Subgroups — C₃₁×#23638 #21480397

Order 7936.

1126 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#427	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃₁×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2280	C₂	1	2	yes	maximal
4	C₃₁×#2077	C₂	1	4	yes	maximal, complemented
5	C₃₁×#2076	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2075	C₂	1	2	yes	maximal, complemented
7	C₃₁×#1735	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1735	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₃₁×#117	C₂²	1	2	yes	—
13	C₂×C₃₁×#117	C₂²	1	2	yes	—
14	C₃₁×#427	—	2	4	no	—
15	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₃₁×#106	C₂²	1	2	yes	complemented
18	C₂×C₃₁×C₂²⋊C₈	—	2	4	no	—
19	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
20	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₃₁×#381	—	2	2	no	—
22	C₃₁×#380	C₂²	1	4	yes	—
23	C₃₁×#380	C₂²	1	4	yes	—
24	C₃₁×#379	—	2	2	no	—
25	C₄×C₂²⋊C₄×C₃₁	—	2	4	no	—
26	C₃₁×#340	C₂²	1	2	yes	complemented
27	C₃₁×#340	C₂²	1	4	yes	complemented
28	C₃₁×#340	C₂²	1	4	yes	complemented
29	C₃₁×#340	C₂²	1	2	yes	complemented
30	C₂⁵×C₃₁	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₃₁	—	2	2	no	—
32	C₂³×C₄×C₃₁	—	2	2	no	—
33	C₂³×C₄×C₃₁	—	2	4	no	—
34	C₂³×C₄×C₃₁	—	2	4	no	—
35	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₃₁	D₄	1	2	yes	—
37	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
38	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
39	C₂²×C₈×C₃₁	—	2	4	no	—
40	C₂²×C₈×C₃₁	—	2	2	no	—
41	C₂²×C₈×C₃₁	—	2	4	no	—
42	C₂²×C₈×C₃₁	D₄	1	4	yes	—
43	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
44	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
46	C₃₁×#117	—	2	4	no	—
47	C₃₁×#117	—	2	4	no	—
48	C₃₁×#117	—	2	4	no	—
49	C₃₁×#117	—	2	4	no	—
50	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
51	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
52	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
53	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
54	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
56	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
57	C₂×C₄²×C₃₁	—	2	2	no	—
58	C₂×C₄²×C₃₁	—	2	2	no	—
59	C₃₁×#107	—	2	2	no	—
60	C₃₁×#107	—	2	2	no	—
61	C₃₁×#106	—	2	4	no	—
62	C₃₁×C₂²⋊C₈	—	2	4	no	—
63	C₃₁×C₂²⋊C₈	—	2	4	no	—
64	C₃₁×#95	—	2	4	no	—
65	C₃₁×#95	—	2	4	no	—
66	C₂⁴×C₃₁	—	2	2	no	—
67	C₂⁴×C₃₁	—	2	4	no	—
68	C₂⁴×C₃₁	—	2	4	no	—
69	C₂⁴×C₃₁	—	4	2	no	—
70	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
71	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₃₁	—	2	2	no	—
73	C₂²×C₄×C₃₁	—	2	4	no	—
74	C₂²×C₄×C₃₁	—	2	4	no	—
75	C₂²×C₄×C₃₁	—	2	8	no	—
76	C₂²×C₄×C₃₁	—	2	2	no	—
77	C₂²×C₄×C₃₁	—	2	2	no	—
78	C₂²×C₄×C₃₁	—	2	4	no	—
79	C₂²×C₄×C₃₁	—	2	4	no	—
80	C₂²×C₄×C₃₁	—	2	2	no	—
81	C₂²×C₄×C₃₁	—	2	2	no	—
82	C₂²×C₄×C₃₁	—	2	4	no	—
83	C₂²×C₄×C₃₁	—	4	4	no	—
84	C₂²×C₄×C₃₁	—	4	4	no	—
85	C₂²×C₄×C₃₁	—	4	8	no	—
86	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₃₁	#41	1	2	yes	—
90	C₂²×C₄×C₃₁	#41	1	4	yes	—
