Subgroups — C₁₃₁×#22831 #45708715

Order 33536.

616 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2295×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#1985×C₁₃₁	C₂	1	2	yes	maximal
3	#1917×C₁₃₁	C₂	1	2	yes	maximal
4	#1916×C₁₃₁	C₂	1	2	yes	maximal
5	#1840×C₁₃₁	C₂	1	2	yes	maximal
6	#1831×C₁₃₁	C₂	1	1	yes	maximal, characteristic
7	#1771×C₁₃₁	C₂	1	2	yes	maximal
8	#1767×C₁₃₁	C₂	1	1	yes	maximal, characteristic
9	#1746×C₁₃₁	C₂	1	2	yes	maximal
10	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	2	yes	—
12	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	2	yes	—
13	C₂×#97×C₁₃₁	C₂²	1	2	yes	—
14	C₂×#97×C₁₃₁	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₁₃₁	C₂²	1	2	yes	—
16	#391×C₁₃₁	C₄	1	1	yes	characteristic
17	#391×C₁₃₁	C₄	1	1	yes	characteristic
18	#389×C₁₃₁	C₄	1	1	yes	characteristic
19	#389×C₁₃₁	C₄	1	1	yes	characteristic
20	#387×C₁₃₁	C₄	1	2	yes	—
21	#387×C₁₃₁	C₄	1	2	yes	—
22	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
23	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
24	#376×C₁₃₁	C₂²	1	2	yes	—
25	C₄³×C₁₃₁	C₂²	1	1	yes	characteristic
26	#336×C₁₃₁	C₂²	1	2	yes	—
27	#336×C₁₃₁	C₂²	1	2	yes	—
28	#336×C₁₃₁	C₂²	1	2	yes	—
29	#336×C₁₃₁	C₂²	1	2	yes	—
30	#336×C₁₃₁	C₂²	1	1	yes	characteristic
31	#336×C₁₃₁	C₂²	1	2	yes	—
32	#336×C₁₃₁	C₂²	1	1	yes	characteristic
33	#336×C₁₃₁	C₂²	1	2	yes	—
34	#336×C₁₃₁	C₂²	1	2	yes	—
35	#336×C₁₃₁	C₂²	1	1	yes	characteristic
36	#336×C₁₃₁	C₂²	1	1	yes	characteristic
37	C₂²×Q₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
39	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
42	C₄×Q₈×C₁₃₁	—	2	2	no	—
43	C₄×Q₈×C₁₃₁	—	2	2	no	—
44	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	2	yes	—
46	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₁₃₁	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₃₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₃₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₃₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
55	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
57	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
58	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
59	C₄⋊C₈×C₁₃₁	—	2	4	no	—
60	C₄⋊C₈×C₁₃₁	—	2	4	no	—
61	#97×C₁₃₁	—	2	4	no	—
62	#97×C₁₃₁	—	2	4	no	—
63	C₄×C₈×C₁₃₁	—	2	4	no	—
64	#95×C₁₃₁	C₂×C₄	1	2	yes	—
65	#95×C₁₃₁	C₂×C₄	1	2	yes	—
66	#95×C₁₃₁	C₂×C₄	1	2	yes	—
67	#95×C₁₃₁	C₂×C₄	1	2	yes	—
68	#95×C₁₃₁	C₂×C₄	1	2	yes	—
69	#95×C₁₃₁	C₂×C₄	1	2	yes	—
70	#95×C₁₃₁	C₂×C₄	1	2	yes	—
71	C₂×Q₈×C₁₃₁	—	2	2	no	—
72	C₂×Q₈×C₁₃₁	—	4	1	no	—
73	C₂×Q₈×C₁₃₁	—	4	1	no	—
74	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
77	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
78	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
85	C₂×C₈×C₁₃₁	—	2	2	no	—
86	C₂×C₈×C₁₃₁	—	2	2	no	—
87	C₂×C₈×C₁₃₁	—	2	2	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	2	no	—
