Subgroups — C₃₁×#22263 #21479022

Order 7936.

1002 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#436	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₈×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2397	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1955	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1955	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1870	C₂	1	4	yes	maximal, complemented
7	C₃₁×#1869	C₂	1	4	yes	maximal, complemented
8	C₃₁×#1832	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#1746	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
11	C₂³×C₈×C₃₁	C₂²	1	2	yes	—
12	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
15	C₃₁×#436	—	2	4	no	—
16	C₈×D₄×C₃₁	—	2	4	no	—
17	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
20	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₃₁×C₂²⋊C₈	C₂²	1	4	yes	—
22	C₂×C₃₁×C₂²⋊C₈	C₂²	1	4	yes	—
23	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
25	C₃₁×#399	C₄	1	2	yes	—
26	C₃₁×#399	C₄	1	2	yes	—
27	C₃₁×#392	C₄	1	2	yes	—
28	C₃₁×#392	C₄	1	2	yes	—
29	C₃₁×#376	C₂²	1	1	yes	characteristic
30	C₃₁×#336	C₂²	1	4	yes	—
31	C₃₁×#336	C₂²	1	2	yes	—
32	C₃₁×#336	C₂²	1	2	yes	—
33	C₂²×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
34	C₂²×D₄×C₃₁	C₂×C₄	1	4	yes	—
35	C₂²×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
37	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
38	C₂×M₁₆×C₃₁	—	2	4	no	—
39	C₂×M₁₆×C₃₁	—	4	4	no	—
40	C₂²×C₈×C₃₁	—	2	4	no	—
41	C₂²×C₈×C₃₁	—	4	4	no	—
42	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
44	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
45	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
47	C₄×D₄×C₃₁	—	2	2	no	—
48	C₄×D₄×C₃₁	—	2	2	no	—
49	C₄×D₄×C₃₁	—	2	2	no	—
50	C₄×D₄×C₃₁	—	2	2	no	—
51	C₄×D₄×C₃₁	—	4	4	no	—
52	C₄×D₄×C₃₁	—	4	4	no	—
53	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
56	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
57	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
58	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
59	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
60	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
61	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
62	C₃₁×C₄⋊C₈	—	2	2	no	—
63	C₃₁×C₄⋊C₈	—	2	2	no	—
64	C₃₁×C₂²⋊C₈	—	2	4	no	—
65	C₃₁×C₂²⋊C₈	—	2	4	no	—
66	C₃₁×C₂²⋊C₈	—	4	4	no	—
67	C₃₁×C₂²⋊C₈	—	4	4	no	—
68	C₃₁×#97	—	2	2	no	—
69	C₄×C₈×C₃₁	D₄	1	4	yes	complemented
70	C₃₁×#95	C₂×C₄	1	2	yes	—
71	C₃₁×#95	C₂×C₄	1	2	yes	—
72	C₂⁴×C₃₁	C₂²×C₄	1	2	yes	—
73	C₂⁴×C₃₁	C₂²×C₄	1	2	yes	—
74	C₂×D₄×C₃₁	—	2	4	no	—
75	C₂×D₄×C₃₁	—	2	8	no	—
76	C₂×D₄×C₃₁	—	2	2	no	—
77	C₂×D₄×C₃₁	—	2	2	no	—
78	C₂×D₄×C₃₁	—	4	4	no	—
79	C₂×D₄×C₃₁	—	4	2	no	—
80	C₂×D₄×C₃₁	—	4	4	no	—
81	C₂²×C₄×C₃₁	—	2	2	no	—
82	C₂²×C₄×C₃₁	—	2	2	no	—
83	C₂²×C₄×C₃₁	—	2	2	no	—
84	C₂²×C₄×C₃₁	—	2	2	no	—
85	C₂²×C₄×C₃₁	—	2	4	no	—
86	C₂²×C₄×C₃₁	—	2	4	no	—
87	C₂²×C₄×C₃₁	—	2	4	no	—
88	C₂²×C₄×C₃₁	—	2	4	no	—
89	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
