Subgroups — C₁₃₁×#23265 #45709149

Order 33536.

624 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#125×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#1917×C₁₃₁	C₂	1	2	yes	maximal
3	#1917×C₁₃₁	C₂	1	2	yes	maximal
4	#1917×C₁₃₁	C₂	1	2	yes	maximal
5	#1916×C₁₃₁	C₂	1	2	yes	maximal
6	#1771×C₁₃₁	C₂	1	2	yes	maximal
7	#1770×C₁₃₁	C₂	1	2	yes	maximal
8	#1745×C₁₃₁	C₂	1	1	yes	maximal, characteristic
9	#1745×C₁₃₁	C₂	1	1	yes	maximal, characteristic
10	C₂×#125×C₁₃₁	C₄	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×#97×C₁₃₁	C₂²	1	2	yes	—
16	C₂×C₄×C₈×C₁₃₁	C₂²	1	2	yes	—
17	#389×C₁₃₁	C₄	1	1	yes	characteristic
18	#389×C₁₃₁	C₄	1	1	yes	characteristic
19	#387×C₁₃₁	C₄	1	2	yes	—
20	#387×C₁₃₁	C₄	1	2	yes	—
21	#382×C₁₃₁	C₄	1	1	yes	characteristic
22	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
23	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
24	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
26	C₄³×C₁₃₁	C₂²	1	1	yes	characteristic
27	#336×C₁₃₁	C₂²	1	1	yes	characteristic
28	#336×C₁₃₁	C₂²	1	1	yes	characteristic
29	#336×C₁₃₁	C₂²	1	2	yes	—
30	#336×C₁₃₁	C₂²	1	2	yes	—
31	#336×C₁₃₁	C₂²	1	1	yes	characteristic
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	2	yes	—
36	#336×C₁₃₁	C₂²	1	2	yes	—
37	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
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	#125×C₁₃₁	—	2	4	no	—
42	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	2	yes	—
44	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	2	yes	—
45	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
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	1	yes	characteristic
57	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
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	#97×C₁₃₁	—	2	4	no	—
64	C₄×C₈×C₁₃₁	—	2	4	no	—
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	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
73	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
77	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
82	C₂×C₈×C₁₃₁	—	2	2	no	—
83	C₂×C₈×C₁₃₁	—	2	2	no	—
84	C₂×C₈×C₁₃₁	—	2	2	no	—
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	#41	1	4	yes	—
93	C₂×C₈×C₁₃₁	#41	1	4	yes	—
94	C₄⋊C₄×C₁₃₁	—	2	4	no	—
95	C₄⋊C₄×C₁₃₁	—	2	4	no	—
96	C₄⋊C₄×C₁₃₁	—	2	2	no	—
97	C₄⋊C₄×C₁₃₁	—	4	1	no	—
98	C₄⋊C₄×C₁₃₁	—	4	1	no	—
99	C₄⋊C₄×C₁₃₁	—	4	2	no	—
100	C₄⋊C₄×C₁₃₁	—	4	2	no	—
101	C₄⋊C₄×C₁₃₁	M₁₆	1	4	yes	—
102	C₄²×C₁₃₁	—	2	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	1	no	—
110	C₄²×C₁₃₁	—	2	1	no	—
111	C₄²×C₁₃₁	—	4	1	no	—
112	C₄²×C₁₃₁	—	4	1	no	—
113	C₄²×C₁₃₁	—	4	1	no	—
114	C₂³×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
115	C₂×C₄×C₁₃₁	—	2	2	no	—
116	C₂×C₄×C₁₃₁	—	2	1	no	—
117	C₂×C₄×C₁₃₁	—	2	1	no	—
118	C₂×C₄×C₁₃₁	—	2	2	no	—
119	C₂×C₄×C₁₃₁	—	2	2	no	—
120	C₂×C₄×C₁₃₁	—	2	1	no	—
121	C₂×C₄×C₁₃₁	—	2	1	no	—
122	C₂×C₄×C₁₃₁	—	2	2	no	—
123	C₂×C₄×C₁₃₁	—	2	1	no	—
124	C₂×C₄×C₁₃₁	—	2	1	no	—
125	C₂×C₄×C₁₃₁	—	2	2	no	—
126	C₂×C₄×C₁₃₁	—	2	1	no	—
127	C₂×C₄×C₁₃₁	—	2	1	no	—
128	C₂×C₄×C₁₃₁	—	2	1	no	—
129	C₂×C₄×C₁₃₁	—	2	2	no	—
130	C₂×C₄×C₁₃₁	—	2	1	no	—
131	C₂×C₄×C₁₃₁	—	2	1	no	—
132	C₂×C₄×C₁₃₁	—	2	1	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	C₂×M₁₆	1	2	yes	—
144	C₂×C₄×C₁₃₁	C₂×M₁₆	1	4	yes	—
145	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
