Subgroups — C₁₃₁×#23368 #45709252

Order 33536.

580 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2399×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#1985×C₁₃₁	C₂	1	2	yes	maximal
3	#1985×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	#1984×C₁₃₁	C₂	1	1	yes	maximal, characteristic
5	#1917×C₁₃₁	C₂	1	2	yes	maximal
6	#1917×C₁₃₁	C₂	1	2	yes	maximal
7	#1917×C₁₃₁	C₂	1	2	yes	maximal
8	#1916×C₁₃₁	C₂	1	2	yes	maximal
9	#1840×C₁₃₁	C₂	1	2	yes	maximal
10	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	2	yes	—
14	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
15	C₂×#97×C₁₃₁	C₂²	1	2	yes	—
16	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
18	#398×C₁₃₁	C₄	1	1	yes	characteristic
19	#398×C₁₃₁	C₄	1	1	yes	characteristic
20	#398×C₁₃₁	C₄	1	2	yes	—
21	#395×C₁₃₁	C₄	1	2	yes	—
22	#395×C₁₃₁	C₄	1	1	yes	characteristic
23	#395×C₁₃₁	C₄	1	1	yes	characteristic
24	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
25	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
26	#376×C₁₃₁	C₂²	1	1	yes	characteristic
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	2	yes	—
31	#336×C₁₃₁	C₂²	1	2	yes	—
32	#336×C₁₃₁	C₂²	1	2	yes	—
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×Q₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
38	C₂²×Q₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
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	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
43	C₄×Q₈×C₁₃₁	—	4	1	no	—
44	C₄×Q₈×C₁₃₁	—	4	1	no	—
45	C₄×Q₈×C₁₃₁	—	4	1	no	—
46	C₄×Q₈×C₁₃₁	—	4	1	no	—
47	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	2	yes	—
53	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	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	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
61	C₄⋊C₈×C₁₃₁	—	4	2	no	—
62	C₄⋊C₈×C₁₃₁	—	4	1	no	—
63	C₄⋊C₈×C₁₃₁	—	4	1	no	—
64	#97×C₁₃₁	—	4	2	no	—
65	#97×C₁₃₁	—	4	1	no	—
66	C₄×C₈×C₁₃₁	—	4	1	no	—
67	#95×C₁₃₁	C₂×C₄	1	2	yes	—
68	#95×C₁₃₁	C₂×C₄	1	2	yes	—
69	#95×C₁₃₁	C₂×C₄	1	1	yes	characteristic
70	#95×C₁₃₁	C₂×C₄	1	2	yes	—
71	#95×C₁₃₁	C₂×C₄	1	1	yes	characteristic
72	#95×C₁₃₁	C₂×C₄	1	2	yes	—
73	#95×C₁₃₁	C₂×C₄	1	2	yes	—
74	C₂×Q₈×C₁₃₁	—	2	2	no	—
75	C₂×Q₈×C₁₃₁	—	4	1	no	—
76	C₂×Q₈×C₁₃₁	—	4	1	no	—
77	C₂×Q₈×C₁₃₁	—	4	1	no	—
78	C₂×Q₈×C₁₃₁	—	4	2	no	—
79	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
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	—	2	4	no	—
97	C₂×C₈×C₁₃₁	—	2	2	no	—
98	C₂×C₈×C₁₃₁	—	2	2	no	—
99	C₂×C₈×C₁₃₁	—	2	4	no	—
100	C₄⋊C₄×C₁₃₁	—	2	4	no	—
101	C₄⋊C₄×C₁₃₁	—	4	2	no	—
102	C₄⋊C₄×C₁₃₁	—	4	2	no	—
103	C₄⋊C₄×C₁₃₁	—	4	2	no	—
104	C₄⋊C₄×C₁₃₁	—	4	1	no	—
105	C₄⋊C₄×C₁₃₁	—	4	1	no	—
106	C₄⋊C₄×C₁₃₁	—	4	1	no	—
107	C₄⋊C₄×C₁₃₁	—	4	2	no	—
108	C₄⋊C₄×C₁₃₁	—	4	1	no	—
109	C₄²×C₁₃₁	—	2	1	no	—
110	C₄²×C₁₃₁	—	2	2	no	—
111	C₄²×C₁₃₁	—	2	1	no	—
112	C₄²×C₁₃₁	—	2	1	no	—
113	C₄²×C₁₃₁	—	2	2	no	—
114	C₄²×C₁₃₁	—	2	1	no	—
115	C₄²×C₁₃₁	—	2	1	no	—
116	C₄²×C₁₃₁	—	2	1	no	—
117	C₄²×C₁₃₁	—	2	2	no	—
118	C₄²×C₁₃₁	—	2	2	no	—
119	C₂³×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
120	Q₈×C₁₃₁	—	4	4	no	—
121	Q₈×C₁₃₁	—	4	4	no	—
122	C₂×C₄×C₁₃₁	—	2	1	no	—
123	C₂×C₄×C₁₃₁	—	2	1	no	—
124	C₂×C₄×C₁₃₁	—	2	1	no	—
125	C₂×C₄×C₁₃₁	—	2	1	no	—
126	C₂×C₄×C₁₃₁	—	2	2	no	—
127	C₂×C₄×C₁₃₁	—	2	1	no	—
