Subgroups — C₁₃₁×#23371 #45709255

Order 33536.

604 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	C₄×#125×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#1940×C₁₃₁	C₂	1	2	yes	maximal
3	#1939×C₁₃₁	C₂	1	2	yes	maximal
4	#1917×C₁₃₁	C₂	1	2	yes	maximal
5	#1917×C₁₃₁	C₂	1	2	yes	maximal
6	#1916×C₁₃₁	C₂	1	2	yes	maximal
7	#1916×C₁₃₁	C₂	1	2	yes	maximal
8	#1831×C₁₃₁	C₂	1	1	yes	maximal, characteristic
9	#1831×C₁₃₁	C₂	1	1	yes	maximal, characteristic
10	C₂×#125×C₁₃₁	C₄	1	1	yes	characteristic
11	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	2	yes	—
16	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	2	yes	—
17	C₂×#97×C₁₃₁	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₁₃₁	C₂²	1	2	yes	—
19	#389×C₁₃₁	C₄	1	1	yes	characteristic
20	#389×C₁₃₁	C₄	1	1	yes	characteristic
21	#387×C₁₃₁	C₄	1	2	yes	—
22	#387×C₁₃₁	C₄	1	2	yes	—
23	#382×C₁₃₁	C₄	1	1	yes	characteristic
24	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
26	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
28	C₄³×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	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×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	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	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	2	yes	—
56	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
58	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
59	C₄⋊C₈×C₁₃₁	—	4	2	no	—
60	C₄⋊C₈×C₁₃₁	—	4	2	no	—
61	C₄⋊C₈×C₁₃₁	—	4	1	no	—
62	C₄⋊C₈×C₁₃₁	—	4	1	no	—
63	C₄⋊C₈×C₁₃₁	—	4	1	no	—
64	C₄⋊C₈×C₁₃₁	—	4	1	no	—
65	#97×C₁₃₁	—	4	2	no	—
66	C₄×C₈×C₁₃₁	—	4	2	no	—
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	#95×C₁₃₁	C₂×C₄	1	2	yes	—
72	#95×C₁₃₁	C₂×C₄	1	2	yes	—
73	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
75	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
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	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
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	—	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	C₄⋊C₄×C₁₃₁	—	2	4	no	—
97	C₄⋊C₄×C₁₃₁	—	2	4	no	—
98	C₄⋊C₄×C₁₃₁	—	2	2	no	—
99	C₄⋊C₄×C₁₃₁	—	2	4	no	—
100	C₄⋊C₄×C₁₃₁	—	2	4	no	—
101	C₄⋊C₄×C₁₃₁	—	4	1	no	—
102	C₄⋊C₄×C₁₃₁	—	4	1	no	—
103	C₄⋊C₄×C₁₃₁	M₁₆	1	4	yes	—
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	—	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	2	no	—
117	C₄²×C₁₃₁	—	4	1	no	—
118	C₂³×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
119	C₂×C₄×C₁₃₁	—	2	1	no	—
120	C₂×C₄×C₁₃₁	—	2	2	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	1	no	—
125	C₂×C₄×C₁₃₁	—	2	1	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	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	2	no	—
136	C₂×C₄×C₁₃₁	—	2	1	no	—
137	C₂×C₄×C₁₃₁	—	2	1	no	—
138	C₂×C₄×C₁₃₁	—	2	1	no	—
139	C₂×C₄×C₁₃₁	—	2	1	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	C₂×M₁₆	1	2	yes	—
146	C₂×C₄×C₁₃₁	C₂×M₁₆	1	4	yes	—
147	C₂×C₄×C₁₃₁	#131	1	2	yes	—
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	1	yes	characteristic
152	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
153	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
154	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
155	C₈×C₁₃₁	—	4	2	no	—
156	C₈×C₁₃₁	—	4	2	no	—
157	C₈×C₁₃₁	—	4	2	no	—
158	C₈×C₁₃₁	—	4	2	no	—
159	C₂²×C₁₃₁	#519	1	1	yes	characteristic
160	C₂²×C₁₃₁	#520	1	1	yes	characteristic
161	C₂²×C₁₃₁	#520	1	1	yes	characteristic
