Subgroups — C₃₁×#20812 #21477571

Order 7936.

854 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#433	C₂	1	2	yes	maximal
2	C₄×C₃₁×#117	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#1842	C₂	1	2	yes	maximal, complemented
4	C₃₁×#1832	C₂	1	2	yes	maximal, complemented
5	C₃₁×#1798	C₂	1	2	yes	maximal
6	C₃₁×#1797	C₂	1	2	yes	maximal
7	C₃₁×#1768	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1767	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₃₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
11	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
13	C₃₁×#433	—	2	8	no	—
14	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₃₁×C₄⋊C₈	C₂²	1	4	yes	—
17	C₂×C₃₁×C₄⋊C₈	C₂²	1	4	yes	—
18	C₂×C₃₁×C₂²⋊C₈	C₂²	1	4	yes	—
19	C₂×C₃₁×#97	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
21	C₄×C₄⋊C₄×C₃₁	C₄	1	2	yes	—
22	C₄×C₄⋊C₄×C₃₁	C₄	1	2	yes	—
23	C₄×C₂²⋊C₄×C₃₁	C₄	1	2	yes	—
24	C₄×C₂²⋊C₄×C₃₁	C₄	1	2	yes	—
25	C₃₁×#376	C₂²	1	1	yes	characteristic
26	C₃₁×#376	C₂²	1	1	yes	characteristic
27	C₄³×C₃₁	C₂²	1	1	yes	characteristic
28	C₄³×C₃₁	C₂²	1	1	yes	characteristic
29	C₃₁×#336	C₂²	1	4	yes	—
30	C₃₁×#336	C₂²	1	2	yes	—
31	C₃₁×#336	C₂²	1	2	yes	—
32	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
35	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
36	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
37	C₃₁×#117	—	2	4	no	—
38	C₃₁×#117	D₄	1	4	yes	—
39	C₃₁×#117	Q₈	1	4	yes	—
40	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
41	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
42	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
43	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
44	C₂×C₄²×C₃₁	—	2	4	no	—
45	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
54	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
57	C₃₁×C₄⋊C₈	—	2	8	no	—
58	C₃₁×C₄⋊C₈	—	2	4	no	—
59	C₃₁×C₄⋊C₈	—	2	4	no	—
60	C₃₁×C₄⋊C₈	—	2	8	no	—
61	C₃₁×C₂²⋊C₈	—	2	8	no	—
62	C₃₁×#97	—	2	4	no	—
63	C₄×C₈×C₃₁	—	2	4	no	—
64	C₃₁×#95	C₂×C₄	1	2	yes	—
65	C₃₁×#95	C₂×C₄	1	2	yes	—
66	C₃₁×#95	C₂×C₄	1	2	yes	—
67	C₃₁×#95	C₂×C₄	1	2	yes	—
68	C₂⁴×C₃₁	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₃₁	—	2	2	no	—
70	C₂²×C₄×C₃₁	—	2	2	no	—
71	C₂²×C₄×C₃₁	—	2	2	no	—
72	C₂²×C₄×C₃₁	—	2	2	no	—
73	C₂²×C₄×C₃₁	—	2	4	no	—
74	C₂²×C₄×C₃₁	—	4	2	no	—
75	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
78	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
86	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
87	C₂×C₈×C₃₁	—	2	4	no	—
88	C₂×C₈×C₃₁	—	2	4	no	—
89	C₂×C₈×C₃₁	—	2	4	no	—
90	C₂×C₈×C₃₁	—	2	4	no	—
91	C₂×C₈×C₃₁	—	2	4	no	—
92	C₂×C₈×C₃₁	—	2	4	no	—
93	C₄⋊C₄×C₃₁	—	2	4	no	—
94	C₄⋊C₄×C₃₁	C₄⋊C₄	1	8	yes	—
95	C₂²⋊C₄×C₃₁	—	2	4	no	—
96	C₂²⋊C₄×C₃₁	C₄⋊C₄	1	8	yes	—
97	C₄²×C₃₁	—	2	2	no	—
98	C₄²×C₃₁	—	2	2	no	—
99	C₄²×C₃₁	—	2	4	no	—
100	C₄²×C₃₁	—	2	4	no	—
101	C₄²×C₃₁	—	2	2	no	—
102	C₄²×C₃₁	—	2	2	no	—
103	C₄²×C₃₁	—	4	2	no	—
104	C₄²×C₃₁	—	4	2	no	—
105	C₄²×C₃₁	C₂×D₄	1	2	yes	—