128	C₂×C₄×C₁₃₁	—	2	1	no	—
129	C₂×C₄×C₁₃₁	—	2	1	no	—
130	C₂×C₄×C₁₃₁	—	2	2	no	—
131	C₂×C₄×C₁₃₁	—	2	2	no	—
132	C₂×C₄×C₁₃₁	—	2	2	no	—
133	C₂×C₄×C₁₃₁	—	2	2	no	—
134	C₂×C₄×C₁₃₁	—	2	2	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	—	2	2	no	—
145	C₂×C₄×C₁₃₁	—	2	1	no	—
146	C₂×C₄×C₁₃₁	—	2	2	no	—
147	C₂×C₄×C₁₃₁	—	2	2	no	—
148	C₂×C₄×C₁₃₁	#131	1	2	yes	—
149	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
150	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
151	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
152	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
153	C₈×C₁₃₁	—	4	2	no	—
154	C₈×C₁₃₁	—	4	2	no	—
155	C₈×C₁₃₁	—	4	2	no	—
156	C₈×C₁₃₁	—	4	2	no	—
157	C₂²×C₁₃₁	#518	1	1	yes	characteristic
158	C₂²×C₁₃₁	#519	1	2	yes	—
159	C₂²×C₁₃₁	C₂×#131	1	1	yes	characteristic
160	C₂²×C₁₃₁	#568	1	1	yes	characteristic
161	C₂²×C₁₃₁	#568	1	2	yes	—
162	C₄×C₁₃₁	—	2	2	no	—
163	C₄×C₁₃₁	—	4	2	no	—
164	C₄×C₁₃₁	—	4	1	no	—
165	C₄×C₁₃₁	—	4	1	no	—
166	C₄×C₁₃₁	—	4	1	no	—
167	C₄×C₁₃₁	—	4	1	no	—
168	C₄×C₁₃₁	—	4	1	no	—
169	C₄×C₁₃₁	—	4	2	no	—
170	C₄×C₁₃₁	—	4	2	no	—
171	C₄×C₁₃₁	—	4	2	no	—
172	C₄×C₁₃₁	#563	1	2	yes	—
173	C₄×C₁₃₁	#563	1	1	yes	characteristic
174	C₄×C₁₃₁	#563	1	1	yes	characteristic
175	C₂×C₁₃₁	#2381	1	1	yes	characteristic
176	C₂×C₁₃₁	#2976	1	1	yes	characteristic
177	C₂×C₁₃₁	#2978	1	1	yes	characteristic
178	C₂×C₁₃₁	#2985	1	2	yes	—
179	C₂×C₁₃₁	#2987	1	2	yes	—
180	#23368	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₁₃₁	#23368	1	1	yes	characteristic, direct product factor, Sylow
182	#2399	C₂×C₁₃₁	1	1	yes	characteristic
183	#1985	C₂×C₁₃₁	1	1	yes	characteristic
184	#1985	C₂×C₁₃₁	1	2	yes	—
185	#1984	C₂×C₁₃₁	1	1	yes	characteristic
186	#1917	C₂×C₁₃₁	1	2	yes	—
187	#1917	C₂×C₁₃₁	1	2	yes	—
188	#1917	C₂×C₁₃₁	1	2	yes	—
189	#1916	C₂×C₁₃₁	1	2	yes	—
190	#1840	C₂×C₁₃₁	1	2	yes	—
191	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
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	1	yes	characteristic
195	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
196	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
197	C₂×#97	C₂²×C₁₃₁	1	2	yes	—
198	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
199	#398	C₄×C₁₃₁	1	1	yes	characteristic
200	#398	C₄×C₁₃₁	1	1	yes	characteristic
201	#398	C₄×C₁₃₁	1	2	yes	—
202	#395	C₄×C₁₃₁	1	2	yes	—
203	#395	C₄×C₁₃₁	1	1	yes	characteristic
204	#395	C₄×C₁₃₁	1	1	yes	characteristic
205	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
206	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
207	#376	C₂²×C₁₃₁	1	1	yes	characteristic
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	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	C₂²×Q₈	C₂×C₄×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	—	4	1	no	—
225	C₄×Q₈	—	4	1	no	—
226	C₄×Q₈	—	4	1	no	—
227	C₄×Q₈	—	4	1	no	—
228	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
229	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
230	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
231	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
232	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
235	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
236	C₂×C₄⋊C₄	C₂×C₄×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	1	yes	characteristic
