Subgroups — C₃₁×#33652 #21490411

Order 7936.

568 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3061	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2913	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2237	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2236	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2234	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2232	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2159	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#366	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2139	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2138	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2113	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
14	C₃₁×#537	—	2	1	no	—
15	C₃₁×#520	—	2	1	no	—
16	C₂×C₃₁×M₃₂	C₂²	1	1	yes	characteristic
17	C₂²×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
18	C₃₁×#468	—	2	2	no	—
19	C₃₁×#467	C₂²	1	2	yes	—
20	C₃₁×#466	C₂²	1	2	yes	—
21	C₃₁×#428	—	2	1	no	—
22	C₃₁×#428	—	2	2	no	—
23	C₃₁×#427	C₂²	1	1	yes	characteristic
24	C₃₁×#427	C₂²	1	2	yes	—
25	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#107	C₂²	1	2	yes	—
27	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
28	C₃₁×#417	—	2	1	no	—
29	C₃₁×#367	C₂²	1	2	yes	—
30	C₃₁×#366	C₂²	1	2	yes	—
31	C₃₁×#366	C₂²	1	2	yes	—
32	C₃₁×#366	C₂²	1	2	yes	—
33	C₃₁×#358	C₂²	1	1	yes	characteristic
34	C₃₁×#358	C₂²	1	1	yes	characteristic
35	C₃₁×#358	C₂²	1	2	yes	—
36	C₃₁×#357	C₂²	1	1	yes	characteristic
37	C₃₁×#357	C₂²	1	1	yes	characteristic
38	C₃₁×#357	C₂²	1	2	yes	—
39	C₃₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
40	C₃₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₂×#41×C₃₁	—	2	1	no	—
42	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
43	C₃₁×#135	—	2	2	no	—
44	C₃₁×#135	—	2	2	no	—
45	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
46	C₂×SD₁₆×C₃₁	—	2	1	no	—
47	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
48	C₃₁×#131	—	2	2	no	—
49	C₃₁×#131	—	2	2	no	—
50	C₂×M₁₆×C₃₁	D₄	1	1	yes	characteristic
51	C₂×M₁₆×C₃₁	D₄	1	2	yes	—
52	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
53	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
54	C₃₁×C₂²⋊Q₈	—	2	2	no	—
55	C₃₁×C₂²⋊Q₈	—	4	1	no	—
56	C₃₁×#121	—	2	2	no	—
57	C₃₁×#121	—	4	1	no	—
58	C₃₁×#121	—	4	2	no	—
59	C₄×Q₈×C₃₁	—	4	1	no	—
60	C₄×D₄×C₃₁	—	4	2	no	—
61	C₄×D₄×C₃₁	—	4	1	no	—
62	C₃₁×#117	—	2	2	no	—
63	C₃₁×#117	—	2	1	no	—
64	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
66	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
67	C₃₁×M₃₂	—	2	2	no	—
68	C₂×C₁₆×C₃₁	—	2	2	no	—
69	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
70	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
71	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
72	C₃₁×#107	—	2	2	no	—
73	C₃₁×#107	—	2	1	no	—
74	C₃₁×#107	—	2	1	no	—
75	C₃₁×#107	C₂³	1	2	yes	—
76	C₃₁×#107	C₂³	1	1	yes	characteristic
77	C₃₁×#107	C₂³	1	2	yes	—
78	C₃₁×#107	C₂³	1	1	yes	characteristic
79	C₃₁×#106	—	2	2	no	—
80	C₃₁×#106	—	2	1	no	—
81	C₃₁×#103	—	2	2	no	—
82	C₃₁×#102	—	2	2	no	—
83	#41×C₃₁	—	2	2	no	—
