Subgroups — C₃₁×#17982 #21474741

Order 7936.

606 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×#3168	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2966	C₂	1	2	yes	maximal, complemented
3	C₃₁×#1588	C₂	1	2	yes	maximal, complemented
4	C₃₁×#1587	C₂	1	2	yes	maximal, complemented
5	C₃₁×#1586	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1585	C₂	1	2	yes	maximal, complemented
7	C₃₁×#1568	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1494	C₂	1	2	yes	maximal, complemented
9	C₂×C₃₁×#322	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#529	C₂²	1	2	yes	—
11	C₃₁×#499	C₄	1	1	yes	characteristic
12	C₃₁×#495	C₄	1	1	yes	characteristic
13	C₃₁×#488	C₄	1	2	yes	—
14	C₃₁×#467	C₄	1	1	yes	characteristic
15	C₃₁×#466	C₄	1	1	yes	characteristic
16	C₃₁×#465	C₄	1	2	yes	—
17	C₃₁×#446	C₂²	1	2	yes	—
18	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
19	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
20	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
21	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
22	C₃₁×#436	C₂²	1	2	yes	—
23	C₃₁×#435	—	2	2	no	—
24	C₈×D₄×C₃₁	—	2	2	no	—
25	C₈×D₄×C₃₁	C₂²	1	2	yes	—
26	C₃₁×#433	—	2	2	no	—
27	C₃₁×#432	C₂²	1	2	yes	—
28	C₃₁×#405	—	2	2	no	—
29	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
32	C₃₁×#335	C₂²	1	1	yes	characteristic
33	C₃₁×#335	C₂²	1	1	yes	characteristic
34	C₃₁×#334	C₂²	1	2	yes	—
35	C₃₁×Q₈⋊C₈	C₂²	1	2	yes	—
36	C₃₁×Q₈⋊C₈	C₂²	1	2	yes	—
37	C₃₁×D₄⋊C₈	C₂²	1	2	yes	—
38	C₃₁×D₄⋊C₈	C₂²	1	2	yes	—
39	C₃₁×#322	C₂²	1	2	yes	—
40	C₃₁×#322	C₂²	1	2	yes	—
41	C₂×Q₁₆×C₃₁	C₂×C₄	1	1	yes	characteristic
42	C₂×SD₁₆×C₃₁	C₂×C₄	1	2	yes	—
43	C₂×D₈×C₃₁	C₂×C₄	1	1	yes	characteristic
44	C₂×M₁₆×C₃₁	—	2	2	no	—
45	C₂²×C₈×C₃₁	—	2	1	no	—
46	C₂²×C₈×C₃₁	—	2	2	no	—
47	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
51	C₃₁×#126	—	2	2	no	—
52	C₃₁×#125	C₂×C₄	1	2	yes	—
53	C₃₁×#124	C₂×C₄	1	2	yes	—
54	C₃₁×#123	—	2	2	no	—
55	C₃₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
56	C₃₁×#121	C₂×C₄	1	2	yes	—
57	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
58	C₄×D₄×C₃₁	—	2	2	no	—
59	C₄×D₄×C₃₁	C₂³	1	2	yes	—
60	C₃₁×#117	—	2	2	no	—
61	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
62	C₃₁×#107	C₂×C₄	1	1	yes	characteristic
63	C₃₁×#107	C₂×C₄	1	1	yes	characteristic
64	C₃₁×#106	C₂×C₄	1	2	yes	—
65	C₃₁×C₄⋊C₈	—	2	2	no	—
66	C₃₁×C₄⋊C₈	—	2	2	no	—
67	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
68	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
69	C₃₁×#103	C₂×C₄	1	2	yes	—
70	C₃₁×#103	C₂×C₄	1	2	yes	—
71	C₃₁×#102	C₂×C₄	1	2	yes	—
72	C₃₁×#102	C₂×C₄	1	2	yes	—
73	C₃₁×C₂²⋊C₈	—	2	2	no	—
74	C₃₁×C₂²⋊C₈	—	2	2	no	—
75	C₃₁×C₂²⋊C₈	—	2	2	no	—
76	C₃₁×#97	—	2	2	no	—
77	C₃₁×#97	—	2	2	no	—
78	C₄×C₈×C₃₁	—	2	2	no	—
79	C₄×C₈×C₃₁	—	2	1	no	—
80	C₄×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₃₁	D₄	1	2	yes	—
83	C₄×C₈×C₃₁	C₂³	1	2	yes	—
84	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
85	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
86	C₄×C₈×C₃₁	C₂³	1	2	yes	—
87	C₂×Q₈×C₃₁	C₂²×C₄	1	2	yes	—