95	M₁₆×C₃₁	—	4	8	no	—
96	C₂×C₈×C₃₁	—	2	2	no	—
97	C₂×C₈×C₃₁	—	2	2	no	—
98	C₂×C₈×C₃₁	—	2	2	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	—	2	2	no	—
103	C₂×C₈×C₃₁	—	2	4	no	—
104	C₂×C₈×C₃₁	—	2	4	no	—
105	C₂×C₈×C₃₁	—	4	8	no	—
106	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
107	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
108	C₄⋊C₄×C₃₁	—	2	2	no	—
109	C₄⋊C₄×C₃₁	—	2	2	no	—
110	C₄⋊C₄×C₃₁	—	4	4	no	—
111	C₂²⋊C₄×C₃₁	—	2	4	no	—
112	C₂²⋊C₄×C₃₁	—	2	4	no	—
113	C₂²⋊C₄×C₃₁	—	4	4	no	—
114	C₂²⋊C₄×C₃₁	—	4	4	no	—
115	C₄²×C₃₁	—	2	2	no	—
116	C₄²×C₃₁	—	2	2	no	—
117	C₄²×C₃₁	C₂×D₄	1	2	yes	—
118	C₄²×C₃₁	#41	1	2	yes	—
119	#22263	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂³×C₃₁	—	2	2	no	—
121	C₂³×C₃₁	—	2	4	no	—
122	C₂³×C₃₁	—	2	2	no	—
123	C₂³×C₃₁	—	2	4	no	—
124	C₂³×C₃₁	—	2	2	no	—
125	C₂³×C₃₁	—	2	4	no	—
126	C₂³×C₃₁	—	2	4	no	—
127	C₂³×C₃₁	—	2	2	no	—
128	C₂³×C₃₁	—	2	2	no	—
129	C₂³×C₃₁	#131	1	4	yes	—
130	C₂³×C₃₁	C₂³×C₄	1	1	yes	characteristic
131	D₄×C₃₁	—	2	8	no	—
132	D₄×C₃₁	—	4	4	no	—
133	D₄×C₃₁	—	4	16	no	—
134	C₂×C₄×C₃₁	—	2	2	no	—
135	C₂×C₄×C₃₁	—	2	2	no	—
136	C₂×C₄×C₃₁	—	2	2	no	—
137	C₂×C₄×C₃₁	—	2	2	no	—
138	C₂×C₄×C₃₁	—	2	4	no	—
139	C₂×C₄×C₃₁	—	2	4	no	—
140	C₂×C₄×C₃₁	—	2	4	no	—
141	C₂×C₄×C₃₁	—	2	4	no	—
142	C₂×C₄×C₃₁	—	2	4	no	—
143	C₂×C₄×C₃₁	—	4	2	no	—
144	C₂×C₄×C₃₁	—	4	2	no	—
145	C₂×C₄×C₃₁	—	4	2	no	—
146	C₂×C₄×C₃₁	—	4	2	no	—
147	C₂×C₄×C₃₁	—	4	4	no	—
148	C₂×C₄×C₃₁	—	4	4	no	—
149	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
150	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
151	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
153	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
154	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
155	C₈×C₃₁	—	2	2	no	—
156	C₈×C₃₁	—	2	2	no	—
157	C₈×C₃₁	—	4	2	no	—
158	C₈×C₃₁	—	4	2	no	—
159	C₈×C₃₁	—	4	2	no	—
160	C₂×#436	C₂×C₃₁	1	1	yes	characteristic, complemented
161	C₂×C₈×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
162	#2397	C₂×C₃₁	1	1	yes	characteristic
163	#1955	C₂×C₃₁	1	1	yes	characteristic, complemented
164	#1955	C₂×C₃₁	1	1	yes	characteristic, complemented
165	#1870	C₂×C₃₁	1	4	yes	complemented
166	#1869	C₂×C₃₁	1	4	yes	complemented
167	#1832	C₂×C₃₁	1	1	yes	characteristic, complemented
168	#1746	C₂×C₃₁	1	1	yes	characteristic, complemented
169	C₂²×C₃₁	—	2	4	no	—
170	C₂²×C₃₁	—	2	8	no	—
171	C₂²×C₃₁	—	4	2	no	—
172	C₂²×C₃₁	—	4	2	no	—
173	C₂²×C₃₁	—	4	4	no	—
174	C₂²×C₃₁	—	4	2	no	—
175	C₂²×C₃₁	—	4	2	no	—
176	C₂²×C₃₁	—	4	2	no	—
177	C₂²×C₃₁	—	4	4	no	—
178	C₂²×C₃₁	—	4	4	no	—
179	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
180	C₂²×C₃₁	#518	1	2	yes	—
181	C₂²×C₃₁	C₂×#131	1	2	yes	—
182	C₂²×C₃₁	#568	1	2	yes	—
183	C₄×C₃₁	—	2	2	no	—
184	C₄×C₃₁	—	2	2	no	—
185	C₄×C₃₁	—	4	2	no	—
186	C₄×C₃₁	—	4	2	no	—
187	C₄×C₃₁	—	4	4	no	—
188	C₄×C₃₁	#535	1	1	yes	characteristic
189	C₄×C₃₁	#535	1	1	yes	characteristic
190	C₄×C₃₁	#540	1	2	yes	—
191	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
192	C₂³×C₈	C₂²×C₃₁	1	2	yes	—