84	#41×C₃₁	—	2	2	no	—
85	#41×C₃₁	—	4	2	no	—
86	#41×C₃₁	—	4	2	no	—
87	C₂×Q₈×C₃₁	—	2	1	no	—
88	C₂×Q₈×C₃₁	D₈	1	1	yes	characteristic
89	C₂×D₄×C₃₁	—	2	1	no	—
90	C₂×D₄×C₃₁	—	4	1	no	—
91	C₂×D₄×C₃₁	—	4	2	no	—
92	C₂×D₄×C₃₁	D₈	1	2	yes	—
93	C₂×D₄×C₃₁	D₈	1	1	yes	characteristic
94	C₂²×C₄×C₃₁	—	4	2	no	—
95	C₂²×C₄×C₃₁	—	4	1	no	—
96	C₂²×C₄×C₃₁	—	4	1	no	—
97	C₂²×C₄×C₃₁	—	4	1	no	—
98	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
100	Q₁₆×C₃₁	—	2	1	no	—
101	Q₁₆×C₃₁	—	2	1	no	—
102	SD₁₆×C₃₁	—	4	2	no	—
103	D₈×C₃₁	—	2	1	no	—
104	D₈×C₃₁	—	2	1	no	—
105	M₁₆×C₃₁	—	2	2	no	—
106	M₁₆×C₃₁	—	2	4	no	—
107	C₂×C₈×C₃₁	—	2	2	no	—
108	C₂×C₈×C₃₁	—	2	2	no	—
109	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
110	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₃₁	#41	1	2	yes	—
112	C₂×C₈×C₃₁	#41	1	2	yes	—
113	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
114	C₄⋊C₄×C₃₁	—	2	2	no	—
115	C₄⋊C₄×C₃₁	—	2	1	no	—
116	C₄⋊C₄×C₃₁	—	2	2	no	—
117	C₄⋊C₄×C₃₁	—	2	1	no	—
118	C₄⋊C₄×C₃₁	—	4	2	no	—
119	C₄⋊C₄×C₃₁	—	4	1	no	—
120	C₄⋊C₄×C₃₁	—	4	1	no	—
121	C₄⋊C₄×C₃₁	—	4	2	no	—
122	C₂²⋊C₄×C₃₁	—	4	2	no	—
123	C₂²⋊C₄×C₃₁	—	4	1	no	—
124	C₂²⋊C₄×C₃₁	—	4	2	no	—
125	C₂²⋊C₄×C₃₁	—	4	2	no	—
126	C₄²×C₃₁	—	4	2	no	—
127	C₄²×C₃₁	—	4	1	no	—
128	C₁₆×C₃₁	—	2	1	no	—
129	C₁₆×C₃₁	—	2	1	no	—
130	C₁₆×C₃₁	—	2	2	no	—
131	#33652	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂³×C₃₁	—	4	1	no	—
133	C₂³×C₃₁	C₂×D₈	1	2	yes	—
134	C₂³×C₃₁	C₂×D₈	1	1	yes	characteristic
135	Q₈×C₃₁	—	2	2	no	—
136	Q₈×C₃₁	—	4	1	no	—
137	Q₈×C₃₁	—	4	1	no	—
138	D₄×C₃₁	—	2	4	no	—
139	D₄×C₃₁	—	2	2	no	—
140	D₄×C₃₁	—	4	1	no	—
141	D₄×C₃₁	—	4	1	no	—
142	D₄×C₃₁	—	8	2	no	—
143	D₄×C₃₁	—	16	2	no	—
144	C₂×C₄×C₃₁	—	2	2	no	—
145	C₂×C₄×C₃₁	—	2	2	no	—
146	C₂×C₄×C₃₁	—	4	1	no	—
147	C₂×C₄×C₃₁	—	4	2	no	—
148	C₂×C₄×C₃₁	—	4	1	no	—
149	C₂×C₄×C₃₁	—	4	2	no	—
150	C₂×C₄×C₃₁	—	4	1	no	—
151	C₂×C₄×C₃₁	—	8	2	no	—
152	C₂×C₄×C₃₁	—	16	1	no	—
153	C₂×C₄×C₃₁	—	16	2	no	—
154	C₂×C₄×C₃₁	—	16	1	no	—
155	C₂×C₄×C₃₁	#123	1	2	yes	—
156	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
157	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
158	C₂×C₄×C₃₁	#137	1	2	yes	—
159	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
160	C₈×C₃₁	—	2	2	no	—
161	C₈×C₃₁	#123	1	2	yes	—
162	C₈×C₃₁	C₂×#41	1	1	yes	characteristic
163	C₈×C₃₁	C₂×#41	1	1	yes	characteristic
164	#3061	C₂×C₃₁	1	1	yes	characteristic
165	#2913	C₂×C₃₁	1	1	yes	characteristic, complemented
166	#2237	C₂×C₃₁	1	2	yes	complemented
167	#2236	C₂×C₃₁	1	2	yes	complemented
168	#2234	C₂×C₃₁	1	2	yes	complemented
169	#2232	C₂×C₃₁	1	2	yes	complemented
170	#2159	C₂×C₃₁	1	1	yes	characteristic, complemented
171	C₂×#366	C₂×C₃₁	1	1	yes	characteristic, complemented
172	#2139	C₂×C₃₁	1	1	yes	characteristic, complemented
173	#2138	C₂×C₃₁	1	1	yes	characteristic, complemented
174	#2113	C₂×C₃₁	1	1	yes	characteristic, complemented
175	C₂²×C₃₁	—	2	1	no	—
176	C₂²×C₃₁	—	2	1	no	—
177	C₂²×C₃₁	—	2	2	no	—
178	C₂²×C₃₁	—	2	2	no	—
179	C₂²×C₃₁	—	2	2	no	—
180	C₂²×C₃₁	—	8	1	no	—
181	C₂²×C₃₁	—	8	1	no	—
182	C₂²×C₃₁	—	8	1	no	—
183	C₂²×C₃₁	#480	1	2	yes	—
184	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