88	C₂×D₄×C₃₁	—	2	2	no	—
89	C₂×D₄×C₃₁	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₃₁	—	2	2	no	—
91	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
94	Q₁₆×C₃₁	—	4	1	no	—
95	SD₁₆×C₃₁	—	4	2	no	—
96	D₈×C₃₁	—	4	1	no	—
97	M₁₆×C₃₁	—	4	4	no	—
98	C₂×C₈×C₃₁	—	2	4	no	—
99	C₂×C₈×C₃₁	—	2	2	no	—
100	C₂×C₈×C₃₁	—	2	2	no	—
101	C₂×C₈×C₃₁	—	2	2	no	—
102	C₂×C₈×C₃₁	—	4	1	no	—
103	C₂×C₈×C₃₁	—	4	1	no	—
104	C₂×C₈×C₃₁	—	4	1	no	—
105	C₂×C₈×C₃₁	—	4	1	no	—
106	C₂×C₈×C₃₁	—	4	4	no	—
107	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
112	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
113	C₄⋊C₄×C₃₁	—	2	2	no	—
114	C₄⋊C₄×C₃₁	—	2	2	no	—
115	C₄⋊C₄×C₃₁	—	2	2	no	—
116	C₄⋊C₄×C₃₁	—	2	2	no	—
117	C₄⋊C₄×C₃₁	C₂²×C₄	1	2	yes	—
118	C₄⋊C₄×C₃₁	C₂²×C₄	1	2	yes	—
119	C₂²⋊C₄×C₃₁	—	2	2	no	—
120	C₂²⋊C₄×C₃₁	—	2	2	no	—
121	C₂²⋊C₄×C₃₁	—	2	2	no	—
122	C₂²⋊C₄×C₃₁	—	2	2	no	—
123	C₂²⋊C₄×C₃₁	—	2	2	no	—
124	C₄²×C₃₁	—	2	2	no	—
125	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₃₁	#41	1	1	yes	characteristic
128	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
129	#17982	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂³×C₃₁	—	2	2	no	—
131	C₂³×C₃₁	C₄×D₄	1	1	yes	characteristic
132	Q₈×C₃₁	—	2	2	no	—
133	Q₈×C₃₁	—	2	2	no	—
134	D₄×C₃₁	—	2	2	no	—
135	D₄×C₃₁	—	2	2	no	—
136	D₄×C₃₁	—	4	4	no	—
137	C₂×C₄×C₃₁	—	2	2	no	—
138	C₂×C₄×C₃₁	—	2	1	no	—
139	C₂×C₄×C₃₁	—	2	1	no	—
140	C₂×C₄×C₃₁	—	2	1	no	—
141	C₂×C₄×C₃₁	—	2	1	no	—
142	C₂×C₄×C₃₁	—	2	2	no	—
143	C₂×C₄×C₃₁	—	2	2	no	—
144	C₂×C₄×C₃₁	—	2	2	no	—
145	C₂×C₄×C₃₁	—	4	2	no	—
146	C₂×C₄×C₃₁	—	4	2	no	—
147	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
153	C₈×C₃₁	—	2	4	no	—
154	C₈×C₃₁	—	2	1	no	—
155	C₈×C₃₁	—	2	1	no	—
156	C₈×C₃₁	—	2	1	no	—
157	C₈×C₃₁	—	2	1	no	—
158	C₈×C₃₁	—	2	2	no	—
159	C₈×C₃₁	—	2	2	no	—
160	C₈×C₃₁	—	4	2	no	—
161	C₈×C₃₁	—	4	2	no	—
162	#3168	C₂×C₃₁	1	1	yes	characteristic
163	#2966	C₂×C₃₁	1	2	yes	complemented
164	#1588	C₂×C₃₁	1	2	yes	complemented
165	#1587	C₂×C₃₁	1	2	yes	complemented
166	#1586	C₂×C₃₁	1	2	yes	complemented
167	#1585	C₂×C₃₁	1	2	yes	complemented
168	#1568	C₂×C₃₁	1	1	yes	characteristic, complemented
169	#1494	C₂×C₃₁	1	2	yes	complemented
170	C₂×#322	C₂×C₃₁	1	1	yes	characteristic, complemented
171	C₂²×C₃₁	—	2	1	no	—
172	C₂²×C₃₁	—	2	1	no	—
173	C₂²×C₃₁	—	4	2	no	—
174	C₂²×C₃₁	—	4	2	no	—
175	C₂²×C₃₁	—	4	2	no	—
176	C₂²×C₃₁	#443	1	2	yes	—
177	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
178	C₄×C₃₁	—	2	1	no	—
179	C₄×C₃₁	—	2	1	no	—
180	C₄×C₃₁	—	2	1	no	—
181	C₄×C₃₁	—	2	1	no	—
182	C₄×C₃₁	—	4	2	no	—
183	C₄×C₃₁	—	4	2	no	—
184	C₄×C₃₁	—	4	2	no	—
185	C₄×C₃₁	#568	1	1	yes	characteristic
186	C₄×C₃₁	#568	1	1	yes	characteristic
187	C₄×C₃₁	#575	1	1	yes	characteristic
188	C₄×C₃₁	#575	1	1	yes	characteristic
189	#529	C₂²×C₃₁	1	2	yes	—
190	#499	C₄×C₃₁	1	1	yes	characteristic
191	#495	C₄×C₃₁	1	1	yes	characteristic
192	#488	C₄×C₃₁	1	2	yes	—
193	#467	C₄×C₃₁	1	1	yes	characteristic
194	#466	C₄×C₃₁	1	1	yes	characteristic
195	#465	C₄×C₃₁	1	2	yes	—
196	#446	C₂²×C₃₁	1	2	yes	—
197	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
