Subgroups — C₁₃₁×#20474 #45706358

Order 33536.

946 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#433×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#405×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#2298×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	#1771×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	C₈×C₄⋊C₄×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#1753×C₁₃₁	C₂	1	2	yes	maximal
7	C₈×C₂²⋊C₄×C₁₃₁	C₂	1	2	yes	maximal
8	#1746×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#1745×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1726×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄²×C₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×M₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂×#117×C₁₃₁	C₂²	1	1	yes	characteristic
15	#433×C₁₃₁	C₄	1	8	yes	complemented
16	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	2	yes	—
17	C₂×C₂²⋊C₈×C₁₃₁	C₂²	1	2	yes	—
18	#405×C₁₃₁	C₄	1	8	yes	complemented
19	C₂×#97×C₁₃₁	C₂²	1	2	yes	—
20	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
22	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₃₁	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₃₁	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₃₁	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
29	#388×C₁₃₁	C₄	1	4	yes	—
30	#387×C₁₃₁	C₄	1	4	yes	—
31	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
32	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
33	#376×C₁₃₁	C₂²	1	1	yes	characteristic
34	C₄³×C₁₃₁	C₂²	1	1	yes	characteristic
35	#336×C₁₃₁	C₂²	1	2	yes	—
36	#336×C₁₃₁	C₂²	1	2	yes	—
37	#336×C₁₃₁	C₂²	1	2	yes	—
38	#336×C₁₃₁	C₂²	1	2	yes	—
39	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
40	C₂×M₁₆×C₁₃₁	—	2	4	no	—
41	C₂×M₁₆×C₁₃₁	C₂×C₄	1	4	yes	—
42	C₂²×C₈×C₁₃₁	—	2	4	no	—
43	C₂²×C₈×C₁₃₁	C₂×C₄	1	4	yes	—
44	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
50	#117×C₁₃₁	C₂×C₄	1	4	yes	—
51	#117×C₁₃₁	C₂×C₄	1	4	yes	—
52	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	4	yes	—
53	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	2	yes	—
54	C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	1	4	yes	—
55	C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₁₃₁	C₂×C₄	1	4	yes	—
57	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
58	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
59	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
61	C₄⋊C₈×C₁₃₁	C₂×C₄	1	8	yes	—
62	C₂²⋊C₈×C₁₃₁	C₂×C₄	1	8	yes	—
63	#97×C₁₃₁	—	2	4	no	—
64	#97×C₁₃₁	C₂×C₄	1	4	yes	—
65	#97×C₁₃₁	C₂×C₄	1	4	yes	—
66	#97×C₁₃₁	C₂×C₄	1	4	yes	—
67	C₄×C₈×C₁₃₁	—	2	4	no	—
68	C₄×C₈×C₁₃₁	—	2	4	no	—
69	C₄×C₈×C₁₃₁	—	2	4	no	—
70	C₄×C₈×C₁₃₁	C₂×C₄	1	4	yes	—
71	C₄×C₈×C₁₃₁	C₂×C₄	1	4	yes	—
72	C₄×C₈×C₁₃₁	C₂×C₄	1	4	yes	—
73	#95×C₁₃₁	C₂×C₄	1	4	yes	—
74	#95×C₁₃₁	C₂×C₄	1	4	yes	—
75	#95×C₁₃₁	C₂×C₄	1	4	yes	—
76	C₂⁴×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₃₁	—	2	2	no	—
78	C₂²×C₄×C₁₃₁	—	2	2	no	—
79	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
80	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
86	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
87	M₁₆×C₁₃₁	—	2	8	no	—
88	C₂×C₈×C₁₃₁	—	2	2	no	—
89	C₂×C₈×C₁₃₁	—	2	2	no	—
