Subgroups — C₁₃₁×#21966 #45707850

Order 33536.

754 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#424×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2314×C₁₃₁	C₂	1	2	yes	maximal
3	#1949×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#1949×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#1948×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#1947×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#1809×C₁₃₁	C₂	1	2	yes	maximal
8	#1808×C₁₃₁	C₂	1	1	yes	maximal, characteristic
9	#1807×C₁₃₁	C₂	1	1	yes	maximal, characteristic
10	C₂²×M₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
12	C₂×#117×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂×#107×C₁₃₁	C₂²	1	2	yes	—
14	C₂×#107×C₁₃₁	C₂²	1	2	yes	—
15	C₂×#106×C₁₃₁	C₂²	1	2	yes	—
16	C₂×#106×C₁₃₁	C₂²	1	2	yes	—
17	#424×C₁₃₁	C₄	1	8	yes	complemented
18	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	2	yes	—
20	#388×C₁₃₁	—	2	2	no	—
21	#388×C₁₃₁	—	2	2	no	—
22	#387×C₁₃₁	—	2	2	no	—
23	#387×C₁₃₁	—	2	2	no	—
24	#384×C₁₃₁	C₂²	1	2	yes	—
25	#382×C₁₃₁	C₂²	1	2	yes	—
26	#380×C₁₃₁	C₂²	1	2	yes	—
27	#380×C₁₃₁	C₂²	1	2	yes	—
28	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
30	#340×C₁₃₁	C₂²	1	1	yes	characteristic
31	#340×C₁₃₁	C₂²	1	1	yes	characteristic
32	#340×C₁₃₁	C₂²	1	1	yes	characteristic
33	#340×C₁₃₁	C₂²	1	1	yes	characteristic
34	#340×C₁₃₁	C₂²	1	2	yes	—
35	#340×C₁₃₁	C₂²	1	2	yes	—
36	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
37	C₂×M₁₆×C₁₃₁	—	4	2	no	—
38	C₂×M₁₆×C₁₃₁	C₂×C₄	1	4	yes	—
39	C₂²×C₈×C₁₃₁	—	4	2	no	—
40	C₂²×C₈×C₁₃₁	C₂×C₄	1	4	yes	—
41	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
44	#117×C₁₃₁	C₂×C₄	1	4	yes	—
45	#117×C₁₃₁	Q₈	1	4	yes	—
46	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
47	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
51	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
52	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
54	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₁₃₁	D₄	1	2	yes	—
57	C₂×C₄²×C₁₃₁	—	2	2	no	—
58	C₂×C₄²×C₁₃₁	—	2	2	no	—
59	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
60	#107×C₁₃₁	—	4	2	no	—
61	#107×C₁₃₁	—	4	2	no	—
62	#106×C₁₃₁	—	4	2	no	—
63	#106×C₁₃₁	—	4	2	no	—
64	C₄⋊C₈×C₁₃₁	C₂×C₄	1	8	yes	—
65	C₄⋊C₈×C₁₃₁	C₂×C₄	1	8	yes	—
66	#95×C₁₃₁	—	2	2	no	—
67	#95×C₁₃₁	—	2	2	no	—
68	#95×C₁₃₁	—	2	2	no	—
69	#95×C₁₃₁	—	2	2	no	—
70	#95×C₁₃₁	—	2	2	no	—
71	#95×C₁₃₁	—	2	2	no	—
72	C₂⁴×C₁₃₁	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₃₁	—	2	2	no	—
74	C₂²×C₄×C₁₃₁	—	2	2	no	—
75	C₂²×C₄×C₁₃₁	—	2	2	no	—
76	C₂²×C₄×C₁₃₁	—	2	2	no	—
77	C₂²×C₄×C₁₃₁	—	2	2	no	—
78	C₂²×C₄×C₁₃₁	—	2	2	no	—
79	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
82	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
83	C₂²×C₄×C₁₃₁	C₂×Q₈	1	2	yes	—
84	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
85	M₁₆×C₁₃₁	—	4	4	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	—	4	4	no	—