198	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
199	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
200	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
201	#436	C₂²×C₃₁	1	2	yes	—
202	#435	—	2	2	no	—
203	C₈×D₄	—	2	2	no	—
204	C₈×D₄	C₂²×C₃₁	1	2	yes	—
205	#433	—	2	2	no	—
206	#432	C₂²×C₃₁	1	2	yes	—
207	#405	—	2	2	no	—
208	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
209	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
210	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
211	#335	C₂²×C₃₁	1	1	yes	characteristic
212	#335	C₂²×C₃₁	1	1	yes	characteristic
213	#334	C₂²×C₃₁	1	2	yes	—
214	Q₈⋊C₈	C₂²×C₃₁	1	2	yes	—
215	Q₈⋊C₈	C₂²×C₃₁	1	2	yes	—
216	D₄⋊C₈	C₂²×C₃₁	1	2	yes	—
217	D₄⋊C₈	C₂²×C₃₁	1	2	yes	—
218	#322	C₂²×C₃₁	1	2	yes	—
219	#322	C₂²×C₃₁	1	2	yes	—
220	C₂×C₃₁	—	2	2	no	—
221	C₂×C₃₁	—	8	2	no	—
222	C₂×C₃₁	#2932	1	1	yes	characteristic
223	C₂×C₃₁	#2943	1	1	yes	characteristic
224	C₂×C₃₁	C₂×#443	1	1	yes	characteristic
225	C₂×Q₁₆	C₂×C₄×C₃₁	1	1	yes	characteristic
226	C₂×SD₁₆	C₂×C₄×C₃₁	1	2	yes	—
227	C₂×D₈	C₂×C₄×C₃₁	1	1	yes	characteristic
228	C₂×M₁₆	—	2	2	no	—
229	C₂²×C₈	—	2	1	no	—
230	C₂²×C₈	—	2	2	no	—
231	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
232	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
233	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
234	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
235	#126	—	2	2	no	—
236	#125	C₂×C₄×C₃₁	1	2	yes	—
237	#124	C₂×C₄×C₃₁	1	2	yes	—
238	#123	—	2	2	no	—
239	C₂²⋊Q₈	C₂×C₄×C₃₁	1	2	yes	—
240	#121	C₂×C₄×C₃₁	1	2	yes	—
241	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
242	C₄×D₄	—	2	2	no	—
243	C₄×D₄	C₂³×C₃₁	1	2	yes	—
244	#117	—	2	2	no	—
245	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
246	#107	C₂×C₄×C₃₁	1	1	yes	characteristic
247	#107	C₂×C₄×C₃₁	1	1	yes	characteristic
248	#106	C₂×C₄×C₃₁	1	2	yes	—
249	C₄⋊C₈	—	2	2	no	—
250	C₄⋊C₈	—	2	2	no	—
251	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
252	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
253	#103	C₂×C₄×C₃₁	1	2	yes	—
254	#103	C₂×C₄×C₃₁	1	2	yes	—
255	#102	C₂×C₄×C₃₁	1	2	yes	—
256	#102	C₂×C₄×C₃₁	1	2	yes	—
257	C₂²⋊C₈	—	2	2	no	—
258	C₂²⋊C₈	—	2	2	no	—
259	C₂²⋊C₈	—	2	2	no	—
260	#97	—	2	2	no	—
261	#97	—	2	2	no	—
262	C₄×C₈	—	2	2	no	—
263	C₄×C₈	—	2	1	no	—
264	C₄×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
265	C₄×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
266	C₄×C₈	D₄×C₃₁	1	2	yes	—
267	C₄×C₈	C₂³×C₃₁	1	2	yes	—
268	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
269	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
270	C₄×C₈	C₂³×C₃₁	1	2	yes	—
271	C₃₁	#17982	1	1	yes	characteristic, direct product factor, Sylow
272	C₂×Q₈	C₂²×C₄×C₃₁	1	2	yes	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	C₂²×C₄×C₃₁	1	2	yes	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
278	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
279	Q₁₆	—	4	1	no	—
280	SD₁₆	—	4	2	no	—
281	D₈	—	4	1	no	—
282	M₁₆	—	4	4	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	4	1	no	—
288	C₂×C₈	—	4	1	no	—