185	C₄×C₃₁	—	2	2	no	—
186	C₄×C₃₁	—	8	1	no	—
187	C₄×C₃₁	—	8	2	no	—
188	C₄×C₃₁	—	8	1	no	—
189	C₄×C₃₁	—	8	2	no	—
190	C₄×C₃₁	—	8	1	no	—
191	C₄×C₃₁	#480	1	2	yes	—
192	C₄×C₃₁	C₂×#123	1	1	yes	characteristic
193	C₄×C₃₁	C₂×#137	1	1	yes	characteristic
194	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
195	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
196	#537	—	2	1	no	—
197	#520	—	2	1	no	—
198	C₂×M₃₂	C₂²×C₃₁	1	1	yes	characteristic
199	C₂²×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
200	#468	—	2	2	no	—
201	#467	C₂²×C₃₁	1	2	yes	—
202	#466	C₂²×C₃₁	1	2	yes	—
203	#428	—	2	1	no	—
204	#428	—	2	2	no	—
205	#427	C₂²×C₃₁	1	1	yes	characteristic
206	#427	C₂²×C₃₁	1	2	yes	—
207	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
208	C₂×#107	C₂²×C₃₁	1	2	yes	—
209	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
210	#417	—	2	1	no	—
211	#367	C₂²×C₃₁	1	2	yes	—
212	#366	C₂²×C₃₁	1	2	yes	—
213	#366	C₂²×C₃₁	1	2	yes	—
214	#366	C₂²×C₃₁	1	2	yes	—
215	#358	C₂²×C₃₁	1	1	yes	characteristic
216	#358	C₂²×C₃₁	1	1	yes	characteristic
217	#358	C₂²×C₃₁	1	2	yes	—
218	#357	C₂²×C₃₁	1	1	yes	characteristic
219	#357	C₂²×C₃₁	1	1	yes	characteristic
220	#357	C₂²×C₃₁	1	2	yes	—
221	C₂²⋊C₁₆	C₂²×C₃₁	1	2	yes	—
222	C₂²⋊C₁₆	C₂²×C₃₁	1	2	yes	—
223	C₂×C₃₁	—	2	2	no	—
224	C₂×C₃₁	—	4	2	no	—
225	C₂×C₃₁	—	16	1	no	—
226	C₂×C₃₁	C₂×#480	1	1	yes	characteristic
227	C₂×C₃₁	#3415	1	1	yes	characteristic
228	C₂×C₃₁	#3417	1	1	yes	characteristic
229	C₂×#41	—	2	1	no	—
230	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
231	#135	—	2	2	no	—
232	#135	—	2	2	no	—
233	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
234	C₂×SD₁₆	—	2	1	no	—
235	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
236	#131	—	2	2	no	—
237	#131	—	2	2	no	—
238	C₂×M₁₆	D₄×C₃₁	1	1	yes	characteristic
239	C₂×M₁₆	D₄×C₃₁	1	2	yes	—
240	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
241	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
242	C₂²⋊Q₈	—	2	2	no	—
243	C₂²⋊Q₈	—	4	1	no	—
244	#121	—	2	2	no	—
245	#121	—	4	1	no	—
246	#121	—	4	2	no	—
247	C₄×Q₈	—	4	1	no	—
248	C₄×D₄	—	4	2	no	—
249	C₄×D₄	—	4	1	no	—
250	#117	—	2	2	no	—
251	#117	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	M₃₂	—	2	2	no	—
256	C₂×C₁₆	—	2	2	no	—
257	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
258	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
259	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
260	#107	—	2	2	no	—
261	#107	—	2	1	no	—
262	#107	—	2	1	no	—
263	#107	C₂³×C₃₁	1	1	yes	characteristic
264	#107	C₂³×C₃₁	1	2	yes	—
265	#107	C₂³×C₃₁	1	1	yes	characteristic
266	#107	C₂³×C₃₁	1	2	yes	—
267	#106	—	2	2	no	—
268	#106	—	2	1	no	—
269	#103	—	2	2	no	—
270	#102	—	2	2	no	—
271	C₃₁	#33652	1	1	yes	characteristic, direct product factor, Sylow
272	#41	—	2	2	no	—
273	#41	—	2	2	no	—
274	#41	—	4	2	no	—
275	#41	—	4	2	no	—
276	C₂×Q₈	—	2	1	no	—
277	C₂×Q₈	D₈×C₃₁	1	1	yes	characteristic
278	C₂×D₄	—	2	1	no	—
279	C₂×D₄	—	4	1	no	—
280	C₂×D₄	—	4	2	no	—
281	C₂×D₄	D₈×C₃₁	1	2	yes	—
282	C₂×D₄	D₈×C₃₁	1	1	yes	characteristic
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
