Subgroups — C₃₁×#33899 #21490658

Order 7936.

590 conjugacy classes of subgroups.

The subgroup lattice has 374 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×#3287	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2240	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2233	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2225	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2218	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2206	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2186	C₂	1	2	yes	maximal, complemented
9	C₄×C₃₁×SD₃₂	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×#550	—	2	1	no	—
14	C₃₁×#547	—	2	1	no	—
15	C₂×C₃₁×SD₃₂	C₂²	1	1	yes	characteristic
16	C₂×C₃₁×D₁₆	C₂²	1	2	yes	—
17	C₂×C₃₁×M₃₂	C₂²	1	2	yes	—
18	C₃₁×#500	C₂²	1	1	yes	characteristic
19	C₃₁×#493	C₂²	1	1	yes	characteristic
20	C₃₁×#480	—	2	2	no	—
21	C₃₁×#474	—	2	1	no	—
22	C₃₁×#466	C₂²	1	2	yes	—
23	C₃₁×#466	C₂²	1	2	yes	—
24	C₃₁×#460	—	2	1	no	—
25	C₃₁×#449	—	2	2	no	—
26	C₄×Q₁₆×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×#367	C₂²	1	1	yes	characteristic
31	C₃₁×#367	C₂²	1	2	yes	—
32	C₃₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
33	C₃₁×#358	C₂²	1	1	yes	characteristic
34	C₃₁×#358	C₂²	1	2	yes	—
35	C₃₁×#357	C₂²	1	2	yes	—
36	C₃₁×#357	C₂²	1	2	yes	—
37	C₃₁×#357	C₂²	1	1	yes	characteristic
38	C₃₁×#357	C₂²	1	2	yes	—
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	C₂³	1	1	yes	characteristic
46	C₂×SD₁₆×C₃₁	—	2	2	no	—
47	C₂×D₈×C₃₁	—	2	1	no	—
48	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
49	C₂×D₈×C₃₁	C₂³	1	2	yes	—
50	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
51	C₃₁×C₄⋊Q₈	—	2	1	no	—
52	C₃₁×#127	—	2	1	no	—
53	C₃₁×#127	—	4	1	no	—
54	C₃₁×#123	—	4	2	no	—
55	C₃₁×C₂²⋊Q₈	—	4	1	no	—
56	C₃₁×#121	—	2	2	no	—
57	C₃₁×#121	—	2	2	no	—
58	C₃₁×#121	—	4	2	no	—
59	C₄×Q₈×C₃₁	—	2	1	no	—
60	C₄×D₄×C₃₁	—	2	1	no	—
61	C₄×D₄×C₃₁	—	4	1	no	—
62	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
64	C₃₁×SD₃₂	—	2	2	no	—
65	C₃₁×D₁₆	—	4	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	1	no	—
77	C₃₁×#102	—	2	1	no	—
78	C₃₁×#102	—	2	2	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	1	no	—
86	C₂×Q₈×C₃₁	—	4	1	no	—
87	C₂×D₄×C₃₁	—	2	1	no	—
88	C₂×D₄×C₃₁	—	2	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	C₂×D₄×C₃₁	—	4	1	no	—
94	C₂×D₄×C₃₁	D₈	1	1	yes	characteristic
95	C₂²×C₄×C₃₁	—	4	2	no	—
96	C₂²×C₄×C₃₁	—	4	1	no	—
97	C₂²×C₄×C₃₁	—	4	2	no	—
98	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
99	Q₁₆×C₃₁	—	2	1	no	—
100	Q₁₆×C₃₁	#41	1	2	yes	complemented
101	SD₁₆×C₃₁	—	4	4	no	—
102	D₈×C₃₁	—	2	1	no	—
103	D₈×C₃₁	—	2	2	no	—
104	D₈×C₃₁	—	2	1	no	—
105	D₈×C₃₁	—	2	2	no	—
106	D₈×C₃₁	—	8	1	no	—
107	C₂×C₈×C₃₁	—	2	2	no	—
108	C₂×C₈×C₃₁	—	2	2	no	—
109	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