106	C₄²×C₃₁	C₂×D₄	1	2	yes	—
107	C₄²×C₃₁	C₂×Q₈	1	2	yes	—
108	C₄²×C₃₁	C₂×Q₈	1	2	yes	—
109	C₄²×C₃₁	#41	1	4	yes	—
110	C₄²×C₃₁	#41	1	4	yes	—
111	#20812	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂³×C₃₁	—	2	1	no	—
113	C₂³×C₃₁	—	2	1	no	—
114	C₂³×C₃₁	—	2	2	no	—
115	C₂³×C₃₁	—	2	2	no	—
116	C₂³×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
117	C₂³×C₃₁	C₂³×C₄	1	1	yes	characteristic
118	C₂×C₄×C₃₁	—	2	1	no	—
119	C₂×C₄×C₃₁	—	2	1	no	—
120	C₂×C₄×C₃₁	—	2	2	no	—
121	C₂×C₄×C₃₁	—	2	2	no	—
122	C₂×C₄×C₃₁	—	2	2	no	—
123	C₂×C₄×C₃₁	—	2	2	no	—
124	C₂×C₄×C₃₁	—	2	2	no	—
125	C₂×C₄×C₃₁	—	2	2	no	—
126	C₂×C₄×C₃₁	—	2	2	no	—
127	C₂×C₄×C₃₁	—	2	4	no	—
128	C₂×C₄×C₃₁	—	2	4	no	—
129	C₂×C₄×C₃₁	—	2	1	no	—
130	C₂×C₄×C₃₁	—	2	1	no	—
131	C₂×C₄×C₃₁	—	2	2	no	—
132	C₂×C₄×C₃₁	—	2	2	no	—
133	C₂×C₄×C₃₁	—	2	2	no	—
134	C₂×C₄×C₃₁	—	2	2	no	—
135	C₂×C₄×C₃₁	—	2	2	no	—
136	C₂×C₄×C₃₁	—	4	4	no	—
137	C₂×C₄×C₃₁	—	4	4	no	—
138	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	4	yes	—
139	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	4	yes	—
140	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
141	C₂×C₄×C₃₁	#117	1	2	yes	—
142	C₂×C₄×C₃₁	#117	1	4	yes	—
143	C₂×C₄×C₃₁	#117	1	2	yes	—
144	C₂×C₄×C₃₁	#131	1	4	yes	—
145	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
146	C₂×C₄×C₃₁	C₂²×Q₈	1	1	yes	characteristic
147	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
148	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
149	C₈×C₃₁	—	4	4	no	—
150	C₈×C₃₁	—	4	4	no	—
151	C₂×#433	C₂×C₃₁	1	2	yes	—
152	C₄×#117	C₂×C₃₁	1	1	yes	characteristic
153	#1842	C₂×C₃₁	1	2	yes	complemented
154	#1832	C₂×C₃₁	1	2	yes	complemented
155	#1798	C₂×C₃₁	1	2	yes	—
156	#1797	C₂×C₃₁	1	2	yes	—
157	#1768	C₂×C₃₁	1	2	yes	complemented
158	#1767	C₂×C₃₁	1	1	yes	characteristic, complemented
159	C₄×C₄⋊C₈	C₂×C₃₁	1	1	yes	characteristic, complemented
160	C₂²×C₃₁	—	2	4	no	—
161	C₂²×C₃₁	—	2	2	no	—
162	C₂²×C₃₁	—	4	1	no	—
163	C₂²×C₃₁	—	4	1	no	—
164	C₂²×C₃₁	—	4	2	no	—
165	C₂²×C₃₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
166	C₂²×C₃₁	C₂×#117	1	1	yes	characteristic
167	C₂²×C₃₁	C₂×#117	1	1	yes	characteristic
168	C₂²×C₃₁	C₂×#131	1	2	yes	—
169	C₂²×C₃₁	#568	1	2	yes	—
170	C₄×C₃₁	—	2	4	no	—
171	C₄×C₃₁	—	2	4	no	—
172	C₄×C₃₁	—	2	2	no	—
173	C₄×C₃₁	—	2	4	no	—
174	C₄×C₃₁	—	2	2	no	—
175	C₄×C₃₁	—	4	1	no	—
176	C₄×C₃₁	—	4	1	no	—
177	C₄×C₃₁	—	4	2	no	—
178	C₄×C₃₁	#433	1	4	yes	complemented
179	C₄×C₃₁	#532	1	2	yes	—
180	C₄×C₃₁	#533	1	2	yes	—
181	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
182	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
183	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
184	#433	—	2	8	no	—
185	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
186	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
187	C₂×C₄⋊C₈	C₂²×C₃₁	1	4	yes	—
188	C₂×C₄⋊C₈	C₂²×C₃₁	1	4	yes	—
189	C₂×C₂²⋊C₈	C₂²×C₃₁	1	4	yes	—
190	C₂×#97	C₂²×C₃₁	1	2	yes	—
191	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
