Subgroups — C₃₁×#17391 #21474150

Order 7936.

876 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#541	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2983	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2982	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#1473	C₂	1	4	yes	maximal
5	C₃₁×#1470	C₂	1	4	yes	maximal, complemented
6	C₃₁×#1461	C₂	1	2	yes	maximal, complemented
7	C₃₁×#1458	C₂	1	2	yes	maximal
8	C₃₁×#541	—	2	4	no	—
9	C₃₁×#541	—	2	4	no	—
10	C₂×C₃₁×C₄⋊Q₈	C₄	1	1	yes	characteristic
11	C₂×C₃₁×#126	C₄	1	2	yes	—
12	C₂×C₃₁×#126	C₂²	1	2	yes	—
13	C₂×C₃₁×#125	C₄	1	1	yes	characteristic
14	C₂×C₃₁×#125	C₄	1	2	yes	—
15	C₂×C₃₁×#125	C₂²	1	2	yes	—
16	C₂×C₃₁×C₂²⋊Q₈	C₄	1	1	yes	characteristic
17	C₂×C₃₁×C₂²⋊Q₈	C₄	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
20	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
21	C₃₁×#446	—	2	4	no	—
22	C₈×Q₈×C₃₁	—	2	4	no	—
23	C₃₁×#432	C₂²	1	4	yes	—
24	C₃₁×#431	C₂²	1	2	yes	—
25	C₃₁×#431	C₂²	1	4	yes	—
26	C₃₁×#431	C₂²	1	2	yes	—
27	C₃₁×#324	C₂²	1	4	yes	—
28	C₃₁×#324	C₂²	1	8	yes	—
29	C₃₁×#323	C₂²	1	4	yes	—
30	C₂²×Q₈×C₃₁	C₂×C₄	1	1	yes	characteristic
31	C₂²×Q₈×C₃₁	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
33	C₃₁×C₄⋊Q₈	—	2	4	no	—
34	C₃₁×#126	—	2	8	no	—
35	C₃₁×#126	—	2	4	no	—
36	C₃₁×#126	—	2	4	no	—
37	C₃₁×#125	—	2	4	no	—
38	C₃₁×#125	—	2	8	no	—
39	C₃₁×#125	—	2	4	no	—
40	C₃₁×#125	—	2	4	no	—
41	C₃₁×C₂²⋊Q₈	—	2	4	no	—
42	C₃₁×C₂²⋊Q₈	—	2	4	no	—
43	C₄×Q₈×C₃₁	—	2	2	no	—
44	C₄×Q₈×C₃₁	—	2	2	no	—
45	C₄×Q₈×C₃₁	D₄	1	4	yes	—
46	C₄×Q₈×C₃₁	D₄	1	4	yes	—
47	C₃₁×#117	—	2	2	no	—
48	C₃₁×#117	—	2	2	no	—
49	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
53	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
54	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
61	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
62	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
63	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
64	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
69	C₃₁×C₄⋊C₈	—	2	2	no	—
70	C₃₁×C₄⋊C₈	—	2	4	no	—
71	C₃₁×C₄⋊C₈	—	2	2	no	—
72	C₃₁×C₄⋊C₈	—	2	4	no	—
73	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
74	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
75	C₃₁×#97	—	2	4	no	—
76	C₄×C₈×C₃₁	—	2	2	no	—
77	C₄×C₈×C₃₁	—	2	4	no	—
78	C₄×C₈×C₃₁	—	2	2	no	—
79	C₂⁴×C₃₁	C₂²×C₄	1	1	yes	characteristic
80	C₂×Q₈×C₃₁	—	2	2	no	—
81	C₂×Q₈×C₃₁	—	2	4	no	—
82	C₂×Q₈×C₃₁	—	2	4	no	—
83	C₂×Q₈×C₃₁	C₂²⋊C₄	1	4	yes	—
84	C₂²×C₄×C₃₁	—	2	2	no	—
85	C₂²×C₄×C₃₁	—	2	4	no	—
86	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
96	C₂×C₈×C₃₁	—	2	4	no	—
97	C₂×C₈×C₃₁	—	2	4	no	—
98	C₄⋊C₄×C₃₁	—	2	2	no	—
99	C₄⋊C₄×C₃₁	—	2	2	no	—
100	C₄⋊C₄×C₃₁	—	2	4	no	—
101	C₄⋊C₄×C₃₁	—	2	4	no	—
102	C₄⋊C₄×C₃₁	—	2	4	no	—
103	C₄⋊C₄×C₃₁	—	2	4	no	—
104	C₄⋊C₄×C₃₁	—	2	4	no	—
105	C₄⋊C₄×C₃₁	—	2	4	no	—