91	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
92	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
93	C₂×C₈×C₁₃₁	C₂²×C₄	1	4	yes	—
94	C₄⋊C₄×C₁₃₁	—	2	2	no	—
95	C₄⋊C₄×C₁₃₁	—	2	2	no	—
96	C₄⋊C₄×C₁₃₁	—	2	2	no	—
97	C₄⋊C₄×C₁₃₁	—	2	2	no	—
98	C₄⋊C₄×C₁₃₁	—	2	2	no	—
99	C₄⋊C₄×C₁₃₁	—	2	2	no	—
100	C₄⋊C₄×C₁₃₁	—	2	2	no	—
101	C₄⋊C₄×C₁₃₁	—	2	2	no	—
102	C₄⋊C₄×C₁₃₁	—	8	2	no	—
103	C₄⋊C₄×C₁₃₁	—	8	2	no	—
104	C₄⋊C₄×C₁₃₁	C₄⋊C₄	1	4	yes	—
105	C₄⋊C₄×C₁₃₁	C₄⋊C₄	1	4	yes	—
106	C₂²⋊C₄×C₁₃₁	—	8	2	no	—
107	C₂²⋊C₄×C₁₃₁	—	8	2	no	—
108	C₂²⋊C₄×C₁₃₁	C₄⋊C₄	1	8	yes	—
109	C₄²×C₁₃₁	—	8	2	no	—
110	C₄²×C₁₃₁	—	8	2	no	—
111	C₄²×C₁₃₁	C₂²×C₄	1	4	yes	—
112	C₄²×C₁₃₁	C₂×Q₈	1	4	yes	—
113	C₂³×C₁₃₁	—	2	2	no	—
114	C₂³×C₁₃₁	—	2	1	no	—
115	C₂³×C₁₃₁	—	2	2	no	—
116	C₂³×C₁₃₁	—	2	1	no	—
117	C₂³×C₁₃₁	C₂×C₄⋊C₄	1	2	yes	—
118	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
119	C₂×C₄×C₁₃₁	—	2	2	no	—
120	C₂×C₄×C₁₃₁	—	2	2	no	—
121	C₂×C₄×C₁₃₁	—	2	2	no	—
122	C₂×C₄×C₁₃₁	—	2	2	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	4	no	—
127	C₂×C₄×C₁₃₁	—	4	2	no	—
128	C₂×C₄×C₁₃₁	—	4	2	no	—
129	C₂×C₄×C₁₃₁	—	4	2	no	—
130	C₂×C₄×C₁₃₁	—	4	2	no	—
131	C₂×C₄×C₁₃₁	—	4	2	no	—
132	C₂×C₄×C₁₃₁	—	4	2	no	—
133	C₂×C₄×C₁₃₁	—	4	2	no	—
134	C₂×C₄×C₁₃₁	—	4	2	no	—
135	C₂×C₄×C₁₃₁	—	4	2	no	—
136	C₂×C₄×C₁₃₁	—	4	2	no	—
137	C₂×C₄×C₁₃₁	—	4	2	no	—
138	C₂×C₄×C₁₃₁	—	4	2	no	—
139	C₂×C₄×C₁₃₁	C₂×C₄⋊C₄	1	4	yes	—
140	C₂×C₄×C₁₃₁	C₂×C₄⋊C₄	1	4	yes	—
141	C₂×C₄×C₁₃₁	C₂×C₄⋊C₄	1	2	yes	—
142	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₃₁	C₂²×Q₈	1	1	yes	characteristic
144	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
145	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
146	C₈×C₁₃₁	—	2	2	no	—
147	C₈×C₁₃₁	—	2	2	no	—
148	C₈×C₁₃₁	—	2	4	no	—
149	C₂²×C₁₃₁	—	2	2	no	—
150	C₂²×C₁₃₁	—	2	2	no	—
151	C₂²×C₁₃₁	—	2	2	no	—
152	C₂²×C₁₃₁	—	4	2	no	—
153	C₂²×C₁₃₁	—	4	2	no	—
154	C₂²×C₁₃₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
155	C₂²×C₁₃₁	#537	1	2	yes	—
156	C₂²×C₁₃₁	#576	1	1	yes	characteristic
157	C₂²×C₁₃₁	#577	1	2	yes	—
158	C₂²×C₁₃₁	#578	1	1	yes	characteristic
159	C₄×C₁₃₁	—	2	2	no	—
160	C₄×C₁₃₁	—	2	4	no	—
161	C₄×C₁₃₁	—	2	4	no	—
162	C₄×C₁₃₁	—	8	2	no	—
163	C₄×C₁₃₁	—	8	2	no	—
164	C₄×C₁₃₁	—	8	2	no	—
165	C₄×C₁₃₁	—	8	2	no	—
166	C₄×C₁₃₁	#518	1	1	yes	characteristic
167	C₄×C₁₃₁	#519	1	1	yes	characteristic
168	C₄×C₁₃₁	#544	1	2	yes	—
169	C₂×C₁₃₁	—	4	2	no	—
170	C₂×C₁₃₁	#2316	1	1	yes	characteristic
171	C₂×C₁₃₁	#2912	1	1	yes	characteristic
172	C₂×C₁₃₁	#2913	1	1	yes	characteristic
173	C₂×C₁₃₁	#3257	1	2	yes	—
174	C₂×C₁₃₁	#3258	1	2	yes	—
175	#21966	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₁₃₁	#21966	1	1	yes	characteristic, direct product factor, Sylow
177	C₂×#424	C₂×C₁₃₁	1	1	yes	characteristic
178	#2314	C₂×C₁₃₁	1	2	yes	—
179	#1949	C₂×C₁₃₁	1	2	yes	complemented
180	#1949	C₂×C₁₃₁	1	2	yes	complemented
181	#1948	C₂×C₁₃₁	1	2	yes	complemented
182	#1947	C₂×C₁₃₁	1	2	yes	complemented