146	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
147	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
148	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
149	C₈×C₁₃₁	—	2	4	no	—
150	C₈×C₁₃₁	—	2	4	no	—
151	C₈×C₁₃₁	—	4	2	no	—
152	C₈×C₁₃₁	—	4	2	no	—
153	C₂²×C₁₃₁	C₄×#41	1	1	yes	characteristic
154	C₂²×C₁₃₁	C₄×#41	1	1	yes	characteristic
155	C₂²×C₁₃₁	#519	1	1	yes	characteristic
156	C₂²×C₁₃₁	C₂²×M₁₆	1	1	yes	characteristic
157	C₂²×C₁₃₁	#568	1	1	yes	characteristic
158	C₂²×C₁₃₁	#568	1	1	yes	characteristic
159	C₂²×C₁₃₁	#568	1	1	yes	characteristic
160	C₄×C₁₃₁	—	2	4	no	—
161	C₄×C₁₃₁	—	2	2	no	—
162	C₄×C₁₃₁	—	4	1	no	—
163	C₄×C₁₃₁	—	4	1	no	—
164	C₄×C₁₃₁	—	4	2	no	—
165	C₄×C₁₃₁	—	4	2	no	—
166	C₄×C₁₃₁	—	4	1	no	—
167	C₄×C₁₃₁	—	4	1	no	—
168	C₄×C₁₃₁	—	4	2	no	—
169	C₄×C₁₃₁	—	4	1	no	—
170	C₄×C₁₃₁	#552	1	2	yes	—
171	C₄×C₁₃₁	#552	1	2	yes	—
172	C₂×C₁₃₁	#2371	1	1	yes	characteristic
173	C₂×C₁₃₁	#2967	1	1	yes	characteristic
174	C₂×C₁₃₁	#2967	1	1	yes	characteristic
175	C₂×C₁₃₁	#2970	1	1	yes	characteristic
176	C₂×C₁₃₁	#2971	1	1	yes	characteristic
177	C₂×C₁₃₁	#2983	1	1	yes	characteristic
178	C₂×C₁₃₁	#2987	1	1	yes	characteristic
179	#23265	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₁₃₁	#23265	1	1	yes	characteristic, direct product factor, Sylow
181	C₄×#125	C₂×C₁₃₁	1	1	yes	characteristic
182	#1917	C₂×C₁₃₁	1	2	yes	—
183	#1917	C₂×C₁₃₁	1	2	yes	—
184	#1917	C₂×C₁₃₁	1	2	yes	—
185	#1916	C₂×C₁₃₁	1	2	yes	—
186	#1771	C₂×C₁₃₁	1	2	yes	—
187	#1770	C₂×C₁₃₁	1	2	yes	—
188	#1745	C₂×C₁₃₁	1	1	yes	characteristic
189	#1745	C₂×C₁₃₁	1	1	yes	characteristic
190	C₂×#125	C₄×C₁₃₁	1	1	yes	characteristic
191	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	2	yes	—
192	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	2	yes	—
193	C₂×#97	C₂²×C₁₃₁	1	2	yes	—
194	C₂×#97	C₂²×C₁₃₁	1	2	yes	—
195	C₂×#97	C₂²×C₁₃₁	1	2	yes	—
196	C₂×C₄×C₈	C₂²×C₁₃₁	1	2	yes	—
197	#389	C₄×C₁₃₁	1	1	yes	characteristic
198	#389	C₄×C₁₃₁	1	1	yes	characteristic
199	#387	C₄×C₁₃₁	1	2	yes	—
200	#387	C₄×C₁₃₁	1	2	yes	—
201	#382	C₄×C₁₃₁	1	1	yes	characteristic
202	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
203	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
204	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
205	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
206	C₄³	C₂²×C₁₃₁	1	1	yes	characteristic
207	#336	C₂²×C₁₃₁	1	2	yes	—
208	#336	C₂²×C₁₃₁	1	2	yes	—
209	#336	C₂²×C₁₃₁	1	2	yes	—
210	#336	C₂²×C₁₃₁	1	2	yes	—
211	#336	C₂²×C₁₃₁	1	2	yes	—
212	#336	C₂²×C₁₃₁	1	1	yes	characteristic
213	#336	C₂²×C₁₃₁	1	1	yes	characteristic
214	#336	C₂²×C₁₃₁	1	2	yes	—
215	#336	C₂²×C₁₃₁	1	1	yes	characteristic
216	#336	C₂²×C₁₃₁	1	1	yes	characteristic
217	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
218	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
219	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
220	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
221	#125	—	2	4	no	—
222	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
223	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
224	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
225	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
226	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
227	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