162	C₂²×C₁₃₁	C₂²×M₁₆	1	1	yes	characteristic
163	C₂²×C₁₃₁	C₂×#131	1	1	yes	characteristic
164	C₂²×C₁₃₁	C₂×#131	1	1	yes	characteristic
165	C₂²×C₁₃₁	#568	1	1	yes	characteristic
166	C₄×C₁₃₁	—	2	2	no	—
167	C₄×C₁₃₁	—	2	4	no	—
168	C₄×C₁₃₁	—	2	2	no	—
169	C₄×C₁₃₁	—	2	2	no	—
170	C₄×C₁₃₁	—	4	1	no	—
171	C₄×C₁₃₁	—	4	1	no	—
172	C₄×C₁₃₁	—	4	1	no	—
173	C₄×C₁₃₁	—	4	2	no	—
174	C₄×C₁₃₁	—	4	2	no	—
175	C₄×C₁₃₁	—	4	2	no	—
176	C₄×C₁₃₁	#562	1	1	yes	characteristic
177	C₄×C₁₃₁	#563	1	1	yes	characteristic
178	C₄×C₁₃₁	#563	1	1	yes	characteristic
179	C₄×C₁₃₁	#564	1	1	yes	characteristic
180	C₂×C₁₃₁	#2382	1	1	yes	characteristic
181	C₂×C₁₃₁	#2983	1	1	yes	characteristic
182	C₂×C₁₃₁	#2986	1	1	yes	characteristic
183	C₂×C₁₃₁	#2990	1	1	yes	characteristic
184	C₂×C₁₃₁	#2991	1	1	yes	characteristic
185	C₂×C₁₃₁	#2992	1	1	yes	characteristic
186	C₂×C₁₃₁	#2992	1	1	yes	characteristic
187	#23371	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₁₃₁	#23371	1	1	yes	characteristic, direct product factor, Sylow
189	C₄×#125	C₂×C₁₃₁	1	1	yes	characteristic
190	#1940	C₂×C₁₃₁	1	2	yes	—
191	#1939	C₂×C₁₃₁	1	2	yes	—
192	#1917	C₂×C₁₃₁	1	2	yes	—
193	#1917	C₂×C₁₃₁	1	2	yes	—
194	#1916	C₂×C₁₃₁	1	2	yes	—
195	#1916	C₂×C₁₃₁	1	2	yes	—
196	#1831	C₂×C₁₃₁	1	1	yes	characteristic
197	#1831	C₂×C₁₃₁	1	1	yes	characteristic
198	C₂×#125	C₄×C₁₃₁	1	1	yes	characteristic
199	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
200	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
201	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
202	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
203	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	2	yes	—
204	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	2	yes	—
205	C₂×#97	C₂²×C₁₃₁	1	2	yes	—
206	C₂×C₄×C₈	C₂²×C₁₃₁	1	2	yes	—
207	#389	C₄×C₁₃₁	1	1	yes	characteristic
208	#389	C₄×C₁₃₁	1	1	yes	characteristic
209	#387	C₄×C₁₃₁	1	2	yes	—
210	#387	C₄×C₁₃₁	1	2	yes	—
211	#382	C₄×C₁₃₁	1	1	yes	characteristic
212	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
213	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
214	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
215	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
216	C₄³	C₂²×C₁₃₁	1	1	yes	characteristic
217	#336	C₂²×C₁₃₁	1	2	yes	—
218	#336	C₂²×C₁₃₁	1	2	yes	—
219	#336	C₂²×C₁₃₁	1	2	yes	—
220	#336	C₂²×C₁₃₁	1	2	yes	—
221	#336	C₂²×C₁₃₁	1	2	yes	—
222	#336	C₂²×C₁₃₁	1	2	yes	—
223	#336	C₂²×C₁₃₁	1	2	yes	—
224	#336	C₂²×C₁₃₁	1	2	yes	—
225	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
226	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
227	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
228	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
229	#125	—	2	4	no	—
230	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
231	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
232	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
234	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	2	yes	—
235	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
236	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
238	C₂×C₄²	C₂×C₄×C₁₃₁	1	1	yes	characteristic
239	C₂×C₄²	C₂×C₄×C₁₃₁	1	1	yes	characteristic
240	C₂×C₄²	C₂×C₄×C₁₃₁	1	1	yes	characteristic
241	C₂×C₄²	C₂×C₄×C₁₃₁	1	1	yes	characteristic
242	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
243	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
244	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