183	#1809	C₂×C₁₃₁	1	2	yes	—
184	#1808	C₂×C₁₃₁	1	1	yes	characteristic
185	#1807	C₂×C₁₃₁	1	1	yes	characteristic
186	C₂²×M₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
187	C₂³×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
188	C₂×#117	C₂²×C₁₃₁	1	1	yes	characteristic
189	C₂×#107	C₂²×C₁₃₁	1	2	yes	—
190	C₂×#107	C₂²×C₁₃₁	1	2	yes	—
191	C₂×#106	C₂²×C₁₃₁	1	2	yes	—
192	C₂×#106	C₂²×C₁₃₁	1	2	yes	—
193	#424	C₄×C₁₃₁	1	8	yes	complemented
194	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	2	yes	—
195	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	2	yes	—
196	#388	—	2	2	no	—
197	#388	—	2	2	no	—
198	#387	—	2	2	no	—
199	#387	—	2	2	no	—
200	#384	C₂²×C₁₃₁	1	2	yes	—
201	#382	C₂²×C₁₃₁	1	2	yes	—
202	#380	C₂²×C₁₃₁	1	2	yes	—
203	#380	C₂²×C₁₃₁	1	2	yes	—
204	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
205	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
206	#340	C₂²×C₁₃₁	1	1	yes	characteristic
207	#340	C₂²×C₁₃₁	1	1	yes	characteristic
208	#340	C₂²×C₁₃₁	1	1	yes	characteristic
209	#340	C₂²×C₁₃₁	1	1	yes	characteristic
210	#340	C₂²×C₁₃₁	1	2	yes	—
211	#340	C₂²×C₁₃₁	1	2	yes	—
212	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
213	C₂×M₁₆	—	4	2	no	—
214	C₂×M₁₆	C₂×C₄×C₁₃₁	1	4	yes	—
215	C₂²×C₈	—	4	2	no	—
216	C₂²×C₈	C₂×C₄×C₁₃₁	1	4	yes	—
217	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
218	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
219	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
220	#117	C₂×C₄×C₁₃₁	1	4	yes	—
221	#117	Q₈×C₁₃₁	1	4	yes	—
222	C₂×C₄⋊C₄	—	2	2	no	—
223	C₂×C₄⋊C₄	—	2	2	no	—
224	C₂×C₄⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
225	C₂×C₄⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
226	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
227	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
228	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
229	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
230	C₂×C₂²⋊C₄	—	2	2	no	—
231	C₂×C₂²⋊C₄	—	2	2	no	—
232	C₂×C₂²⋊C₄	D₄×C₁₃₁	1	2	yes	—
233	C₂×C₄²	—	2	2	no	—
234	C₂×C₄²	—	2	2	no	—
235	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
236	#107	—	4	2	no	—
237	#107	—	4	2	no	—
238	#106	—	4	2	no	—
239	#106	—	4	2	no	—
240	C₄⋊C₈	C₂×C₄×C₁₃₁	1	8	yes	—
241	C₄⋊C₈	C₂×C₄×C₁₃₁	1	8	yes	—
242	#95	—	2	2	no	—
243	#95	—	2	2	no	—
244	#95	—	2	2	no	—
245	#95	—	2	2	no	—
246	#95	—	2	2	no	—
247	#95	—	2	2	no	—
248	C₂⁴	C₂×D₄×C₁₃₁	1	1	yes	characteristic
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
256	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
257	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
258	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
259	C₂²×C₄	C₂×Q₈×C₁₃₁	1	2	yes	—
260	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
261	M₁₆	—	4	4	no	—
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	—	4	4	no	—
267	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