110	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
112	C₄⋊C₄×C₃₁	—	2	1	no	—
113	C₄⋊C₄×C₃₁	—	2	1	no	—
114	C₄⋊C₄×C₃₁	—	2	2	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	1	no	—
120	C₂²⋊C₄×C₃₁	—	4	2	no	—
121	C₂²⋊C₄×C₃₁	—	4	2	no	—
122	C₂²⋊C₄×C₃₁	D₈	1	2	yes	—
123	C₄²×C₃₁	—	4	1	no	—
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	#33899	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂³×C₃₁	—	4	1	no	—
130	C₂³×C₃₁	—	4	2	no	—
131	C₂³×C₃₁	C₂×D₈	1	2	yes	—
132	Q₈×C₃₁	—	2	2	no	—
133	Q₈×C₃₁	—	4	1	no	—
134	Q₈×C₃₁	—	8	2	no	—
135	D₄×C₃₁	—	2	2	no	—
136	D₄×C₃₁	—	4	2	no	—
137	D₄×C₃₁	—	4	1	no	—
138	D₄×C₃₁	—	4	2	no	—
139	D₄×C₃₁	—	4	1	no	—
140	D₄×C₃₁	—	8	4	no	—
141	D₄×C₃₁	—	8	4	no	—
142	D₄×C₃₁	—	8	2	no	—
143	D₄×C₃₁	—	16	1	no	—
144	D₄×C₃₁	—	16	2	no	—
145	C₂×C₄×C₃₁	—	2	2	no	—
146	C₂×C₄×C₃₁	—	2	2	no	—
147	C₂×C₄×C₃₁	—	4	1	no	—
148	C₂×C₄×C₃₁	—	4	1	no	—
149	C₂×C₄×C₃₁	—	4	1	no	—
150	C₂×C₄×C₃₁	—	4	2	no	—
151	C₂×C₄×C₃₁	—	8	4	no	—
152	C₂×C₄×C₃₁	—	8	4	no	—
153	C₂×C₄×C₃₁	—	8	2	no	—
154	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
155	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
156	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
157	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
158	C₈×C₃₁	—	2	2	no	—
159	C₈×C₃₁	—	2	1	no	—
160	C₈×C₃₁	C₂×#41	1	1	yes	characteristic
161	C₈×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
162	#3334	C₂×C₃₁	1	1	yes	characteristic, complemented
163	#3287	C₂×C₃₁	1	1	yes	characteristic, complemented
164	#2240	C₂×C₃₁	1	1	yes	characteristic, complemented
165	#2233	C₂×C₃₁	1	2	yes	complemented
166	#2225	C₂×C₃₁	1	1	yes	characteristic, complemented
167	#2218	C₂×C₃₁	1	2	yes	complemented
168	#2206	C₂×C₃₁	1	1	yes	characteristic, complemented
169	#2186	C₂×C₃₁	1	2	yes	complemented
170	C₄×SD₃₂	C₂×C₃₁	1	1	yes	characteristic, complemented
171	#2169	C₂×C₃₁	1	1	yes	characteristic, complemented
172	#2139	C₂×C₃₁	1	2	yes	complemented
173	C₂²×C₃₁	—	2	2	no	—
174	C₂²×C₃₁	—	2	2	no	—
175	C₂²×C₃₁	—	2	2	no	—
176	C₂²×C₃₁	—	8	1	no	—
177	C₂²×C₃₁	—	8	2	no	—
178	C₂²×C₃₁	—	8	2	no	—
179	C₂²×C₃₁	—	8	1	no	—
180	C₂²×C₃₁	—	8	2	no	—
181	C₂²×C₃₁	—	8	1	no	—
182	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
183	C₄×C₃₁	—	2	1	no	—
184	C₄×C₃₁	—	2	2	no	—
185	C₄×C₃₁	—	4	2	no	—
186	C₄×C₃₁	—	8	1	no	—
187	C₄×C₃₁	—	8	2	no	—
188	C₄×C₃₁	—	8	1	no	—
189	C₄×C₃₁	#509	1	2	yes	—
190	C₄×C₃₁	#546	1	1	yes	characteristic
191	C₄×C₃₁	#577	1	1	yes	characteristic
192	C₂×#135	C₂²×C₃₁	1	2	yes	—
193	#550	—	2	1	no	—
194	#547	—	2	1	no	—
195	C₂×SD₃₂	C₂²×C₃₁	1	1	yes	characteristic
196	C₂×D₁₆	C₂²×C₃₁	1	2	yes	—
197	C₂×M₃₂	C₂²×C₃₁	1	2	yes	—
198	#500	C₂²×C₃₁	1	1	yes	characteristic
199	#493	C₂²×C₃₁	1	1	yes	characteristic
200	#480	—	2	2	no	—
201	#474	—	2	1	no	—
202	#466	C₂²×C₃₁	1	2	yes	—