95	C₂×C₈×C₁₃₁	—	2	2	no	—
96	C₂×C₈×C₁₃₁	#41	1	4	yes	—
97	C₄⋊C₄×C₁₃₁	—	2	2	no	—
98	C₄⋊C₄×C₁₃₁	—	2	4	no	—
99	C₄⋊C₄×C₁₃₁	—	2	4	no	—
100	C₄⋊C₄×C₁₃₁	—	4	1	no	—
101	C₄⋊C₄×C₁₃₁	—	4	1	no	—
102	C₄⋊C₄×C₁₃₁	—	4	2	no	—
103	C₄²×C₁₃₁	—	2	2	no	—
104	C₄²×C₁₃₁	—	2	2	no	—
105	C₄²×C₁₃₁	—	2	2	no	—
106	C₄²×C₁₃₁	—	2	2	no	—
107	C₄²×C₁₃₁	—	2	2	no	—
108	C₄²×C₁₃₁	—	2	2	no	—
109	C₄²×C₁₃₁	—	2	2	no	—
110	C₄²×C₁₃₁	—	4	1	no	—
111	C₄²×C₁₃₁	—	4	1	no	—
112	C₄²×C₁₃₁	—	4	1	no	—
113	C₄²×C₁₃₁	#41	1	2	yes	—
114	C₄²×C₁₃₁	#41	1	2	yes	—
115	C₂³×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
116	Q₈×C₁₃₁	—	4	4	no	—
117	C₂×C₄×C₁₃₁	—	2	1	no	—
118	C₂×C₄×C₁₃₁	—	2	1	no	—
119	C₂×C₄×C₁₃₁	—	2	1	no	—
120	C₂×C₄×C₁₃₁	—	2	1	no	—
121	C₂×C₄×C₁₃₁	—	2	1	no	—
122	C₂×C₄×C₁₃₁	—	2	1	no	—
123	C₂×C₄×C₁₃₁	—	2	2	no	—
124	C₂×C₄×C₁₃₁	—	2	2	no	—
125	C₂×C₄×C₁₃₁	—	2	2	no	—
126	C₂×C₄×C₁₃₁	—	2	1	no	—
127	C₂×C₄×C₁₃₁	—	2	2	no	—
128	C₂×C₄×C₁₃₁	—	2	1	no	—
129	C₂×C₄×C₁₃₁	—	2	1	no	—
130	C₂×C₄×C₁₃₁	—	2	1	no	—
131	C₂×C₄×C₁₃₁	—	2	2	no	—
132	C₂×C₄×C₁₃₁	—	2	2	no	—
133	C₂×C₄×C₁₃₁	—	2	1	no	—
134	C₂×C₄×C₁₃₁	—	2	1	no	—
135	C₂×C₄×C₁₃₁	—	2	1	no	—
136	C₂×C₄×C₁₃₁	—	2	1	no	—
137	C₂×C₄×C₁₃₁	—	2	1	no	—
138	C₂×C₄×C₁₃₁	—	2	2	no	—
139	C₂×C₄×C₁₃₁	—	2	2	no	—
140	C₂×C₄×C₁₃₁	—	2	2	no	—
141	C₂×C₄×C₁₃₁	—	2	2	no	—
142	C₂×C₄×C₁₃₁	—	2	2	no	—
143	C₂×C₄×C₁₃₁	—	2	2	no	—
144	C₂×C₄×C₁₃₁	#117	1	2	yes	—
145	C₂×C₄×C₁₃₁	#117	1	2	yes	—
146	C₂×C₄×C₁₃₁	#131	1	2	yes	—
147	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
148	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
149	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
150	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
151	C₈×C₁₃₁	—	2	4	no	—
152	C₈×C₁₃₁	—	4	2	no	—
153	C₈×C₁₃₁	—	4	2	no	—
154	C₈×C₁₃₁	—	4	2	no	—
155	C₂²×C₁₃₁	C₂×#117	1	1	yes	characteristic
156	C₂²×C₁₃₁	C₄×#41	1	1	yes	characteristic
157	C₂²×C₁₃₁	#519	1	1	yes	characteristic
158	C₂²×C₁₃₁	C₂×#131	1	1	yes	characteristic
159	C₂²×C₁₃₁	#568	1	1	yes	characteristic
160	C₂²×C₁₃₁	#568	1	1	yes	characteristic
161	C₂²×C₁₃₁	#568	1	1	yes	characteristic
162	C₄×C₁₃₁	—	2	2	no	—
163	C₄×C₁₃₁	—	2	2	no	—
164	C₄×C₁₃₁	—	2	2	no	—
165	C₄×C₁₃₁	—	4	2	no	—
166	C₄×C₁₃₁	—	4	2	no	—
167	C₄×C₁₃₁	—	4	1	no	—
168	C₄×C₁₃₁	—	4	2	no	—
169	C₄×C₁₃₁	—	4	2	no	—
170	C₄×C₁₃₁	—	4	1	no	—
171	C₄×C₁₃₁	—	4	1	no	—
172	C₄×C₁₃₁	#552	1	2	yes	—
173	C₄×C₁₃₁	#556	1	2	yes	—
174	C₂×C₁₃₁	#2356	1	1	yes	characteristic
175	C₂×C₁₃₁	#2921	1	1	yes	characteristic
176	C₂×C₁₃₁	#2925	1	1	yes	characteristic
177	C₂×C₁₃₁	#2967	1	1	yes	characteristic
178	C₂×C₁₃₁	#2968	1	1	yes	characteristic
179	C₂×C₁₃₁	#2985	1	1	yes	characteristic
180	C₂×C₁₃₁	#2987	1	1	yes	characteristic
181	#22831	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₁₃₁	#22831	1	1	yes	characteristic, direct product factor, Sylow
183	#2295	C₂×C₁₃₁	1	1	yes	characteristic
184	#1985	C₂×C₁₃₁	1	2	yes	—
185	#1917	C₂×C₁₃₁	1	2	yes	—