106	C₄⋊C₄×C₃₁	—	2	1	no	—
107	C₄⋊C₄×C₃₁	—	2	1	no	—
108	C₄⋊C₄×C₃₁	—	2	2	no	—
109	C₄⋊C₄×C₃₁	—	2	2	no	—
110	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	4	yes	—
111	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	8	yes	—
112	C₂²⋊C₄×C₃₁	—	2	2	no	—
113	C₂²⋊C₄×C₃₁	—	2	4	no	—
114	C₂²⋊C₄×C₃₁	—	2	4	no	—
115	C₂²⋊C₄×C₃₁	—	2	1	no	—
116	C₂²⋊C₄×C₃₁	—	2	1	no	—
117	C₄²×C₃₁	—	2	2	no	—
118	C₄²×C₃₁	—	2	4	no	—
119	C₄²×C₃₁	C₂×D₄	1	2	yes	—
120	C₄²×C₃₁	C₂×D₄	1	2	yes	—
121	C₄²×C₃₁	C₂×D₄	1	4	yes	—
122	C₄²×C₃₁	C₂×D₄	1	4	yes	—
123	#17391	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂³×C₃₁	—	2	1	no	—
125	C₂³×C₃₁	—	2	2	no	—
126	C₂³×C₃₁	—	4	1	no	—
127	C₂³×C₃₁	—	4	1	no	—
128	C₂³×C₃₁	C₂³×C₄	1	1	yes	characteristic
129	Q₈×C₃₁	—	2	8	no	—
130	Q₈×C₃₁	—	4	4	no	—
131	C₂×C₄×C₃₁	—	2	4	no	—
132	C₂×C₄×C₃₁	—	2	1	no	—
133	C₂×C₄×C₃₁	—	2	2	no	—
134	C₂×C₄×C₃₁	—	2	1	no	—
135	C₂×C₄×C₃₁	—	2	2	no	—
136	C₂×C₄×C₃₁	—	2	1	no	—
137	C₂×C₄×C₃₁	—	2	2	no	—
138	C₂×C₄×C₃₁	—	2	4	no	—
139	C₂×C₄×C₃₁	—	4	1	no	—
140	C₂×C₄×C₃₁	—	4	2	no	—
141	C₂×C₄×C₃₁	—	4	1	no	—
142	C₂×C₄×C₃₁	—	4	4	no	—
143	C₂×C₄×C₃₁	—	4	1	no	—
144	C₂×C₄×C₃₁	—	4	2	no	—
145	C₂×C₄×C₃₁	—	4	1	no	—
146	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
147	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	4	yes	—
148	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	4	yes	—
149	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
150	C₂×C₄×C₃₁	#131	1	4	yes	—
151	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
153	C₈×C₃₁	—	4	4	no	—
154	C₈×C₃₁	—	4	4	no	—
155	C₂×#541	C₂×C₃₁	1	1	yes	characteristic
156	#2983	C₂×C₃₁	1	1	yes	characteristic, complemented
157	#2982	C₂×C₃₁	1	1	yes	characteristic, complemented
158	#1473	C₂×C₃₁	1	4	yes	—
159	#1470	C₂×C₃₁	1	4	yes	complemented
160	#1461	C₂×C₃₁	1	2	yes	complemented
161	#1458	C₂×C₃₁	1	2	yes	—
162	C₂²×C₃₁	—	2	1	no	—
163	C₂²×C₃₁	—	2	1	no	—
164	C₂²×C₃₁	—	4	1	no	—
165	C₂²×C₃₁	—	4	1	no	—
166	C₂²×C₃₁	—	4	1	no	—
167	C₂²×C₃₁	—	8	2	no	—
168	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
169	C₂²×C₃₁	C₂×#131	1	2	yes	—
170	C₄×C₃₁	—	2	4	no	—
171	C₄×C₃₁	—	2	1	no	—
172	C₄×C₃₁	—	2	1	no	—
173	C₄×C₃₁	—	2	2	no	—
174	C₄×C₃₁	—	2	4	no	—
175	C₄×C₃₁	—	4	1	no	—
176	C₄×C₃₁	—	4	2	no	—
177	C₄×C₃₁	—	4	1	no	—
178	C₄×C₃₁	—	4	2	no	—
179	C₄×C₃₁	—	4	1	no	—
180	C₄×C₃₁	#408	1	4	yes	—
181	#541	—	2	4	no	—
182	#541	—	2	4	no	—
183	C₂×C₄⋊Q₈	C₄×C₃₁	1	1	yes	characteristic
184	C₂×#126	C₄×C₃₁	1	2	yes	—
185	C₂×#126	C₂²×C₃₁	1	2	yes	—
186	C₂×#125	C₄×C₃₁	1	1	yes	characteristic
187	C₂×#125	C₄×C₃₁	1	2	yes	—
188	C₂×#125	C₂²×C₃₁	1	2	yes	—
189	C₂×C₂²⋊Q₈	C₄×C₃₁	1	1	yes	characteristic
190	C₂×C₂²⋊Q₈	C₄×C₃₁	1	1	yes	characteristic
191	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
192	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
193	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
