented
105	C₂×C₈×C₃₁	—	2	2	no	—
106	C₂×C₈×C₃₁	—	2	2	no	—
107	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
108	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
109	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
110	C₄⋊C₄×C₃₁	—	2	1	no	—
111	C₄⋊C₄×C₃₁	—	2	1	no	—
112	C₄⋊C₄×C₃₁	—	2	2	no	—
113	C₄⋊C₄×C₃₁	—	4	2	no	—
114	C₄⋊C₄×C₃₁	—	4	1	no	—
115	C₄⋊C₄×C₃₁	—	4	2	no	—
116	C₄⋊C₄×C₃₁	—	4	1	no	—
117	C₄⋊C₄×C₃₁	—	4	1	no	—
118	C₄⋊C₄×C₃₁	D₈	1	1	yes	characteristic
119	C₂²⋊C₄×C₃₁	—	4	2	no	—
120	C₂²⋊C₄×C₃₁	—	4	1	no	—
121	C₂²⋊C₄×C₃₁	—	4	1	no	—
122	C₂²⋊C₄×C₃₁	—	4	2	no	—
123	C₂²⋊C₄×C₃₁	D₈	1	2	yes	—
124	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
125	C₁₆×C₃₁	—	2	1	no	—
126	C₁₆×C₃₁	—	2	1	no	—
127	C₁₆×C₃₁	—	2	2	no	—
128	#33897	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂³×C₃₁	—	4	1	no	—
130	C₂³×C₃₁	—	4	1	no	—
131	C₂³×C₃₁	C₂×D₈	1	2	yes	—
132	Q₈×C₃₁	—	4	2	no	—
133	Q₈×C₃₁	—	4	2	no	—
134	Q₈×C₃₁	—	8	2	no	—
135	D₄×C₃₁	—	2	2	no	—
136	D₄×C₃₁	—	2	2	no	—
137	D₄×C₃₁	—	4	1	no	—
138	D₄×C₃₁	—	4	1	no	—
139	D₄×C₃₁	—	4	1	no	—
140	D₄×C₃₁	—	8	4	no	—
141	D₄×C₃₁	—	8	4	no	—
142	C₂×C₄×C₃₁	—	2	2	no	—
143	C₂×C₄×C₃₁	—	2	2	no	—
144	C₂×C₄×C₃₁	—	4	1	no	—
145	C₂×C₄×C₃₁	—	4	1	no	—
146	C₂×C₄×C₃₁	—	4	2	no	—
147	C₂×C₄×C₃₁	—	4	2	no	—
148	C₂×C₄×C₃₁	—	8	4	no	—
149	C₂×C₄×C₃₁	—	8	4	no	—
150	C₂×C₄×C₃₁	—	8	2	no	—
151	C₂×C₄×C₃₁	—	8	2	no	—
152	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
153	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
154	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
155	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
156	C₈×C₃₁	—	2	2	no	—
157	C₈×C₃₁	—	2	1	no	—
158	C₈×C₃₁	C₂×#41	1	1	yes	characteristic
159	C₈×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
160	#3334	C₂×C₃₁	1	1	yes	characteristic, complemented
161	#3283	C₂×C₃₁	1	1	yes	characteristic, complemented
162	#2241	C₂×C₃₁	1	1	yes	characteristic, complemented
163	#2236	C₂×C₃₁	1	2	yes	complemented
164	#2224	C₂×C₃₁	1	1	yes	characteristic, complemented
165	#2220	C₂×C₃₁	1	2	yes	complemented
166	#2208	C₂×C₃₁	1	1	yes	characteristic, complemented
167	#2186	C₂×C₃₁	1	2	yes	complemented
168	C₄×D₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
169	#2169	C₂×C₃₁	1	1	yes	characteristic, complemented
170	#2139	C₂×C₃₁	1	2	yes	complemented
171	C₂²×C₃₁	—	2	2	no	—
172	C₂²×C₃₁	—	2	2	no	—
173	C₂²×C₃₁	—	2	2	no	—
174	C₂²×C₃₁	—	4	2	no	—
175	C₂²×C₃₁	—	8	1	no	—
176	C₂²×C₃₁	—	8	1	no	—
177	C₂²×C₃₁	—	8	1	no	—
178	C₂²×C₃₁	—	8	1	no	—
179	C₂²×C₃₁	—	8	1	no	—
180	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
181	C₄×C₃₁	—	2	1	no	—
182	C₄×C₃₁	—	2	2	no	—
183	C₄×C₃₁	—	8	1	no	—
184	C₄×C₃₁	—	8	1	no	—
185	C₄×C₃₁	—	8	2	no	—
186	C₄×C₃₁	—	8	2	no	—
187	C₄×C₃₁	#509	1	2	yes	—
188	C₄×C₃₁	#546	1	1	yes	characteristic
189	C₄×C₃₁	#577	1	1	yes	characteristic
190	C₂×#135	C₂²×C₃₁	1	2	yes	—
191	#547	—	2	1	no	—
192	#547	—	2	1	no	—
193	C₂×SD₃₂	C₂²×C₃₁	1	2	yes	—
194	C₂×D₁₆	C₂²×C₃₁	1	1	yes	characteristic
195	C₂×M₃₂	C₂²×C₃₁	1	2	yes	—
196	#500	C₂²×C₃₁	1	1	yes	characteristic