186	#1916	C₂×C₁₃₁	1	2	yes	—
187	#1840	C₂×C₁₃₁	1	2	yes	—
188	#1831	C₂×C₁₃₁	1	1	yes	characteristic
189	#1771	C₂×C₁₃₁	1	2	yes	—
190	#1767	C₂×C₁₃₁	1	1	yes	characteristic
191	#1746	C₂×C₁₃₁	1	2	yes	—
192	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
193	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	2	yes	—
194	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	2	yes	—
195	C₂×#97	C₂²×C₁₃₁	1	2	yes	—
196	C₂×#97	C₂²×C₁₃₁	1	2	yes	—
197	C₂×C₄×C₈	C₂²×C₁₃₁	1	2	yes	—
198	#391	C₄×C₁₃₁	1	1	yes	characteristic
199	#391	C₄×C₁₃₁	1	1	yes	characteristic
200	#389	C₄×C₁₃₁	1	1	yes	characteristic
201	#389	C₄×C₁₃₁	1	1	yes	characteristic
202	#387	C₄×C₁₃₁	1	2	yes	—
203	#387	C₄×C₁₃₁	1	2	yes	—
204	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
205	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
206	#376	C₂²×C₁₃₁	1	2	yes	—
207	C₄³	C₂²×C₁₃₁	1	1	yes	characteristic
208	#336	C₂²×C₁₃₁	1	2	yes	—
209	#336	C₂²×C₁₃₁	1	1	yes	characteristic
210	#336	C₂²×C₁₃₁	1	1	yes	characteristic
211	#336	C₂²×C₁₃₁	1	1	yes	characteristic
212	#336	C₂²×C₁₃₁	1	2	yes	—
213	#336	C₂²×C₁₃₁	1	2	yes	—
214	#336	C₂²×C₁₃₁	1	2	yes	—
215	#336	C₂²×C₁₃₁	1	2	yes	—
216	#336	C₂²×C₁₃₁	1	2	yes	—
217	#336	C₂²×C₁₃₁	1	2	yes	—
218	#336	C₂²×C₁₃₁	1	1	yes	characteristic
219	C₂²×Q₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
220	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
221	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
222	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
223	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
224	C₄×Q₈	—	2	2	no	—
225	C₄×Q₈	—	2	2	no	—
226	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
227	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
229	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
230	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
231	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
232	C₂×C₄²	C₂×C₄×C₁₃₁	1	1	yes	characteristic
233	C₂×C₄²	C₂×C₄×C₁₃₁	1	1	yes	characteristic
234	C₂×C₄²	C₂×C₄×C₁₃₁	1	1	yes	characteristic
235	C₂×C₄²	C₂×C₄×C₁₃₁	1	1	yes	characteristic
236	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
237	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
238	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
239	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
240	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
241	C₄⋊C₈	—	2	4	no	—
242	C₄⋊C₈	—	2	4	no	—
243	#97	—	2	4	no	—
244	#97	—	2	4	no	—
245	C₄×C₈	—	2	4	no	—
246	#95	C₂×C₄×C₁₃₁	1	2	yes	—
247	#95	C₂×C₄×C₁₃₁	1	2	yes	—
248	#95	C₂×C₄×C₁₃₁	1	2	yes	—
249	#95	C₂×C₄×C₁₃₁	1	2	yes	—
250	#95	C₂×C₄×C₁₃₁	1	2	yes	—
251	#95	C₂×C₄×C₁₃₁	1	2	yes	—
252	#95	C₂×C₄×C₁₃₁	1	2	yes	—
253	C₂×Q₈	—	2	2	no	—
254	C₂×Q₈	—	4	1	no	—
255	C₂×Q₈	—	4	1	no	—
256	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
257	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