90	C₂×C₈×C₁₃₁	—	2	2	no	—
91	C₂×C₈×C₁₃₁	—	2	2	no	—
92	C₂×C₈×C₁₃₁	—	2	2	no	—
93	C₂×C₈×C₁₃₁	—	2	2	no	—
94	C₂×C₈×C₁₃₁	—	2	8	no	—
95	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
96	C₂×C₈×C₁₃₁	C₂²×C₄	1	4	yes	—
97	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
98	C₂×C₈×C₁₃₁	C₂²×C₄	1	4	yes	—
99	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
100	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
101	C₂×C₈×C₁₃₁	#41	1	4	yes	—
102	C₂×C₈×C₁₃₁	#41	1	4	yes	—
103	C₄⋊C₄×C₁₃₁	—	2	8	no	—
104	C₄⋊C₄×C₁₃₁	C₄²	1	8	yes	—
105	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
106	C₂²⋊C₄×C₁₃₁	C₄²	1	8	yes	—
107	C₄²×C₁₃₁	—	2	8	no	—
108	C₄²×C₁₃₁	—	2	2	no	—
109	C₄²×C₁₃₁	—	2	2	no	—
110	C₄²×C₁₃₁	—	2	2	no	—
111	C₄²×C₁₃₁	—	2	2	no	—
112	C₄²×C₁₃₁	C₂²×C₄	1	2	yes	—
113	C₄²×C₁₃₁	C₂²×C₄	1	2	yes	—
114	C₄²×C₁₃₁	C₂²×C₄	1	2	yes	—
115	C₄²×C₁₃₁	C₂²×C₄	1	2	yes	—
116	C₂³×C₁₃₁	—	2	2	no	—
117	C₂³×C₁₃₁	—	2	4	no	—
118	C₂³×C₁₃₁	C₂×C₄²	1	2	yes	—
119	C₂³×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
120	C₂×C₄×C₁₃₁	—	2	4	no	—
121	C₂×C₄×C₁₃₁	—	2	2	no	—
122	C₂×C₄×C₁₃₁	—	2	4	no	—
123	C₂×C₄×C₁₃₁	—	2	4	no	—
124	C₂×C₄×C₁₃₁	—	2	4	no	—
125	C₂×C₄×C₁₃₁	—	2	2	no	—
126	C₂×C₄×C₁₃₁	—	2	2	no	—
127	C₂×C₄×C₁₃₁	—	2	4	no	—
128	C₂×C₄×C₁₃₁	—	2	4	no	—
129	C₂×C₄×C₁₃₁	—	2	4	no	—
130	C₂×C₄×C₁₃₁	—	2	4	no	—
131	C₂×C₄×C₁₃₁	C₂×C₄²	1	4	yes	—
132	C₂×C₄×C₁₃₁	C₂×C₄²	1	4	yes	—
133	C₂×C₄×C₁₃₁	C₂×C₄²	1	2	yes	—
134	C₂×C₄×C₁₃₁	#131	1	8	yes	—
135	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
136	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
137	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
138	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
139	C₈×C₁₃₁	—	2	2	no	—
140	C₈×C₁₃₁	—	2	2	no	—
141	C₈×C₁₃₁	—	2	4	no	—
142	C₈×C₁₃₁	—	2	4	no	—
143	C₈×C₁₃₁	#117	1	4	yes	—
144	C₈×C₁₃₁	#117	1	4	yes	—
145	C₂²×C₁₃₁	—	2	4	no	—
146	C₂²×C₁₃₁	—	2	2	no	—
147	C₂²×C₁₃₁	—	4	4	no	—
148	C₂²×C₁₃₁	C₂²×C₄²	1	1	yes	characteristic
149	C₂²×C₁₃₁	C₄×#41	1	2	yes	—
150	C₂²×C₁₃₁	C₂×#131	1	4	yes	—
151	C₄×C₁₃₁	—	2	4	no	—
152	C₄×C₁₃₁	—	2	4	no	—
153	C₄×C₁₃₁	—	2	8	no	—
154	C₄×C₁₃₁	—	2	2	no	—
155	C₄×C₁₃₁	—	4	4	no	—
156	C₄×C₁₃₁	C₂×#117	1	1	yes	characteristic
157	C₄×C₁₃₁	C₂×#117	1	1	yes	characteristic
158	C₄×C₁₃₁	C₄×#41	1	2	yes	—
159	C₂×C₁₃₁	—	4	2	no	—
160	C₂×C₁₃₁	C₄×#117	1	1	yes	characteristic
161	C₂×C₁₃₁	C₄×#131	1	2	yes	—
162	C₂×C₁₃₁	#2966	1	4	yes	—
163	#20474	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₁₃₁	#20474	1	1	yes	characteristic, direct product factor, Sylow
165	C₂×#433	C₂×C₁₃₁	1	1	yes	characteristic
166	C₂×#405	C₂×C₁₃₁	1	1	yes	characteristic
167	#2298	C₂×C₁₃₁	1	1	yes	characteristic
168	#1771	C₂×C₁₃₁	1	2	yes	complemented
169	C₈×C₄⋊C₄	C₂×C₁₃₁	1	2	yes	complemented
170	#1753	C₂×C₁₃₁	1	2	yes	—
171	C₈×C₂²⋊C₄	C₂×C₁₃₁	1	2	yes	—
172	#1746	C₂×C₁₃₁	1	1	yes	characteristic, complemented
173	#1745	C₂×C₁₃₁	1	1	yes	characteristic, complemented
174	#1726	C₂×C₁₃₁	1	1	yes	characteristic, complemented
175	C₄²×C₈	C₂×C₁₃₁	1	1	yes	characteristic, complemented
176	C₂²×M₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
177	C₂³×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
178	C₂×#117	C₂²×C₁₃₁	1	1	yes	characteristic
179	#433	C₄×C₁₃₁	1	8	yes	complemented