240	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
241	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
242	C₄⋊C₈	—	4	2	no	—
243	C₄⋊C₈	—	4	1	no	—
244	C₄⋊C₈	—	4	1	no	—
245	#97	—	4	2	no	—
246	#97	—	4	1	no	—
247	C₄×C₈	—	4	1	no	—
248	#95	C₂×C₄×C₁₃₁	1	1	yes	characteristic
249	#95	C₂×C₄×C₁₃₁	1	2	yes	—
250	#95	C₂×C₄×C₁₃₁	1	1	yes	characteristic
251	#95	C₂×C₄×C₁₃₁	1	2	yes	—
252	#95	C₂×C₄×C₁₃₁	1	2	yes	—
253	#95	C₂×C₄×C₁₃₁	1	2	yes	—
254	#95	C₂×C₄×C₁₃₁	1	2	yes	—
255	C₂×Q₈	—	2	2	no	—
256	C₂×Q₈	—	4	1	no	—
257	C₂×Q₈	—	4	1	no	—
258	C₂×Q₈	—	4	1	no	—
259	C₂×Q₈	—	4	2	no	—
260	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
261	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
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	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
267	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
268	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
269	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
270	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
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	4	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	4	no	—
281	C₄⋊C₄	—	2	4	no	—
282	C₄⋊C₄	—	4	2	no	—
283	C₄⋊C₄	—	4	2	no	—
284	C₄⋊C₄	—	4	2	no	—
285	C₄⋊C₄	—	4	1	no	—
286	C₄⋊C₄	—	4	1	no	—
287	C₄⋊C₄	—	4	1	no	—
288	C₄⋊C₄	—	4	2	no	—
289	C₄⋊C₄	—	4	1	no	—
290	C₄²	—	2	1	no	—
291	C₄²	—	2	2	no	—
292	C₄²	—	2	1	no	—
293	C₄²	—	2	1	no	—
294	C₄²	—	2	2	no	—
295	C₄²	—	2	1	no	—
296	C₄²	—	2	1	no	—
297	C₄²	—	2	1	no	—
298	C₄²	—	2	2	no	—
299	C₄²	—	2	2	no	—
300	C₂³	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
301	Q₈	—	4	4	no	—
302	Q₈	—	4	4	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	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	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	#131×C₁₃₁	1	2	yes	—
330	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
331	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
332	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
333	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
334	C₈	—	4	2	no	—
335	C₈	—	4	2	no	—
336	C₈	—	4	2	no	—
337	C₈	—	4	2	no	—
338	C₂²	#518×C₁₃₁	1	1	yes	characteristic
339	C₂²	#519×C₁₃₁	1	2	yes	—
340	C₂²	C₂×#131×C₁₃₁	1	1	yes	characteristic
341	C₂²	#568×C₁₃₁	1	2	yes	—
342	C₂²	#568×C₁₃₁	1	1	yes	characteristic
343	C₄	—	2	2	no	—
344	C₄	—	4	2	no	—
345	C₄	—	4	2	no	—
346	C₄	—	4	1	no	—
347	C₄	—	4	1	no	—
348	C₄	—	4	2	no	—
349	C₄	—	4	1	no	—
350	C₄	—	4	2	no	—
351	C₄	—	4	1	no	—
352	C₄	—	4	1	no	—
353	C₄	#563×C₁₃₁	1	2	yes	—
354	C₄	#563×C₁₃₁	1	1	yes	characteristic
355	C₄	#563×C₁₃₁	1	1	yes	characteristic
356	C₂	#2381×C₁₃₁	1	1	yes	characteristic
357	C₂	#2976×C₁₃₁	1	1	yes	characteristic
358	C₂	#2978×C₁₃₁	1	1	yes	characteristic
359	C₂	#2985×C₁₃₁	1	2	yes	—
360	C₂	#2987×C₁₃₁	1	2	yes	—

	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
180. #23368	C₁₃₁	direct (N × H)
181. C₁₃₁	#23368	direct (N × H)

Maximal subgroups

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

subgroup	index
#2399×C₁₃₁	2
#1985×C₁₃₁	2
#1984×C₁₃₁	2
#1917×C₁₃₁	2
#1916×C₁₃₁	2
#1840×C₁₃₁	2
#23368	131

Subgroups — C131×#23368 #45709252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#23368 #45709252