194	#446	—	2	4	no	—
195	C₈×Q₈	—	2	4	no	—
196	#432	C₂²×C₃₁	1	4	yes	—
197	#431	C₂²×C₃₁	1	2	yes	—
198	#431	C₂²×C₃₁	1	4	yes	—
199	#431	C₂²×C₃₁	1	2	yes	—
200	#324	C₂²×C₃₁	1	4	yes	—
201	#324	C₂²×C₃₁	1	8	yes	—
202	#323	C₂²×C₃₁	1	4	yes	—
203	C₂×C₃₁	—	2	2	no	—
204	C₂×C₃₁	—	8	1	no	—
205	C₂×C₃₁	C₂×#408	1	1	yes	characteristic
206	C₂×C₃₁	#2884	1	1	yes	characteristic
207	C₂×C₃₁	#2889	1	1	yes	characteristic
208	C₂²×Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic
209	C₂²×Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic
210	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
211	C₄⋊Q₈	—	2	4	no	—
212	#126	—	2	8	no	—
213	#126	—	2	4	no	—
214	#126	—	2	4	no	—
215	#125	—	2	4	no	—
216	#125	—	2	8	no	—
217	#125	—	2	4	no	—
218	#125	—	2	4	no	—
219	C₂²⋊Q₈	—	2	4	no	—
220	C₂²⋊Q₈	—	2	4	no	—
221	C₄×Q₈	—	2	2	no	—
222	C₄×Q₈	—	2	2	no	—
223	C₄×Q₈	D₄×C₃₁	1	4	yes	—
224	C₄×Q₈	D₄×C₃₁	1	4	yes	—
225	#117	—	2	2	no	—
226	#117	—	2	2	no	—
227	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
229	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
230	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
231	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
232	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
233	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
234	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
235	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
236	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
237	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
239	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
240	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
241	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
242	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
243	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
244	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
245	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
246	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
247	C₄⋊C₈	—	2	2	no	—
248	C₄⋊C₈	—	2	4	no	—
249	C₄⋊C₈	—	2	2	no	—
250	C₄⋊C₈	—	2	4	no	—
251	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
252	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
253	#97	—	2	4	no	—
254	C₄×C₈	—	2	2	no	—
255	C₄×C₈	—	2	4	no	—
256	C₄×C₈	—	2	2	no	—
257	C₃₁	#17391	1	1	yes	characteristic, direct product factor, Sylow
258	C₂⁴	C₂²×C₄×C₃₁	1	1	yes	characteristic
259	C₂×Q₈	—	2	2	no	—
260	C₂×Q₈	—	2	4	no	—
261	C₂×Q₈	—	2	4	no	—
262	C₂×Q₈	C₂²⋊C₄×C₃₁	1	4	yes	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
266	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
267	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
268	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
269	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