258	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
259	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
260	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
261	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
262	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
263	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
264	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
265	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
266	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	2	2	no	—
274	C₂×C₈	—	2	2	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	#41×C₁₃₁	1	4	yes	—
279	C₄⋊C₄	—	2	2	no	—
280	C₄⋊C₄	—	2	4	no	—
281	C₄⋊C₄	—	2	4	no	—
282	C₄⋊C₄	—	4	1	no	—
283	C₄⋊C₄	—	4	1	no	—
284	C₄⋊C₄	—	4	2	no	—
285	C₄²	—	2	2	no	—
286	C₄²	—	2	2	no	—
287	C₄²	—	2	2	no	—
288	C₄²	—	2	2	no	—
289	C₄²	—	2	2	no	—
290	C₄²	—	2	2	no	—
291	C₄²	—	2	2	no	—
292	C₄²	—	4	1	no	—
293	C₄²	—	4	1	no	—
294	C₄²	—	4	1	no	—
295	C₄²	#41×C₁₃₁	1	2	yes	—
296	C₄²	#41×C₁₃₁	1	2	yes	—
297	C₂³	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
298	Q₈	—	4	4	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	2	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	2	no	—
326	C₂×C₄	#117×C₁₃₁	1	2	yes	—
327	C₂×C₄	#117×C₁₃₁	1	2	yes	—
328	C₂×C₄	#131×C₁₃₁	1	2	yes	—
329	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
330	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
331	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
332	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
333	C₈	—	2	4	no	—
334	C₈	—	4	2	no	—
335	C₈	—	4	2	no	—
336	C₈	—	4	2	no	—
337	C₂²	C₂×#117×C₁₃₁	1	1	yes	characteristic
338	C₂²	C₄×#41×C₁₃₁	1	1	yes	characteristic
339	C₂²	#519×C₁₃₁	1	1	yes	characteristic
340	C₂²	C₂×#131×C₁₃₁	1	1	yes	characteristic
341	C₂²	#568×C₁₃₁	1	1	yes	characteristic
342	C₂²	#568×C₁₃₁	1	1	yes	characteristic
343	C₂²	#568×C₁₃₁	1	1	yes	characteristic
344	C₄	—	2	2	no	—
345	C₄	—	2	2	no	—
346	C₄	—	2	2	no	—
347	C₄	—	4	1	no	—
348	C₄	—	4	1	no	—
349	C₄	—	4	2	no	—
350	C₄	—	4	2	no	—
351	C₄	—	4	1	no	—
352	C₄	—	4	2	no	—
353	C₄	—	4	2	no	—
354	C₄	#552×C₁₃₁	1	2	yes	—
355	C₄	#556×C₁₃₁	1	2	yes	—
356	C₂	#2356×C₁₃₁	1	1	yes	characteristic
357	C₂	#2921×C₁₃₁	1	1	yes	characteristic
358	C₂	#2925×C₁₃₁	1	1	yes	characteristic
359	C₂	#2967×C₁₃₁	1	1	yes	characteristic
360	C₂	#2968×C₁₃₁	1	1	yes	characteristic
361	C₂	#2985×C₁₃₁	1	1	yes	characteristic
362	C₂	#2987×C₁₃₁	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
181. #22831	C₁₃₁	direct (N × H)
182. C₁₃₁	#22831	direct (N × H)

Maximal subgroups

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

subgroup	index
#2295×C₁₃₁	2
#1985×C₁₃₁	2
#1917×C₁₃₁	2
#1916×C₁₃₁	2
#1840×C₁₃₁	2
#1831×C₁₃₁	2
#1771×C₁₃₁	2
#1767×C₁₃₁	2
#1746×C₁₃₁	2
#22831	131

Subgroups — C131×#22831 #45708715

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#22831 #45708715