91	C₂²×C₄×C₃₁	#41	1	4	yes	—
92	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
93	C₂×C₈×C₃₁	—	2	8	no	—
94	C₂×C₈×C₃₁	—	2	2	no	—
95	C₂×C₈×C₃₁	—	2	2	no	—
96	C₂×C₈×C₃₁	—	2	2	no	—
97	C₂×C₈×C₃₁	—	2	4	no	—
98	C₂×C₈×C₃₁	—	4	4	no	—
99	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
100	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
101	C₄⋊C₄×C₃₁	—	2	2	no	—
102	C₄⋊C₄×C₃₁	—	2	2	no	—
103	C₄⋊C₄×C₃₁	—	2	2	no	—
104	C₄⋊C₄×C₃₁	—	2	2	no	—
105	C₄⋊C₄×C₃₁	—	2	4	no	—
106	C₄⋊C₄×C₃₁	—	2	4	no	—
107	C₂²⋊C₄×C₃₁	—	4	8	no	—
108	C₂²⋊C₄×C₃₁	—	4	4	no	—
109	C₂²⋊C₄×C₃₁	—	4	4	no	—
110	C₂²⋊C₄×C₃₁	—	4	8	no	—
111	C₄²×C₃₁	—	4	4	no	—
112	C₄²×C₃₁	—	4	4	no	—
113	#23638	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
114	C₂³×C₃₁	—	2	2	no	—
115	C₂³×C₃₁	—	2	2	no	—
116	C₂³×C₃₁	—	2	8	no	—
117	C₂³×C₃₁	—	2	2	no	—
118	C₂³×C₃₁	—	2	4	no	—
119	C₂³×C₃₁	—	2	2	no	—
120	C₂³×C₃₁	—	2	4	no	—
121	C₂³×C₃₁	—	4	16	no	—
122	C₂³×C₃₁	—	4	4	no	—
123	C₂³×C₃₁	—	4	4	no	—
124	C₂³×C₃₁	#121	1	2	yes	—
125	C₂³×C₃₁	#123	1	4	yes	—
126	C₂³×C₃₁	#135	1	4	yes	—
127	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
128	C₂×C₄×C₃₁	—	2	2	no	—
129	C₂×C₄×C₃₁	—	2	4	no	—
130	C₂×C₄×C₃₁	—	4	4	no	—
131	C₂×C₄×C₃₁	—	4	2	no	—
132	C₂×C₄×C₃₁	—	4	2	no	—
133	C₂×C₄×C₃₁	—	4	4	no	—
134	C₂×C₄×C₃₁	—	4	8	no	—
135	C₂×C₄×C₃₁	—	4	2	no	—
136	C₂×C₄×C₃₁	—	4	2	no	—
137	C₂×C₄×C₃₁	—	4	4	no	—
138	C₂×C₄×C₃₁	—	4	4	no	—
139	C₂×C₄×C₃₁	—	4	4	no	—
140	C₂×C₄×C₃₁	—	4	4	no	—
141	C₂×C₄×C₃₁	—	4	4	no	—
142	C₂×C₄×C₃₁	#121	1	2	yes	—
143	C₂×C₄×C₃₁	#123	1	4	yes	—
144	C₂×C₄×C₃₁	#123	1	4	yes	—
145	C₂×C₄×C₃₁	#124	1	4	yes	—
146	C₂×C₄×C₃₁	#126	1	8	yes	—
147	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
149	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
150	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
151	C₈×C₃₁	—	2	2	no	—
152	C₈×C₃₁	—	2	2	no	—
153	C₈×C₃₁	—	4	2	no	—
154	C₂×#427	C₂×C₃₁	1	1	yes	characteristic, complemented
155	C₂²×C₂²⋊C₈	C₂×C₃₁	1	1	yes	characteristic
156	#2280	C₂×C₃₁	1	2	yes	—
157	#2077	C₂×C₃₁	1	4	yes	complemented
158	#2076	C₂×C₃₁	1	2	yes	complemented
159	#2075	C₂×C₃₁	1	2	yes	complemented
160	#1735	C₂×C₃₁	1	2	yes	complemented
161	#1735	C₂×C₃₁	1	1	yes	characteristic, complemented
162	C₂²×C₃₁	—	2	8	no	—
163	C₂²×C₃₁	—	2	2	no	—
164	C₂²×C₃₁	—	2	2	no	—
165	C₂²×C₃₁	—	2	8	no	—
166	C₂²×C₃₁	—	2	4	no	—
167	C₂²×C₃₁	—	4	16	no	—
168	C₂²×C₃₁	—	4	4	no	—
169	C₂²×C₃₁	—	4	2	no	—
170	C₂²×C₃₁	—	4	2	no	—
171	C₂²×C₃₁	#397	1	4	yes	—
172	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
173	C₂²×C₃₁	C₂×#123	1	2	yes	—
174	C₂²×C₃₁	C₂×#135	1	2	yes	—
175	C₂²×C₃₁	#575	1	2	yes	—
176	C₄×C₃₁	—	4	2	no	—
177	C₄×C₃₁	—	8	4	no	—
178	C₄×C₃₁	—	8	2	no	—
179	C₄×C₃₁	—	8	2	no	—
180	C₄×C₃₁	#397	1	4	yes	—
181	C₄×C₃₁	C₂×#123	1	1	yes	characteristic
182	C₄×C₃₁	C₂×#124	1	1	yes	characteristic
183	C₄×C₃₁	C₂×#126	1	2	yes	—
184	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
185	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
186	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