268	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
269	C₂×C₈	C₂²×C₄×C₁₃₁	1	4	yes	—
270	C₄⋊C₄	—	2	2	no	—
271	C₄⋊C₄	—	2	2	no	—
272	C₄⋊C₄	—	2	2	no	—
273	C₄⋊C₄	—	2	2	no	—
274	C₄⋊C₄	—	2	2	no	—
275	C₄⋊C₄	—	2	2	no	—
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	2	2	no	—
278	C₄⋊C₄	—	8	2	no	—
279	C₄⋊C₄	—	8	2	no	—
280	C₄⋊C₄	C₄⋊C₄×C₁₃₁	1	4	yes	—
281	C₄⋊C₄	C₄⋊C₄×C₁₃₁	1	4	yes	—
282	C₂²⋊C₄	—	8	2	no	—
283	C₂²⋊C₄	—	8	2	no	—
284	C₂²⋊C₄	C₄⋊C₄×C₁₃₁	1	8	yes	—
285	C₄²	—	8	2	no	—
286	C₄²	—	8	2	no	—
287	C₄²	C₂²×C₄×C₁₃₁	1	4	yes	—
288	C₄²	C₂×Q₈×C₁₃₁	1	4	yes	—
289	C₂³	—	2	2	no	—
290	C₂³	—	2	1	no	—
291	C₂³	—	2	2	no	—
292	C₂³	—	2	1	no	—
293	C₂³	C₂×C₄⋊C₄×C₁₃₁	1	2	yes	—
294	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	4	2	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	—	4	2	no	—
306	C₂×C₄	—	4	2	no	—
307	C₂×C₄	—	4	2	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	4	2	no	—
310	C₂×C₄	—	4	2	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	C₂×C₄⋊C₄×C₁₃₁	1	4	yes	—
316	C₂×C₄	C₂×C₄⋊C₄×C₁₃₁	1	4	yes	—
317	C₂×C₄	C₂×C₄⋊C₄×C₁₃₁	1	2	yes	—
318	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
319	C₂×C₄	C₂²×Q₈×C₁₃₁	1	1	yes	characteristic
320	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
321	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
322	C₈	—	2	2	no	—
323	C₈	—	2	2	no	—
324	C₈	—	2	4	no	—
325	C₂²	—	2	2	no	—
326	C₂²	—	2	2	no	—
327	C₂²	—	2	2	no	—
328	C₂²	—	4	2	no	—
329	C₂²	—	4	2	no	—
330	C₂²	C₂²×C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
331	C₂²	#537×C₁₃₁	1	2	yes	—
332	C₂²	#576×C₁₃₁	1	1	yes	characteristic
333	C₂²	#577×C₁₃₁	1	2	yes	—
334	C₂²	#578×C₁₃₁	1	1	yes	characteristic
335	C₄	—	2	2	no	—
336	C₄	—	2	4	no	—
337	C₄	—	2	4	no	—
338	C₄	—	8	2	no	—
339	C₄	—	8	2	no	—
340	C₄	—	8	2	no	—
341	C₄	—	8	2	no	—
342	C₄	#518×C₁₃₁	1	1	yes	characteristic
343	C₄	#519×C₁₃₁	1	1	yes	characteristic
344	C₄	#544×C₁₃₁	1	2	yes	—
345	C₂	—	4	2	no	—
346	C₂	#2316×C₁₃₁	1	1	yes	characteristic
347	C₂	#2912×C₁₃₁	1	1	yes	characteristic
348	C₂	#2913×C₁₃₁	1	1	yes	characteristic
349	C₂	#3257×C₁₃₁	1	2	yes	—
350	C₂	#3258×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂⁴×C₁₃₁	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ C₂×#117×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. #1949×C₁₃₁	C₂	semidirect
4. #1949×C₁₃₁	C₂	semidirect
5. #1948×C₁₃₁	C₂	semidirect
6. #1947×C₁₃₁	C₂	semidirect
17. #424×C₁₃₁	C₄	semidirect
175. #21966	C₁₃₁	direct (N × H)
176. C₁₃₁	#21966	direct (N × H)
179. #1949	C₂×C₁₃₁	semidirect
180. #1949	C₂×C₁₃₁	semidirect
181. #1948	C₂×C₁₃₁	semidirect
182. #1947	C₂×C₁₃₁	semidirect
193. #424	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×#424×C₁₃₁	2
#2314×C₁₃₁	2
#1949×C₁₃₁	2
#1948×C₁₃₁	2
#1947×C₁₃₁	2
#1809×C₁₃₁	2
#1808×C₁₃₁	2
#1807×C₁₃₁	2
#21966	131

Subgroups — C131×#21966 #45707850

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#21966 #45707850