192	C₄×C₄⋊C₄	C₄×C₃₁	1	2	yes	—
193	C₄×C₄⋊C₄	C₄×C₃₁	1	2	yes	—
194	C₄×C₂²⋊C₄	C₄×C₃₁	1	2	yes	—
195	C₄×C₂²⋊C₄	C₄×C₃₁	1	2	yes	—
196	#376	C₂²×C₃₁	1	1	yes	characteristic
197	#376	C₂²×C₃₁	1	1	yes	characteristic
198	C₄³	C₂²×C₃₁	1	1	yes	characteristic
199	C₄³	C₂²×C₃₁	1	1	yes	characteristic
200	#336	C₂²×C₃₁	1	4	yes	—
201	#336	C₂²×C₃₁	1	2	yes	—
202	#336	C₂²×C₃₁	1	2	yes	—
203	C₂×C₃₁	—	4	2	no	—
204	C₂×C₃₁	#2285	1	1	yes	characteristic
205	C₂×C₃₁	#2906	1	2	yes	—
206	C₂×C₃₁	C₂×#433	1	1	yes	characteristic
207	C₂×C₃₁	#2921	1	1	yes	characteristic
208	C₂×C₃₁	#2925	1	2	yes	—
209	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
210	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
211	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
212	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
213	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
214	#117	—	2	4	no	—
215	#117	D₄×C₃₁	1	4	yes	—
216	#117	Q₈×C₃₁	1	4	yes	—
217	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
218	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
219	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
220	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
221	C₂×C₄²	—	2	4	no	—
222	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
223	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
224	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
225	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
226	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
227	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
228	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
229	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
230	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
231	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
232	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
233	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
234	C₄⋊C₈	—	2	8	no	—
235	C₄⋊C₈	—	2	4	no	—
236	C₄⋊C₈	—	2	4	no	—
237	C₄⋊C₈	—	2	8	no	—
238	C₂²⋊C₈	—	2	8	no	—
239	#97	—	2	4	no	—
240	C₄×C₈	—	2	4	no	—
241	#95	C₂×C₄×C₃₁	1	2	yes	—
242	#95	C₂×C₄×C₃₁	1	2	yes	—
243	#95	C₂×C₄×C₃₁	1	2	yes	—
244	#95	C₂×C₄×C₃₁	1	2	yes	—
245	C₃₁	#20812	1	1	yes	characteristic, direct product factor, Sylow
246	C₂⁴	C₂²×C₄×C₃₁	1	1	yes	characteristic
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	4	2	no	—
253	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
254	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
255	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
256	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
257	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
258	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
259	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
260	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
261	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
262	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