245	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
246	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
247	C₄⋊C₈	—	4	2	no	—
248	C₄⋊C₈	—	4	2	no	—
249	C₄⋊C₈	—	4	1	no	—
250	C₄⋊C₈	—	4	1	no	—
251	C₄⋊C₈	—	4	1	no	—
252	C₄⋊C₈	—	4	1	no	—
253	#97	—	4	2	no	—
254	C₄×C₈	—	4	2	no	—
255	#95	C₂×C₄×C₁₃₁	1	2	yes	—
256	#95	C₂×C₄×C₁₃₁	1	2	yes	—
257	#95	C₂×C₄×C₁₃₁	1	2	yes	—
258	#95	C₂×C₄×C₁₃₁	1	2	yes	—
259	#95	C₂×C₄×C₁₃₁	1	2	yes	—
260	#95	C₂×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	2	yes	—
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	2	yes	—
267	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
268	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
269	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
270	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
271	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
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	—	2	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₄⋊C₄	—	2	4	no	—
285	C₄⋊C₄	—	2	4	no	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	2	4	no	—
289	C₄⋊C₄	—	4	1	no	—
290	C₄⋊C₄	—	4	1	no	—
291	C₄⋊C₄	M₁₆×C₁₃₁	1	4	yes	—
292	C₄²	—	2	2	no	—
293	C₄²	—	2	2	no	—
294	C₄²	—	2	2	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	2	1	no	—
298	C₄²	—	2	1	no	—
299	C₄²	—	2	1	no	—
300	C₄²	—	2	1	no	—
301	C₄²	—	2	1	no	—
302	C₄²	—	2	1	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	4	1	no	—
306	C₂³	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	2	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	2	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	C₂×M₁₆×C₁₃₁	1	2	yes	—
334	C₂×C₄	C₂×M₁₆×C₁₃₁	1	4	yes	—
335	C₂×C₄	#131×C₁₃₁	1	2	yes	—
336	C₂×C₄	#131×C₁₃₁	1	2	yes	—
337	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
338	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
339	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
340	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
341	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
342	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
343	C₈	—	4	2	no	—
344	C₈	—	4	2	no	—
345	C₈	—	4	2	no	—
346	C₈	—	4	2	no	—
347	C₂²	#519×C₁₃₁	1	1	yes	characteristic
348	C₂²	#520×C₁₃₁	1	1	yes	characteristic
349	C₂²	#520×C₁₃₁	1	1	yes	characteristic
350	C₂²	C₂²×M₁₆×C₁₃₁	1	1	yes	characteristic
351	C₂²	C₂×#131×C₁₃₁	1	1	yes	characteristic
352	C₂²	C₂×#131×C₁₃₁	1	1	yes	characteristic
353	C₂²	#568×C₁₃₁	1	1	yes	characteristic
354	C₄	—	2	4	no	—
355	C₄	—	2	2	no	—
356	C₄	—	2	2	no	—
357	C₄	—	2	2	no	—
358	C₄	—	4	1	no	—
359	C₄	—	4	1	no	—
360	C₄	—	4	1	no	—
361	C₄	—	4	2	no	—
362	C₄	—	4	2	no	—
363	C₄	—	4	2	no	—
364	C₄	#562×C₁₃₁	1	1	yes	characteristic
365	C₄	#563×C₁₃₁	1	1	yes	characteristic
366	C₄	#563×C₁₃₁	1	1	yes	characteristic
367	C₄	#564×C₁₃₁	1	1	yes	characteristic
368	C₂	#2382×C₁₃₁	1	1	yes	characteristic
369	C₂	#2983×C₁₃₁	1	1	yes	characteristic
370	C₂	#2986×C₁₃₁	1	1	yes	characteristic
371	C₂	#2990×C₁₃₁	1	1	yes	characteristic
372	C₂	#2991×C₁₃₁	1	1	yes	characteristic
373	C₂	#2992×C₁₃₁	1	1	yes	characteristic
374	C₂	#2992×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
187. #23371	C₁₃₁	direct (N × H)
188. C₁₃₁	#23371	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
#1940×C₁₃₁	2
#1939×C₁₃₁	2
#1917×C₁₃₁	2
#1916×C₁₃₁	2
#1831×C₁₃₁	2
#23371	131

Subgroups — C131×#23371 #45709255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#23371 #45709255