228	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
229	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
230	C₂×C₄²	C₂×C₄×C₁₃₁	1	1	yes	characteristic
231	C₂×C₄²	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	C₂³×C₁₃₁	1	1	yes	characteristic
235	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
236	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
237	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
238	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
239	C₄⋊C₈	—	2	4	no	—
240	C₄⋊C₈	—	2	4	no	—
241	#97	—	2	4	no	—
242	#97	—	2	4	no	—
243	#97	—	2	4	no	—
244	C₄×C₈	—	2	4	no	—
245	#95	C₂×C₄×C₁₃₁	1	2	yes	—
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	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
252	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
253	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
254	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
255	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
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	1	yes	characteristic
261	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	—	2	2	no	—
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	#41×C₁₃₁	1	4	yes	—
273	C₂×C₈	#41×C₁₃₁	1	4	yes	—
274	C₄⋊C₄	—	2	4	no	—
275	C₄⋊C₄	—	2	4	no	—
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	4	1	no	—
278	C₄⋊C₄	—	4	1	no	—
279	C₄⋊C₄	—	4	2	no	—
280	C₄⋊C₄	—	4	2	no	—
281	C₄⋊C₄	M₁₆×C₁₃₁	1	4	yes	—
282	C₄²	—	2	2	no	—
283	C₄²	—	2	2	no	—
284	C₄²	—	2	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	1	no	—
290	C₄²	—	2	1	no	—
291	C₄²	—	4	1	no	—
292	C₄²	—	4	1	no	—
293	C₄²	—	4	1	no	—
294	C₂³	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	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	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	C₂×M₁₆×C₁₃₁	1	2	yes	—
324	C₂×C₄	C₂×M₁₆×C₁₃₁	1	4	yes	—
325	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
326	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
327	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
328	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
329	C₈	—	2	4	no	—
330	C₈	—	2	4	no	—
331	C₈	—	4	2	no	—
332	C₈	—	4	2	no	—
333	C₂²	C₄×#41×C₁₃₁	1	1	yes	characteristic
334	C₂²	C₄×#41×C₁₃₁	1	1	yes	characteristic
335	C₂²	#519×C₁₃₁	1	1	yes	characteristic
336	C₂²	C₂²×M₁₆×C₁₃₁	1	1	yes	characteristic
337	C₂²	#568×C₁₃₁	1	1	yes	characteristic
338	C₂²	#568×C₁₃₁	1	1	yes	characteristic
339	C₂²	#568×C₁₃₁	1	1	yes	characteristic
340	C₄	—	2	4	no	—
341	C₄	—	2	2	no	—
342	C₄	—	4	1	no	—
343	C₄	—	4	1	no	—
344	C₄	—	4	1	no	—
345	C₄	—	4	2	no	—
346	C₄	—	4	2	no	—
347	C₄	—	4	1	no	—
348	C₄	—	4	1	no	—
349	C₄	—	4	2	no	—
350	C₄	#552×C₁₃₁	1	2	yes	—
351	C₄	#552×C₁₃₁	1	2	yes	—
352	C₂	#2371×C₁₃₁	1	1	yes	characteristic
353	C₂	#2967×C₁₃₁	1	1	yes	characteristic
354	C₂	#2967×C₁₃₁	1	1	yes	characteristic
355	C₂	#2970×C₁₃₁	1	1	yes	characteristic
356	C₂	#2971×C₁₃₁	1	1	yes	characteristic
357	C₂	#2983×C₁₃₁	1	1	yes	characteristic
358	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
179. #23265	C₁₃₁	direct (N × H)
180. C₁₃₁	#23265	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×#125×C₁₃₁	2
#1917×C₁₃₁	2
#1916×C₁₃₁	2
#1771×C₁₃₁	2
#1770×C₁₃₁	2
#1745×C₁₃₁	2
#23265	131

Subgroups — C131×#23265 #45709149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#23265 #45709149