197	#494	C₂²×C₃₁	1	1	yes	characteristic
198	#480	—	2	2	no	—
199	#474	—	2	1	no	—
200	#467	C₂²×C₃₁	1	2	yes	—
201	#466	C₂²×C₃₁	1	2	yes	—
202	#461	—	2	1	no	—
203	#452	—	2	2	no	—
204	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
205	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
206	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
207	C₂×#107	C₂²×C₃₁	1	2	yes	—
208	#366	C₂²×C₃₁	1	1	yes	characteristic
209	#366	C₂²×C₃₁	1	2	yes	—
210	C₄⋊C₁₆	C₂²×C₃₁	1	1	yes	characteristic
211	#358	C₂²×C₃₁	1	2	yes	—
212	#358	C₂²×C₃₁	1	2	yes	—
213	#358	C₂²×C₃₁	1	2	yes	—
214	#357	C₂²×C₃₁	1	1	yes	characteristic
215	#357	C₂²×C₃₁	1	2	yes	—
216	#357	C₂²×C₃₁	1	1	yes	characteristic
217	C₂²⋊C₁₆	C₂²×C₃₁	1	2	yes	—
218	C₄×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
219	C₂×C₃₁	—	4	2	no	—
220	C₂×C₃₁	—	8	2	no	—
221	C₂×C₃₁	—	16	1	no	—
222	C₂×C₃₁	#3294	1	1	yes	characteristic
223	C₂×C₃₁	C₂×#509	1	1	yes	characteristic
224	C₂×C₃₁	#3417	1	1	yes	characteristic
225	C₂×#41	—	2	2	no	—
226	C₂×#41	—	4	1	no	—
227	#135	—	2	4	no	—
228	#135	—	4	2	no	—
229	C₂×Q₁₆	—	2	1	no	—
230	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
231	C₂×SD₁₆	—	2	2	no	—
232	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
233	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
235	C₄⋊Q₈	—	2	1	no	—
236	C₄⋊Q₈	—	2	1	no	—
237	#123	—	4	2	no	—
238	#123	—	4	2	no	—
239	C₂²⋊Q₈	—	2	2	no	—
240	C₂²⋊Q₈	—	4	1	no	—
241	#121	—	2	2	no	—
242	#121	—	4	1	no	—
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	—	2	1	no	—
245	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	4	1	no	—
248	SD₃₂	—	4	2	no	—
249	D₁₆	—	2	2	no	—
250	M₃₂	—	4	2	no	—
251	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
252	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
253	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
254	#107	—	2	2	no	—
255	#107	—	2	1	no	—
256	#107	C₂³×C₃₁	1	1	yes	characteristic
257	#107	C₂³×C₃₁	1	2	yes	—
258	#107	C₂³×C₃₁	1	1	yes	characteristic
259	C₄⋊C₈	D₄×C₃₁	1	1	yes	characteristic
260	#103	—	2	2	no	—
261	#102	—	2	1	no	—
262	#102	—	2	1	no	—
263	#102	—	2	2	no	—
264	C₂²⋊C₈	D₄×C₃₁	1	2	yes	—
265	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
266	C₃₁	#33897	1	1	yes	characteristic, direct product factor, Sylow
267	#41	—	4	4	no	—
268	#41	—	8	2	no	—
269	#41	—	8	4	no	—
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	—	4	1	no	—
272	C₂×D₄	—	2	1	no	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	4	2	no	—
275	C₂×D₄	—	4	2	no	—
276	C₂×D₄	D₈×C₃₁	1	1	yes	characteristic
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	4	1	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	—	4	1	no	—
281	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
282	Q₁₆	—	2	2	no	—
283	Q₁₆	—	2	2	no	—
284	Q₁₆	—	8	1	no	—
285	SD₁₆	—	4	4	no	—
286	D₈	—	2	1	no	—
287	D₈	—	2	1	no	—
288	D₈	—	2	1	no	—
289	D₈	#41×C₃₁	1	2	yes	complemented
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
293	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
294	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