288	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
289	Q₁₆	—	2	1	no	—
290	Q₁₆	—	2	1	no	—
291	SD₁₆	—	4	2	no	—
292	D₈	—	2	1	no	—
293	D₈	—	2	1	no	—
294	M₁₆	—	2	2	no	—
295	M₁₆	—	2	4	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
299	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
300	C₂×C₈	#41×C₃₁	1	2	yes	—
301	C₂×C₈	#41×C₃₁	1	2	yes	—
302	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	—	4	2	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₂²⋊C₄	—	4	2	no	—
312	C₂²⋊C₄	—	4	1	no	—
313	C₂²⋊C₄	—	4	2	no	—
314	C₂²⋊C₄	—	4	2	no	—
315	C₄²	—	4	2	no	—
316	C₄²	—	4	1	no	—
317	C₁₆	—	2	1	no	—
318	C₁₆	—	2	1	no	—
319	C₁₆	—	2	2	no	—
320	C₂³	—	4	1	no	—
321	C₂³	C₂×D₈×C₃₁	1	2	yes	—
322	C₂³	C₂×D₈×C₃₁	1	1	yes	characteristic
323	Q₈	—	2	2	no	—
324	Q₈	—	4	1	no	—
325	Q₈	—	4	1	no	—
326	D₄	—	2	4	no	—
327	D₄	—	2	2	no	—
328	D₄	—	4	1	no	—
329	D₄	—	4	1	no	—
330	D₄	—	8	2	no	—
331	D₄	—	16	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	8	2	no	—
340	C₂×C₄	—	16	1	no	—
341	C₂×C₄	—	16	2	no	—
342	C₂×C₄	—	16	1	no	—
343	C₂×C₄	C₃₁×#123	1	2	yes	—
344	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
345	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
346	C₂×C₄	C₃₁×#137	1	2	yes	—
347	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
348	C₈	—	2	2	no	—
349	C₈	C₃₁×#123	1	2	yes	—
350	C₈	C₂×#41×C₃₁	1	1	yes	characteristic
351	C₈	C₂×#41×C₃₁	1	1	yes	characteristic
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	8	1	no	—
358	C₂²	—	8	1	no	—
359	C₂²	—	8	1	no	—
360	C₂²	C₃₁×#480	1	2	yes	—
361	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
362	C₄	—	2	2	no	—
363	C₄	—	8	1	no	—
364	C₄	—	8	2	no	—
365	C₄	—	8	1	no	—
366	C₄	—	8	2	no	—
367	C₄	—	8	1	no	—
368	C₄	C₃₁×#480	1	2	yes	—
369	C₄	C₂×C₃₁×#123	1	1	yes	characteristic
370	C₄	C₂×C₃₁×#137	1	1	yes	characteristic
371	C₂	—	2	2	no	—
372	C₂	—	4	2	no	—
373	C₂	—	16	1	no	—
374	C₂	C₂×C₃₁×#480	1	1	yes	characteristic
375	C₂	C₃₁×#3415	1	1	yes	characteristic
376	C₂	C₃₁×#3417	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃₁
prime radical	C₃₁×#3061	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×#41×C₃₁ ◁ C₂×C₃₁×#131 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2913	C₂	semidirect
3. C₃₁×#2237	C₂	semidirect
4. C₃₁×#2236	C₂	semidirect
5. C₃₁×#2234	C₂	semidirect
6. C₃₁×#2232	C₂	semidirect
7. C₃₁×#2159	C₂	semidirect
8. C₂×C₃₁×#366	C₂	semidirect
9. C₃₁×#2139	C₂	semidirect
10. C₃₁×#2138	C₂	semidirect
11. C₃₁×#2113	C₂	semidirect
131. #33652	C₃₁	direct (N × H)
165. #2913	C₂×C₃₁	semidirect
166. #2237	C₂×C₃₁	semidirect
167. #2236	C₂×C₃₁	semidirect
168. #2234	C₂×C₃₁	semidirect
169. #2232	C₂×C₃₁	semidirect
170. #2159	C₂×C₃₁	semidirect
171. C₂×#366	C₂×C₃₁	semidirect
172. #2139	C₂×C₃₁	semidirect
173. #2138	C₂×C₃₁	semidirect
174. #2113	C₂×C₃₁	semidirect
271. C₃₁	#33652	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×#3061	2
C₃₁×#2913	2
C₃₁×#2237	2
C₃₁×#2236	2
C₃₁×#2234	2
C₃₁×#2232	2
C₃₁×#2159	2
C₂×C₃₁×#366	2
C₃₁×#2139	2
C₃₁×#2138	2
C₃₁×#2113	2
#33652	31

Subgroups — C31×#33652 #21490411

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33652 #21490411