289	C₂×C₈	—	4	1	no	—
290	C₂×C₈	—	4	1	no	—
291	C₂×C₈	—	4	4	no	—
292	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
293	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
294	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
295	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
296	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
297	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
303	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
304	C₂²⋊C₄	—	2	2	no	—
305	C₂²⋊C₄	—	2	2	no	—
306	C₂²⋊C₄	—	2	2	no	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₂²⋊C₄	—	2	2	no	—
309	C₄²	—	2	2	no	—
310	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
311	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
312	C₄²	#41×C₃₁	1	1	yes	characteristic
313	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
314	C₂³	—	2	2	no	—
315	C₂³	C₄×D₄×C₃₁	1	1	yes	characteristic
316	Q₈	—	2	2	no	—
317	Q₈	—	2	2	no	—
318	D₄	—	2	2	no	—
319	D₄	—	2	2	no	—
320	D₄	—	4	4	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
332	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
333	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
334	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
335	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
336	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
337	C₈	—	2	4	no	—
338	C₈	—	2	1	no	—
339	C₈	—	2	1	no	—
340	C₈	—	2	1	no	—
341	C₈	—	2	1	no	—
342	C₈	—	2	2	no	—
343	C₈	—	2	2	no	—
344	C₈	—	4	2	no	—
345	C₈	—	4	2	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	4	2	no	—
349	C₂²	—	4	2	no	—
350	C₂²	—	4	2	no	—
351	C₂²	C₃₁×#443	1	2	yes	—
352	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	4	2	no	—
358	C₄	—	4	2	no	—
359	C₄	—	4	2	no	—
360	C₄	C₃₁×#568	1	1	yes	characteristic
361	C₄	C₃₁×#568	1	1	yes	characteristic
362	C₄	C₃₁×#575	1	1	yes	characteristic
363	C₄	C₃₁×#575	1	1	yes	characteristic
364	C₂	—	2	2	no	—
365	C₂	—	8	2	no	—
366	C₂	C₃₁×#2932	1	1	yes	characteristic
367	C₂	C₃₁×#2943	1	1	yes	characteristic
368	C₂	C₂×C₃₁×#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₄²	C₂⁴×C₃₁
socle	C₂²×C₃₁	C₂×C₄×D₄
prime radical	C₃₁×#466	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₂×C₄×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2966	C₂	semidirect
3. C₃₁×#1588	C₂	semidirect
4. C₃₁×#1587	C₂	semidirect
5. C₃₁×#1586	C₂	semidirect
6. C₃₁×#1585	C₂	semidirect
7. C₃₁×#1568	C₂	semidirect
8. C₃₁×#1494	C₂	semidirect
9. C₂×C₃₁×#322	C₂	semidirect
129. #17982	C₃₁	direct (N × H)
163. #2966	C₂×C₃₁	semidirect
164. #1588	C₂×C₃₁	semidirect
165. #1587	C₂×C₃₁	semidirect
166. #1586	C₂×C₃₁	semidirect
167. #1585	C₂×C₃₁	semidirect
168. #1568	C₂×C₃₁	semidirect
169. #1494	C₂×C₃₁	semidirect
170. C₂×#322	C₂×C₃₁	semidirect
271. C₃₁	#17982	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×#3168	2
C₃₁×#2966	2
C₃₁×#1588	2
C₃₁×#1587	2
C₃₁×#1586	2
C₃₁×#1585	2
C₃₁×#1568	2
C₃₁×#1494	2
C₂×C₃₁×#322	2
#17982	31

Subgroups — C31×#17982 #21474741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#17982 #21474741