295	C₄⋊C₄	—	2	1	no	—
296	C₄⋊C₄	—	2	1	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	4	2	no	—
299	C₄⋊C₄	—	4	1	no	—
300	C₄⋊C₄	—	4	2	no	—
301	C₄⋊C₄	—	4	1	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₄⋊C₄	D₈×C₃₁	1	1	yes	characteristic
304	C₂²⋊C₄	—	4	2	no	—
305	C₂²⋊C₄	—	4	1	no	—
306	C₂²⋊C₄	—	4	1	no	—
307	C₂²⋊C₄	—	4	2	no	—
308	C₂²⋊C₄	D₈×C₃₁	1	2	yes	—
309	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
310	C₁₆	—	2	1	no	—
311	C₁₆	—	2	1	no	—
312	C₁₆	—	2	2	no	—
313	C₂³	—	4	1	no	—
314	C₂³	—	4	1	no	—
315	C₂³	C₂×D₈×C₃₁	1	2	yes	—
316	Q₈	—	4	2	no	—
317	Q₈	—	4	2	no	—
318	Q₈	—	8	2	no	—
319	D₄	—	2	2	no	—
320	D₄	—	2	2	no	—
321	D₄	—	4	1	no	—
322	D₄	—	4	1	no	—
323	D₄	—	4	1	no	—
324	D₄	—	8	4	no	—
325	D₄	—	8	4	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	8	4	no	—
333	C₂×C₄	—	8	4	no	—
334	C₂×C₄	—	8	2	no	—
335	C₂×C₄	—	8	2	no	—
336	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
337	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
338	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
339	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
340	C₈	—	2	2	no	—
341	C₈	—	2	1	no	—
342	C₈	C₂×#41×C₃₁	1	1	yes	characteristic
343	C₈	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
344	C₂²	—	2	2	no	—
345	C₂²	—	2	2	no	—
346	C₂²	—	2	2	no	—
347	C₂²	—	4	2	no	—
348	C₂²	—	8	1	no	—
349	C₂²	—	8	1	no	—
350	C₂²	—	8	1	no	—
351	C₂²	—	8	1	no	—
352	C₂²	—	8	1	no	—
353	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
354	C₄	—	2	1	no	—
355	C₄	—	2	2	no	—
356	C₄	—	8	1	no	—
357	C₄	—	8	2	no	—
358	C₄	—	8	1	no	—
359	C₄	—	8	2	no	—
360	C₄	C₃₁×#509	1	2	yes	—
361	C₄	C₃₁×#546	1	1	yes	characteristic
362	C₄	C₃₁×#577	1	1	yes	characteristic
363	C₂	—	4	2	no	—
364	C₂	—	8	2	no	—
365	C₂	—	16	1	no	—
366	C₂	C₃₁×#3294	1	1	yes	characteristic
367	C₂	C₂×C₃₁×#509	1	1	yes	characteristic
368	C₂	C₃₁×#3417	1	1	yes	characteristic

	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 ◁ C₄×D₄×C₃₁ ◁ C₈×D₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3334	C₂	semidirect
2. C₃₁×#3283	C₂	semidirect
3. C₃₁×#2241	C₂	semidirect
4. C₃₁×#2236	C₂	semidirect
5. C₃₁×#2224	C₂	semidirect
6. C₃₁×#2220	C₂	semidirect
7. C₃₁×#2208	C₂	semidirect
8. C₃₁×#2186	C₂	semidirect
9. C₄×C₃₁×D₁₆	C₂	semidirect
10. C₃₁×#2169	C₂	semidirect
11. C₃₁×#2139	C₂	semidirect
104. D₈×C₃₁	#41	semidirect
128. #33897	C₃₁	direct (N × H)
160. #3334	C₂×C₃₁	semidirect
161. #3283	C₂×C₃₁	semidirect
162. #2241	C₂×C₃₁	semidirect
163. #2236	C₂×C₃₁	semidirect
164. #2224	C₂×C₃₁	semidirect
165. #2220	C₂×C₃₁	semidirect
166. #2208	C₂×C₃₁	semidirect
167. #2186	C₂×C₃₁	semidirect
168. C₄×D₁₆	C₂×C₃₁	semidirect
169. #2169	C₂×C₃₁	semidirect
170. #2139	C₂×C₃₁	semidirect
266. C₃₁	#33897	direct (N × H)
289. D₈	#41×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3334	2
C₃₁×#3283	2
C₃₁×#2241	2
C₃₁×#2236	2
C₃₁×#2224	2
C₃₁×#2220	2
C₃₁×#2208	2
C₃₁×#2186	2
C₄×C₃₁×D₁₆	2
C₃₁×#2169	2
C₃₁×#2139	2
#33897	31

Subgroups — C31×#33897 #21490656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33897 #21490656