187	C₂×#117	C₂²×C₃₁	1	2	yes	—
188	C₂×#117	C₂²×C₃₁	1	2	yes	—
189	#427	—	2	4	no	—
190	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
191	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
192	C₂×#106	C₂²×C₃₁	1	2	yes	complemented
193	C₂×C₂²⋊C₈	—	2	4	no	—
194	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
195	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
196	#381	—	2	2	no	—
197	#380	C₂²×C₃₁	1	4	yes	—
198	#380	C₂²×C₃₁	1	4	yes	—
199	#379	—	2	2	no	—
200	C₄×C₂²⋊C₄	—	2	4	no	—
201	#340	C₂²×C₃₁	1	2	yes	complemented
202	#340	C₂²×C₃₁	1	4	yes	complemented
203	#340	C₂²×C₃₁	1	4	yes	complemented
204	#340	C₂²×C₃₁	1	2	yes	complemented
205	C₂×C₃₁	—	2	4	no	—
206	C₂×C₃₁	—	4	4	no	—
207	C₂×C₃₁	C₂×#397	1	1	yes	characteristic
208	C₂×C₃₁	#3050	1	1	yes	characteristic
209	C₂×C₃₁	#3054	1	1	yes	characteristic
210	C₂×C₃₁	#3091	1	4	yes	—
211	C₂⁵	D₄×C₃₁	1	1	yes	characteristic
212	C₂³×C₄	—	2	2	no	—
213	C₂³×C₄	—	2	2	no	—
214	C₂³×C₄	—	2	4	no	—
215	C₂³×C₄	—	2	4	no	—
216	C₂³×C₄	D₄×C₃₁	1	2	yes	—
217	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
218	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
219	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
220	C₂²×C₈	—	2	4	no	—
221	C₂²×C₈	—	2	2	no	—
222	C₂²×C₈	—	2	4	no	—
223	C₂²×C₈	D₄×C₃₁	1	4	yes	—
224	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
225	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
226	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
227	#117	—	2	4	no	—
228	#117	—	2	4	no	—
229	#117	—	2	4	no	—
230	#117	—	2	4	no	—
231	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
232	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
233	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
234	C₂×C₂²⋊C₄	—	2	2	no	—
235	C₂×C₂²⋊C₄	—	2	2	no	—
236	C₂×C₂²⋊C₄	—	2	4	no	—
237	C₂×C₂²⋊C₄	—	2	4	no	—
238	C₂×C₄²	—	2	2	no	—
239	C₂×C₄²	—	2	2	no	—
240	#107	—	2	2	no	—
241	#107	—	2	2	no	—
242	#106	—	2	4	no	—
243	C₂²⋊C₈	—	2	4	no	—
244	C₂²⋊C₈	—	2	4	no	—
245	#95	—	2	4	no	—
246	#95	—	2	4	no	—
247	C₃₁	#23638	1	1	yes	characteristic, direct product factor, Sylow
248	C₂⁴	—	2	2	no	—
249	C₂⁴	—	2	4	no	—
250	C₂⁴	—	2	4	no	—
251	C₂⁴	—	4	2	no	—
252	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
253	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	8	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	4	4	no	—
266	C₂²×C₄	—	4	4	no	—
267	C₂²×C₄	—	4	8	no	—
268	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
269	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
271	C₂²×C₄	#41×C₃₁	1	2	yes	—
272	C₂²×C₄	#41×C₃₁	1	4	yes	—
273	C₂²×C₄	#41×C₃₁	1	4	yes	—
274	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
275	C₂×C₈	—	2	8	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	4	4	no	—
281	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
282	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	—	2	2	no	—
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	2	4	no	—
289	C₂²⋊C₄	—	4	8	no	—
290	C₂²⋊C₄	—	4	4	no	—
291	C₂²⋊C₄	—	4	4	no	—