193	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
194	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
195	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
196	#436	—	2	4	no	—
197	C₈×D₄	—	2	4	no	—
198	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
199	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
200	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
201	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
202	C₂×C₂²⋊C₈	C₂²×C₃₁	1	4	yes	—
203	C₂×C₂²⋊C₈	C₂²×C₃₁	1	4	yes	—
204	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
205	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
206	#399	C₄×C₃₁	1	2	yes	—
207	#399	C₄×C₃₁	1	2	yes	—
208	#392	C₄×C₃₁	1	2	yes	—
209	#392	C₄×C₃₁	1	2	yes	—
210	#376	C₂²×C₃₁	1	1	yes	characteristic
211	#336	C₂²×C₃₁	1	4	yes	—
212	#336	C₂²×C₃₁	1	2	yes	—
213	#336	C₂²×C₃₁	1	2	yes	—
214	C₂×C₃₁	—	4	4	no	—
215	C₂×C₃₁	—	8	2	no	—
216	C₂×C₃₁	#2328	1	1	yes	characteristic
217	C₂×C₃₁	#2929	1	1	yes	characteristic
218	C₂×C₃₁	#2930	1	1	yes	characteristic
219	C₂×C₃₁	#2976	1	4	yes	—
220	C₂²×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
221	C₂²×D₄	C₂×C₄×C₃₁	1	4	yes	—
222	C₂²×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
223	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
224	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
225	C₂×M₁₆	—	2	4	no	—
226	C₂×M₁₆	—	4	4	no	—
227	C₂²×C₈	—	2	4	no	—
228	C₂²×C₈	—	4	4	no	—
229	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
230	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
231	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
232	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
233	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
234	C₄×D₄	—	2	2	no	—
235	C₄×D₄	—	2	2	no	—
236	C₄×D₄	—	2	2	no	—
237	C₄×D₄	—	2	2	no	—
238	C₄×D₄	—	4	4	no	—
239	C₄×D₄	—	4	4	no	—
240	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
243	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
244	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
245	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
246	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
247	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
248	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
249	C₄⋊C₈	—	2	2	no	—
250	C₄⋊C₈	—	2	2	no	—
251	C₂²⋊C₈	—	2	4	no	—
252	C₂²⋊C₈	—	2	4	no	—
253	C₂²⋊C₈	—	4	4	no	—
254	C₂²⋊C₈	—	4	4	no	—
255	#97	—	2	2	no	—
256	C₄×C₈	D₄×C₃₁	1	4	yes	complemented
257	#95	C₂×C₄×C₃₁	1	2	yes	—
258	#95	C₂×C₄×C₃₁	1	2	yes	—
259	C₃₁	#22263	1	1	yes	characteristic, direct product factor, Sylow
260	C₂⁴	C₂²×C₄×C₃₁	1	2	yes	—
261	C₂⁴	C₂²×C₄×C₃₁	1	2	yes	—
262	C₂×D₄	—	2	4	no	—
263	C₂×D₄	—	2	8	no	—
264	C₂×D₄	—	2	2	no	—
265	C₂×D₄	—	2	2	no	—
266	C₂×D₄	—	4	4	no	—
267	C₂×D₄	—	4	2	no	—
268	C₂×D₄	—	4	4	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
278	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
279	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
280	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