203	#466	C₂²×C₃₁	1	2	yes	—
204	#460	—	2	1	no	—
205	#449	—	2	2	no	—
206	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
207	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
208	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
209	C₂×#107	C₂²×C₃₁	1	2	yes	—
210	#367	C₂²×C₃₁	1	1	yes	characteristic
211	#367	C₂²×C₃₁	1	2	yes	—
212	C₄⋊C₁₆	C₂²×C₃₁	1	1	yes	characteristic
213	#358	C₂²×C₃₁	1	1	yes	characteristic
214	#358	C₂²×C₃₁	1	2	yes	—
215	#357	C₂²×C₃₁	1	2	yes	—
216	#357	C₂²×C₃₁	1	2	yes	—
217	#357	C₂²×C₃₁	1	1	yes	characteristic
218	#357	C₂²×C₃₁	1	2	yes	—
219	C₂²⋊C₁₆	C₂²×C₃₁	1	2	yes	—
220	C₄×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
221	C₂×C₃₁	—	4	2	no	—
222	C₂×C₃₁	—	16	1	no	—
223	C₂×C₃₁	—	16	2	no	—
224	C₂×C₃₁	#3294	1	1	yes	characteristic
225	C₂×C₃₁	C₂×#509	1	1	yes	characteristic
226	C₂×C₃₁	#3416	1	1	yes	characteristic
227	C₂×#41	—	2	2	no	—
228	C₂×#41	—	4	1	no	—
229	#135	—	2	4	no	—
230	#135	—	4	2	no	—
231	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
232	C₂×SD₁₆	—	2	2	no	—
233	C₂×D₈	—	2	1	no	—
234	C₂×D₈	C₂³×C₃₁	1	2	yes	—
235	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
236	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
237	C₄⋊Q₈	—	2	1	no	—
238	#127	—	2	1	no	—
239	#127	—	4	1	no	—
240	#123	—	4	2	no	—
241	C₂²⋊Q₈	—	4	1	no	—
242	#121	—	2	2	no	—
243	#121	—	2	2	no	—
244	#121	—	4	2	no	—
245	C₄×Q₈	—	2	1	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	—	4	1	no	—
248	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
249	C₂×C₄⋊C₄	—	2	2	no	—
250	SD₃₂	—	2	2	no	—
251	D₁₆	—	4	2	no	—
252	M₃₂	—	4	2	no	—
253	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
254	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
255	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
256	#107	—	2	2	no	—
257	#107	—	2	1	no	—
258	#107	C₂³×C₃₁	1	1	yes	characteristic
259	#107	C₂³×C₃₁	1	2	yes	—
260	#107	C₂³×C₃₁	1	1	yes	characteristic
261	C₄⋊C₈	D₄×C₃₁	1	1	yes	characteristic
262	#103	—	2	1	no	—
263	#102	—	2	1	no	—
264	#102	—	2	2	no	—
265	#102	—	2	2	no	—
266	C₂²⋊C₈	D₄×C₃₁	1	2	yes	—
267	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
268	C₃₁	#33899	1	1	yes	characteristic, direct product factor, Sylow
269	#41	—	4	4	no	—
270	#41	—	8	2	no	—
271	#41	—	8	4	no	—
272	C₂×Q₈	—	2	1	no	—
273	C₂×Q₈	—	4	1	no	—
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	1	no	—
280	C₂×D₄	—	4	1	no	—
281	C₂×D₄	D₈×C₃₁	1	1	yes	characteristic
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
286	Q₁₆	—	2	1	no	—
287	Q₁₆	#41×C₃₁	1	2	yes	complemented
288	SD₁₆	—	4	4	no	—
289	D₈	—	2	1	no	—
290	D₈	—	2	2	no	—
291	D₈	—	2	1	no	—
292	D₈	—	2	2	no	—
293	D₈	—	8	1	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
297	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