270	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
271	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
272	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
273	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
274	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
275	C₂×C₈	—	2	4	no	—
276	C₂×C₈	—	2	4	no	—
277	C₄⋊C₄	—	2	2	no	—
278	C₄⋊C₄	—	2	2	no	—
279	C₄⋊C₄	—	2	4	no	—
280	C₄⋊C₄	—	2	4	no	—
281	C₄⋊C₄	—	2	4	no	—
282	C₄⋊C₄	—	2	4	no	—
283	C₄⋊C₄	—	2	4	no	—
284	C₄⋊C₄	—	2	4	no	—
285	C₄⋊C₄	—	2	1	no	—
286	C₄⋊C₄	—	2	1	no	—
287	C₄⋊C₄	—	2	2	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	4	yes	—
290	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	8	yes	—
291	C₂²⋊C₄	—	2	2	no	—
292	C₂²⋊C₄	—	2	4	no	—
293	C₂²⋊C₄	—	2	4	no	—
294	C₂²⋊C₄	—	2	1	no	—
295	C₂²⋊C₄	—	2	1	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	2	4	no	—
298	C₄²	C₂×D₄×C₃₁	1	2	yes	—
299	C₄²	C₂×D₄×C₃₁	1	2	yes	—
300	C₄²	C₂×D₄×C₃₁	1	4	yes	—
301	C₄²	C₂×D₄×C₃₁	1	4	yes	—
302	C₂³	—	2	1	no	—
303	C₂³	—	2	2	no	—
304	C₂³	—	4	1	no	—
305	C₂³	—	4	1	no	—
306	C₂³	C₂³×C₄×C₃₁	1	1	yes	characteristic
307	Q₈	—	2	8	no	—
308	Q₈	—	4	4	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
325	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	4	yes	—
326	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	4	yes	—
327	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
328	C₂×C₄	C₃₁×#131	1	4	yes	—
329	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
330	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
331	C₈	—	4	4	no	—
332	C₈	—	4	4	no	—
333	C₂²	—	2	1	no	—
334	C₂²	—	2	1	no	—
335	C₂²	—	4	1	no	—
336	C₂²	—	4	1	no	—
337	C₂²	—	4	1	no	—
338	C₂²	—	8	2	no	—
339	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
340	C₂²	C₂×C₃₁×#131	1	2	yes	—
341	C₄	—	2	4	no	—
342	C₄	—	2	1	no	—
343	C₄	—	2	1	no	—
344	C₄	—	2	2	no	—
345	C₄	—	2	4	no	—
346	C₄	—	4	1	no	—
347	C₄	—	4	2	no	—
348	C₄	—	4	1	no	—
349	C₄	—	4	2	no	—
350	C₄	—	4	1	no	—
351	C₄	C₃₁×#408	1	4	yes	—
352	C₂	—	2	2	no	—
353	C₂	—	8	1	no	—
354	C₂	C₂×C₃₁×#408	1	1	yes	characteristic
355	C₂	C₃₁×#2884	1	1	yes	characteristic
356	C₂	C₃₁×#2889	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂⁴×C₃₁	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₄×Q₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2983	C₂	semidirect
3. C₃₁×#2982	C₂	semidirect
5. C₃₁×#1470	C₂	semidirect
6. C₃₁×#1461	C₂	semidirect
123. #17391	C₃₁	direct (N × H)
156. #2983	C₂×C₃₁	semidirect
157. #2982	C₂×C₃₁	semidirect
159. #1470	C₂×C₃₁	semidirect
160. #1461	C₂×C₃₁	semidirect
257. C₃₁	#17391	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×#541	2
C₃₁×#2983	2
C₃₁×#2982	2
C₃₁×#1473	2
C₃₁×#1470	2
C₃₁×#1461	2
C₃₁×#1458	2
#17391	31

Subgroups — C31×#17391 #21474150

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#17391 #21474150