281	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
282	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
283	M₁₆	—	4	8	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	4	no	—
292	C₂×C₈	—	2	4	no	—
293	C₂×C₈	—	4	8	no	—
294	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
295	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	4	4	no	—
299	C₂²⋊C₄	—	2	4	no	—
300	C₂²⋊C₄	—	2	4	no	—
301	C₂²⋊C₄	—	4	4	no	—
302	C₂²⋊C₄	—	4	4	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	2	no	—
305	C₄²	C₂×D₄×C₃₁	1	2	yes	—
306	C₄²	#41×C₃₁	1	2	yes	—
307	C₂³	—	2	2	no	—
308	C₂³	—	2	4	no	—
309	C₂³	—	2	2	no	—
310	C₂³	—	2	4	no	—
311	C₂³	—	2	2	no	—
312	C₂³	—	2	4	no	—
313	C₂³	—	2	4	no	—
314	C₂³	—	2	2	no	—
315	C₂³	—	2	2	no	—
316	C₂³	C₃₁×#131	1	4	yes	—
317	C₂³	C₂³×C₄×C₃₁	1	1	yes	characteristic
318	D₄	—	2	8	no	—
319	D₄	—	4	4	no	—
320	D₄	—	4	16	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
337	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
338	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
339	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
340	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
341	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
342	C₈	—	2	2	no	—
343	C₈	—	2	2	no	—
344	C₈	—	4	2	no	—
345	C₈	—	4	2	no	—
346	C₈	—	4	2	no	—
347	C₂²	—	2	4	no	—
348	C₂²	—	2	8	no	—
349	C₂²	—	4	2	no	—
350	C₂²	—	4	2	no	—
351	C₂²	—	4	4	no	—
352	C₂²	—	4	2	no	—
353	C₂²	—	4	2	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	4	4	no	—
356	C₂²	—	4	4	no	—
357	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
358	C₂²	C₃₁×#518	1	2	yes	—
359	C₂²	C₂×C₃₁×#131	1	2	yes	—
360	C₂²	C₃₁×#568	1	2	yes	—
361	C₄	—	2	2	no	—
362	C₄	—	2	2	no	—
363	C₄	—	4	2	no	—
364	C₄	—	4	2	no	—
365	C₄	—	4	4	no	—
366	C₄	C₃₁×#535	1	1	yes	characteristic
367	C₄	C₃₁×#535	1	1	yes	characteristic
368	C₄	C₃₁×#540	1	2	yes	—
369	C₂	—	4	4	no	—
370	C₂	—	8	2	no	—
371	C₂	C₃₁×#2328	1	1	yes	characteristic
372	C₂	C₃₁×#2929	1	1	yes	characteristic
373	C₂	C₃₁×#2930	1	1	yes	characteristic
374	C₂	C₃₁×#2976	1	4	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	C₃₁×#2397	C₂
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
1. C₂×C₃₁×#436	C₂	semidirect
2. C₂×C₈×D₄×C₃₁	C₂	semidirect
4. C₃₁×#1955	C₂	semidirect
5. C₃₁×#1955	C₂	semidirect
6. C₃₁×#1870	C₂	semidirect
7. C₃₁×#1869	C₂	semidirect
8. C₃₁×#1832	C₂	semidirect
9. C₃₁×#1746	C₂	semidirect
69. C₄×C₈×C₃₁	D₄	semidirect
119. #22263	C₃₁	direct (N × H)
160. C₂×#436	C₂×C₃₁	semidirect
161. C₂×C₈×D₄	C₂×C₃₁	semidirect
163. #1955	C₂×C₃₁	semidirect
164. #1955	C₂×C₃₁	semidirect
165. #1870	C₂×C₃₁	semidirect
166. #1869	C₂×C₃₁	semidirect
167. #1832	C₂×C₃₁	semidirect
168. #1746	C₂×C₃₁	semidirect
256. C₄×C₈	D₄×C₃₁	semidirect
259. C₃₁	#22263	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×#436	2
C₂×C₈×D₄×C₃₁	2
C₃₁×#2397	2
C₃₁×#1955	2
C₃₁×#1870	2
C₃₁×#1869	2
C₃₁×#1832	2
C₃₁×#1746	2
#22263	31

Subgroups — C31×#22263 #21479022

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#22263 #21479022