180	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	2	yes	—
181	C₂×C₂²⋊C₈	C₂²×C₁₃₁	1	2	yes	—
182	#405	C₄×C₁₃₁	1	8	yes	complemented
183	C₂×#97	C₂²×C₁₃₁	1	2	yes	—
184	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
185	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
186	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
187	C₂×C₄×C₈	C₂²×C₁₃₁	1	2	yes	—
188	C₂×C₄×C₈	C₂²×C₁₃₁	1	2	yes	—
189	C₂×C₄×C₈	C₂²×C₁₃₁	1	2	yes	—
190	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
191	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
192	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
193	#388	C₄×C₁₃₁	1	4	yes	—
194	#387	C₄×C₁₃₁	1	4	yes	—
195	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
196	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
197	#376	C₂²×C₁₃₁	1	1	yes	characteristic
198	C₄³	C₂²×C₁₃₁	1	1	yes	characteristic
199	#336	C₂²×C₁₃₁	1	2	yes	—
200	#336	C₂²×C₁₃₁	1	2	yes	—
201	#336	C₂²×C₁₃₁	1	2	yes	—
202	#336	C₂²×C₁₃₁	1	2	yes	—
203	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
204	C₂×M₁₆	—	2	4	no	—
205	C₂×M₁₆	C₂×C₄×C₁₃₁	1	4	yes	—
206	C₂²×C₈	—	2	4	no	—
207	C₂²×C₈	C₂×C₄×C₁₃₁	1	4	yes	—
208	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
209	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
210	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
211	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
212	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
213	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
214	#117	C₂×C₄×C₁₃₁	1	4	yes	—
215	#117	C₂×C₄×C₁₃₁	1	4	yes	—
216	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	4	yes	—
217	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
218	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	1	4	yes	—
219	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
220	C₂×C₄²	C₂×C₄×C₁₃₁	1	4	yes	—
221	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
222	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
223	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
224	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
225	C₄⋊C₈	C₂×C₄×C₁₃₁	1	8	yes	—
226	C₂²⋊C₈	C₂×C₄×C₁₃₁	1	8	yes	—
227	#97	—	2	4	no	—
228	#97	C₂×C₄×C₁₃₁	1	4	yes	—
229	#97	C₂×C₄×C₁₃₁	1	4	yes	—
230	#97	C₂×C₄×C₁₃₁	1	4	yes	—
231	C₄×C₈	—	2	4	no	—
232	C₄×C₈	—	2	4	no	—
233	C₄×C₈	—	2	4	no	—
234	C₄×C₈	C₂×C₄×C₁₃₁	1	4	yes	—
235	C₄×C₈	C₂×C₄×C₁₃₁	1	4	yes	—
236	C₄×C₈	C₂×C₄×C₁₃₁	1	4	yes	—
237	#95	C₂×C₄×C₁₃₁	1	4	yes	—
238	#95	C₂×C₄×C₁₃₁	1	4	yes	—
239	#95	C₂×C₄×C₁₃₁	1	4	yes	—
240	C₂⁴	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
241	C₂²×C₄	—	2	2	no	—
242	C₂²×C₄	—	2	2	no	—
243	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
244	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
245	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
246	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
247	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
248	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
249	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
250	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
251	M₁₆	—	2	8	no	—
252	C₂×C₈	—	2	2	no	—
253	C₂×C₈	—	2	2	no	—
254	C₂×C₈	—	2	2	no	—