263	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
264	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
265	C₂×C₈	—	2	4	no	—
266	C₂×C₈	—	2	4	no	—
267	C₂×C₈	—	2	4	no	—
268	C₂×C₈	—	2	4	no	—
269	C₂×C₈	—	2	4	no	—
270	C₂×C₈	—	2	4	no	—
271	C₄⋊C₄	—	2	4	no	—
272	C₄⋊C₄	C₄⋊C₄×C₃₁	1	8	yes	—
273	C₂²⋊C₄	—	2	4	no	—
274	C₂²⋊C₄	C₄⋊C₄×C₃₁	1	8	yes	—
275	C₄²	—	2	2	no	—
276	C₄²	—	2	2	no	—
277	C₄²	—	2	4	no	—
278	C₄²	—	2	4	no	—
279	C₄²	—	2	2	no	—
280	C₄²	—	2	2	no	—
281	C₄²	—	4	2	no	—
282	C₄²	—	4	2	no	—
283	C₄²	C₂×D₄×C₃₁	1	2	yes	—
284	C₄²	C₂×D₄×C₃₁	1	2	yes	—
285	C₄²	C₂×Q₈×C₃₁	1	2	yes	—
286	C₄²	C₂×Q₈×C₃₁	1	2	yes	—
287	C₄²	#41×C₃₁	1	4	yes	—
288	C₄²	#41×C₃₁	1	4	yes	—
289	C₂³	—	2	1	no	—
290	C₂³	—	2	1	no	—
291	C₂³	—	2	2	no	—
292	C₂³	—	2	2	no	—
293	C₂³	C₂×C₄⋊C₄×C₃₁	1	2	yes	—
294	C₂³	C₂³×C₄×C₃₁	1	1	yes	characteristic
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	4	4	no	—
314	C₂×C₄	—	4	4	no	—
315	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	4	yes	—
316	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	4	yes	—
317	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	2	yes	—
318	C₂×C₄	C₃₁×#117	1	2	yes	—
319	C₂×C₄	C₃₁×#117	1	4	yes	—
320	C₂×C₄	C₃₁×#117	1	2	yes	—
321	C₂×C₄	C₃₁×#131	1	4	yes	—
322	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
323	C₂×C₄	C₂²×Q₈×C₃₁	1	1	yes	characteristic
324	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
325	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
326	C₈	—	4	4	no	—
327	C₈	—	4	4	no	—
328	C₂²	—	2	4	no	—
329	C₂²	—	2	2	no	—
330	C₂²	—	4	1	no	—
331	C₂²	—	4	1	no	—
332	C₂²	—	4	2	no	—
333	C₂²	C₂²×C₄⋊C₄×C₃₁	1	1	yes	characteristic
334	C₂²	C₂×C₃₁×#117	1	1	yes	characteristic
335	C₂²	C₂×C₃₁×#117	1	1	yes	characteristic
336	C₂²	C₂×C₃₁×#131	1	2	yes	—
337	C₂²	C₃₁×#568	1	2	yes	—
338	C₄	—	2	4	no	—
339	C₄	—	2	4	no	—
340	C₄	—	2	2	no	—
341	C₄	—	2	4	no	—
342	C₄	—	2	2	no	—
343	C₄	—	4	1	no	—
344	C₄	—	4	1	no	—
345	C₄	—	4	2	no	—
346	C₄	C₃₁×#433	1	4	yes	complemented
347	C₄	C₃₁×#532	1	2	yes	—
348	C₄	C₃₁×#533	1	2	yes	—
349	C₂	—	4	2	no	—
350	C₂	C₃₁×#2285	1	1	yes	characteristic
351	C₂	C₃₁×#2906	1	2	yes	—
352	C₂	C₂×C₃₁×#433	1	1	yes	characteristic
353	C₂	C₃₁×#2921	1	1	yes	characteristic
354	C₂	C₃₁×#2925	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₃₁×#1842	C₂	semidirect
4. C₃₁×#1832	C₂	semidirect
7. C₃₁×#1768	C₂	semidirect
8. C₃₁×#1767	C₂	semidirect
9. C₄×C₃₁×C₄⋊C₈	C₂	semidirect
111. #20812	C₃₁	direct (N × H)
153. #1842	C₂×C₃₁	semidirect
154. #1832	C₂×C₃₁	semidirect
157. #1768	C₂×C₃₁	semidirect
158. #1767	C₂×C₃₁	semidirect
159. C₄×C₄⋊C₈	C₂×C₃₁	semidirect
178. C₄×C₃₁	#433	semidirect
245. C₃₁	#20812	direct (N × H)
346. C₄	C₃₁×#433	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃₁×#433	2
C₄×C₃₁×#117	2
C₃₁×#1842	2
C₃₁×#1832	2
C₃₁×#1798	2
C₃₁×#1797	2
C₃₁×#1768	2
C₃₁×#1767	2
C₄×C₃₁×C₄⋊C₈	2
#20812	31

Subgroups — C31×#20812 #21477571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#20812 #21477571