298	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	4	2	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	D₈×C₃₁	1	1	yes	characteristic
306	C₂²⋊C₄	—	4	1	no	—
307	C₂²⋊C₄	—	4	2	no	—
308	C₂²⋊C₄	—	4	2	no	—
309	C₂²⋊C₄	D₈×C₃₁	1	2	yes	—
310	C₄²	—	4	1	no	—
311	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
312	C₁₆	—	2	1	no	—
313	C₁₆	—	2	1	no	—
314	C₁₆	—	2	2	no	—
315	C₂³	—	4	1	no	—
316	C₂³	—	4	2	no	—
317	C₂³	C₂×D₈×C₃₁	1	2	yes	—
318	Q₈	—	2	2	no	—
319	Q₈	—	4	1	no	—
320	Q₈	—	8	2	no	—
321	D₄	—	2	2	no	—
322	D₄	—	4	2	no	—
323	D₄	—	4	1	no	—
324	D₄	—	4	2	no	—
325	D₄	—	4	1	no	—
326	D₄	—	8	4	no	—
327	D₄	—	8	4	no	—
328	D₄	—	8	2	no	—
329	D₄	—	16	1	no	—
330	D₄	—	16	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	8	4	no	—
338	C₂×C₄	—	8	4	no	—
339	C₂×C₄	—	8	2	no	—
340	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
341	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
342	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
343	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
344	C₈	—	2	2	no	—
345	C₈	—	2	1	no	—
346	C₈	C₂×#41×C₃₁	1	1	yes	characteristic
347	C₈	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
348	C₂²	—	2	2	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	8	1	no	—
352	C₂²	—	8	2	no	—
353	C₂²	—	8	2	no	—
354	C₂²	—	8	1	no	—
355	C₂²	—	8	2	no	—
356	C₂²	—	8	1	no	—
357	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
358	C₄	—	2	1	no	—
359	C₄	—	2	2	no	—
360	C₄	—	4	2	no	—
361	C₄	—	8	1	no	—
362	C₄	—	8	2	no	—
363	C₄	—	8	1	no	—
364	C₄	C₃₁×#509	1	2	yes	—
365	C₄	C₃₁×#546	1	1	yes	characteristic
366	C₄	C₃₁×#577	1	1	yes	characteristic
367	C₂	—	4	2	no	—
368	C₂	—	16	1	no	—
369	C₂	—	16	2	no	—
370	C₂	C₃₁×#3294	1	1	yes	characteristic
371	C₂	C₂×C₃₁×#509	1	1	yes	characteristic
372	C₂	C₃₁×#3416	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×#3287	C₂	semidirect
3. C₃₁×#2240	C₂	semidirect
4. C₃₁×#2233	C₂	semidirect
5. C₃₁×#2225	C₂	semidirect
6. C₃₁×#2218	C₂	semidirect
7. C₃₁×#2206	C₂	semidirect
8. C₃₁×#2186	C₂	semidirect
9. C₄×C₃₁×SD₃₂	C₂	semidirect
10. C₃₁×#2169	C₂	semidirect
11. C₃₁×#2139	C₂	semidirect
100. Q₁₆×C₃₁	#41	semidirect
128. #33899	C₃₁	direct (N × H)
162. #3334	C₂×C₃₁	semidirect
163. #3287	C₂×C₃₁	semidirect
164. #2240	C₂×C₃₁	semidirect
165. #2233	C₂×C₃₁	semidirect
166. #2225	C₂×C₃₁	semidirect
167. #2218	C₂×C₃₁	semidirect
168. #2206	C₂×C₃₁	semidirect
169. #2186	C₂×C₃₁	semidirect
170. C₄×SD₃₂	C₂×C₃₁	semidirect
171. #2169	C₂×C₃₁	semidirect
172. #2139	C₂×C₃₁	semidirect
268. C₃₁	#33899	direct (N × H)
287. Q₁₆	#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×#3287	2
C₃₁×#2240	2
C₃₁×#2233	2
C₃₁×#2225	2
C₃₁×#2218	2
C₃₁×#2206	2
C₃₁×#2186	2
C₄×C₃₁×SD₃₂	2
C₃₁×#2169	2
C₃₁×#2139	2
#33899	31

Subgroups — C31×#33899 #21490658

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33899 #21490658