255	C₂×C₈	—	2	2	no	—
256	C₂×C₈	—	2	2	no	—
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	—	2	8	no	—
259	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
260	C₂×C₈	C₂²×C₄×C₁₃₁	1	4	yes	—
261	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
262	C₂×C₈	C₂²×C₄×C₁₃₁	1	4	yes	—
263	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
264	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
265	C₂×C₈	#41×C₁₃₁	1	4	yes	—
266	C₂×C₈	#41×C₁₃₁	1	4	yes	—
267	C₄⋊C₄	—	2	8	no	—
268	C₄⋊C₄	C₄²×C₁₃₁	1	8	yes	—
269	C₂²⋊C₄	—	2	8	no	—
270	C₂²⋊C₄	C₄²×C₁₃₁	1	8	yes	—
271	C₄²	—	2	8	no	—
272	C₄²	—	2	2	no	—
273	C₄²	—	2	2	no	—
274	C₄²	—	2	2	no	—
275	C₄²	—	2	2	no	—
276	C₄²	C₂²×C₄×C₁₃₁	1	2	yes	—
277	C₄²	C₂²×C₄×C₁₃₁	1	2	yes	—
278	C₄²	C₂²×C₄×C₁₃₁	1	2	yes	—
279	C₄²	C₂²×C₄×C₁₃₁	1	2	yes	—
280	C₂³	—	2	2	no	—
281	C₂³	—	2	4	no	—
282	C₂³	C₂×C₄²×C₁₃₁	1	2	yes	—
283	C₂³	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
284	C₂×C₄	—	2	4	no	—
285	C₂×C₄	—	2	2	no	—
286	C₂×C₄	—	2	4	no	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	4	no	—
292	C₂×C₄	—	2	4	no	—
293	C₂×C₄	—	2	4	no	—
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	C₂×C₄²×C₁₃₁	1	4	yes	—
296	C₂×C₄	C₂×C₄²×C₁₃₁	1	4	yes	—
297	C₂×C₄	C₂×C₄²×C₁₃₁	1	2	yes	—
298	C₂×C₄	#131×C₁₃₁	1	8	yes	—
299	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
300	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
301	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
302	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
303	C₈	—	2	2	no	—
304	C₈	—	2	2	no	—
305	C₈	—	2	4	no	—
306	C₈	—	2	4	no	—
307	C₈	#117×C₁₃₁	1	4	yes	—
308	C₈	#117×C₁₃₁	1	4	yes	—
309	C₂²	—	2	2	no	—
310	C₂²	—	2	4	no	—
311	C₂²	—	4	4	no	—
312	C₂²	C₂²×C₄²×C₁₃₁	1	1	yes	characteristic
313	C₂²	C₄×#41×C₁₃₁	1	2	yes	—
314	C₂²	C₂×#131×C₁₃₁	1	4	yes	—
315	C₄	—	2	2	no	—
316	C₄	—	2	4	no	—
317	C₄	—	2	4	no	—
318	C₄	—	2	8	no	—
319	C₄	—	4	4	no	—
320	C₄	C₂×#117×C₁₃₁	1	1	yes	characteristic
321	C₄	C₂×#117×C₁₃₁	1	1	yes	characteristic
322	C₄	C₄×#41×C₁₃₁	1	2	yes	—
323	C₂	—	4	2	no	—
324	C₂	C₄×#117×C₁₃₁	1	1	yes	characteristic
325	C₂	C₄×#131×C₁₃₁	1	2	yes	—
326	C₂	#2966×C₁₃₁	1	4	yes	—

	subgroup	G/H
center	C₂²×C₈×C₁₃₁	C₂³
commutator	C₂²	C₂²×C₄²×C₁₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
socle	C₂³×C₁₃₁	C₂³×C₄
prime radical	C₂⁴×C₁₃₁	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. #1771×C₁₃₁	C₂	semidirect
5. C₈×C₄⋊C₄×C₁₃₁	C₂	semidirect
8. #1746×C₁₃₁	C₂	semidirect
9. #1745×C₁₃₁	C₂	semidirect
10. #1726×C₁₃₁	C₂	semidirect
11. C₄²×C₈×C₁₃₁	C₂	semidirect
15. #433×C₁₃₁	C₄	semidirect
18. #405×C₁₃₁	C₄	semidirect
163. #20474	C₁₃₁	direct (N × H)
164. C₁₃₁	#20474	direct (N × H)
168. #1771	C₂×C₁₃₁	semidirect
169. C₈×C₄⋊C₄	C₂×C₁₃₁	semidirect
172. #1746	C₂×C₁₃₁	semidirect
173. #1745	C₂×C₁₃₁	semidirect
174. #1726	C₂×C₁₃₁	semidirect
175. C₄²×C₈	C₂×C₁₃₁	semidirect
179. #433	C₄×C₁₃₁	semidirect
182. #405	C₄×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#433×C₁₃₁	2
C₂×#405×C₁₃₁	2
#2298×C₁₃₁	2
#1771×C₁₃₁	2
C₈×C₄⋊C₄×C₁₃₁	2
#1753×C₁₃₁	2
C₈×C₂²⋊C₄×C₁₃₁	2
#1746×C₁₃₁	2
#1745×C₁₃₁	2
#1726×C₁₃₁	2
C₄²×C₈×C₁₃₁	2
#20474	131

Subgroups — C131×#20474 #45706358

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#20474 #45706358