292	C₂²⋊C₄	—	4	8	no	—
293	C₄²	—	4	4	no	—
294	C₄²	—	4	4	no	—
295	C₂³	—	2	2	no	—
296	C₂³	—	2	2	no	—
297	C₂³	—	2	8	no	—
298	C₂³	—	2	2	no	—
299	C₂³	—	2	4	no	—
300	C₂³	—	2	2	no	—
301	C₂³	—	2	4	no	—
302	C₂³	—	4	16	no	—
303	C₂³	—	4	4	no	—
304	C₂³	—	4	4	no	—
305	C₂³	C₃₁×#121	1	2	yes	—
306	C₂³	C₃₁×#123	1	4	yes	—
307	C₂³	C₃₁×#135	1	4	yes	—
308	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	4	4	no	—
312	C₂×C₄	—	4	8	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	4	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	C₃₁×#121	1	2	yes	—
324	C₂×C₄	C₃₁×#123	1	4	yes	—
325	C₂×C₄	C₃₁×#123	1	4	yes	—
326	C₂×C₄	C₃₁×#124	1	4	yes	—
327	C₂×C₄	C₃₁×#126	1	8	yes	—
328	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
329	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
330	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
331	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
332	C₈	—	2	2	no	—
333	C₈	—	2	2	no	—
334	C₈	—	4	2	no	—
335	C₂²	—	2	8	no	—
336	C₂²	—	2	2	no	—
337	C₂²	—	2	2	no	—
338	C₂²	—	2	8	no	—
339	C₂²	—	2	4	no	—
340	C₂²	—	4	16	no	—
341	C₂²	—	4	4	no	—
342	C₂²	—	4	2	no	—
343	C₂²	—	4	2	no	—
344	C₂²	C₃₁×#397	1	4	yes	—
345	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
346	C₂²	C₂×C₃₁×#123	1	2	yes	—
347	C₂²	C₂×C₃₁×#135	1	2	yes	—
348	C₂²	C₃₁×#575	1	2	yes	—
349	C₄	—	4	2	no	—
350	C₄	—	8	4	no	—
351	C₄	—	8	2	no	—
352	C₄	—	8	2	no	—
353	C₄	C₃₁×#397	1	4	yes	—
354	C₄	C₂×C₃₁×#123	1	1	yes	characteristic
355	C₄	C₂×C₃₁×#124	1	1	yes	characteristic
356	C₄	C₂×C₃₁×#126	1	2	yes	—
357	C₂	—	2	4	no	—
358	C₂	—	4	4	no	—
359	C₂	C₂×C₃₁×#397	1	1	yes	characteristic
360	C₂	C₃₁×#3050	1	1	yes	characteristic
361	C₂	C₃₁×#3054	1	1	yes	characteristic
362	C₂	C₃₁×#3091	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
socle	C₂³×C₃₁	C₂²×D₄
prime radical	C₂⁵×C₃₁	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ C₂⁴×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#427	C₂	semidirect
4. C₃₁×#2077	C₂	semidirect
5. C₃₁×#2076	C₂	semidirect
6. C₃₁×#2075	C₂	semidirect
7. C₃₁×#1735	C₂	semidirect
8. C₃₁×#1735	C₂	semidirect
15. C₂×C₃₁×#107	C₂²	semidirect
16. C₂×C₃₁×#107	C₂²	semidirect
17. C₂×C₃₁×#106	C₂²	semidirect
26. C₃₁×#340	C₂²	semidirect
27. C₃₁×#340	C₂²	semidirect
28. C₃₁×#340	C₂²	semidirect
29. C₃₁×#340	C₂²	semidirect
113. #23638	C₃₁	direct (N × H)
154. C₂×#427	C₂×C₃₁	semidirect
157. #2077	C₂×C₃₁	semidirect
158. #2076	C₂×C₃₁	semidirect
159. #2075	C₂×C₃₁	semidirect
160. #1735	C₂×C₃₁	semidirect
161. #1735	C₂×C₃₁	semidirect
190. C₂×#107	C₂²×C₃₁	semidirect
191. C₂×#107	C₂²×C₃₁	semidirect
192. C₂×#106	C₂²×C₃₁	semidirect
201. #340	C₂²×C₃₁	semidirect
202. #340	C₂²×C₃₁	semidirect
203. #340	C₂²×C₃₁	semidirect
204. #340	C₂²×C₃₁	semidirect
247. C₃₁	#23638	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×#427	2
C₂²×C₃₁×C₂²⋊C₈	2
C₃₁×#2280	2
C₃₁×#2077	2
C₃₁×#2076	2
C₃₁×#2075	2
C₃₁×#1735	2
#23638	31

Subgroups — C31×#23638 #21480397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#23638 #21480397