Subgroups — C₁₃₁×#23170 #45709054

Order 33536.

638 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3160×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2962×C₁₃₁	C₂	1	2	yes	maximal
3	#1986×C₁₃₁	C₂	1	2	yes	maximal
4	#1945×C₁₃₁	C₂	1	2	yes	maximal
5	#1922×C₁₃₁	C₂	1	4	yes	maximal
6	C₄×#108×C₁₃₁	C₂	1	1	yes	maximal, characteristic
7	#1772×C₁₃₁	C₂	1	2	yes	maximal
8	C₈×C₄⋊C₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic
9	#533×C₁₃₁	C₂²	1	2	yes	—
10	#500×C₁₃₁	C₄	1	1	yes	characteristic, complemented
11	#500×C₁₃₁	C₄	1	1	yes	characteristic, complemented
12	#499×C₁₃₁	C₄	1	2	yes	complemented
13	#499×C₁₃₁	C₄	1	2	yes	complemented
14	#498×C₁₃₁	C₄	1	2	yes	complemented
15	#446×C₁₃₁	—	2	4	no	—
16	#446×C₁₃₁	—	2	2	no	—
17	C₈×Q₈×C₁₃₁	—	2	2	no	—
18	C₂×#108×C₁₃₁	C₂²	1	1	yes	characteristic
19	C₂×#108×C₁₃₁	C₂²	1	1	yes	characteristic
20	#427×C₁₃₁	C₂²	1	2	yes	—
21	#427×C₁₃₁	C₂²	1	2	yes	—
22	#424×C₁₃₁	C₂²	1	4	yes	—
23	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
24	#405×C₁₃₁	C₂²	1	4	yes	—
25	C₄×M₁₆×C₁₃₁	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₁₃₁	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
29	#341×C₁₃₁	C₂²	1	2	yes	—
30	#339×C₁₃₁	C₂²	1	4	yes	—
31	#339×C₁₃₁	C₂²	1	4	yes	—
32	#336×C₁₃₁	C₂²	1	2	yes	—
33	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
34	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
35	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
36	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
37	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
38	C₄⋊Q₈×C₁₃₁	C₂×C₄	1	2	yes	—
39	C₄⋊Q₈×C₁₃₁	C₂×C₄	1	2	yes	—
40	#125×C₁₃₁	C₂×C₄	1	4	yes	—
41	C₂²⋊Q₈×C₁₃₁	—	2	2	no	—
42	C₂²⋊Q₈×C₁₃₁	—	2	2	no	—
43	C₄×Q₈×C₁₃₁	—	2	2	no	—
44	C₄×Q₈×C₁₃₁	—	2	2	no	—
45	#117×C₁₃₁	C₂³	1	4	yes	—
46	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
47	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
48	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
49	#108×C₁₃₁	—	2	2	no	—
50	#108×C₁₃₁	Q₈	1	4	yes	complemented
51	#107×C₁₃₁	C₂×C₄	1	2	yes	—
52	#107×C₁₃₁	C₂×C₄	1	2	yes	—
53	#107×C₁₃₁	C₂×C₄	1	2	yes	—
54	#107×C₁₃₁	C₂×C₄	1	2	yes	—
55	#106×C₁₃₁	C₂×C₄	1	4	yes	—
56	#106×C₁₃₁	C₂×C₄	1	4	yes	—
57	C₄⋊C₈×C₁₃₁	—	2	4	no	—
58	C₄⋊C₈×C₁₃₁	—	2	4	no	—
59	C₄⋊C₈×C₁₃₁	D₄	1	1	yes	characteristic
60	C₄⋊C₈×C₁₃₁	D₄	1	1	yes	characteristic
61	C₄⋊C₈×C₁₃₁	D₄	1	2	yes	—
62	#97×C₁₃₁	—	2	4	no	—
63	#97×C₁₃₁	—	2	2	no	—
64	C₄×C₈×C₁₃₁	—	2	4	no	—
65	C₄×C₈×C₁₃₁	—	2	4	no	—
66	C₄×C₈×C₁₃₁	—	2	2	no	—
67	C₄×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
68	C₄×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
69	C₄×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
70	C₄×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
71	#95×C₁₃₁	—	2	1	no	—
72	C₂×Q₈×C₁₃₁	—	2	2	no	—
73	C₂×Q₈×C₁₃₁	—	2	2	no	—
74	C₂²×C₄×C₁₃₁	—	2	2	no	—
75	C₂²×C₄×C₁₃₁	#41	1	1	yes	characteristic
76	C₂²×C₄×C₁₃₁	#41	1	1	yes	characteristic
77	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
78	M₁₆×C₁₃₁	—	2	2	no	—
79	M₁₆×C₁₃₁	—	2	2	no	—
80	M₁₆×C₁₃₁	—	2	2	no	—
81	M₁₆×C₁₃₁	C₂×Q₈	1	4	yes	—
82	C₂×C₈×C₁₃₁	—	2	2	no	—
83	C₂×C₈×C₁₃₁	—	2	2	no	—
84	C₂×C₈×C₁₃₁	—	2	1	no	—
85	C₂×C₈×C₁₃₁	—	2	1	no	—
86	C₂×C₈×C₁₃₁	—	2	2	no	—
87	C₂×C₈×C₁₃₁	—	2	2	no	—
88	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
89	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
93	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
94	C₂×C₈×C₁₃₁	C₂×Q₈	1	2	yes	—
95	C₂×C₈×C₁₃₁	#41	1	2	yes	—
96	C₄⋊C₄×C₁₃₁	—	2	4	no	—
97	C₄⋊C₄×C₁₃₁	—	2	4	no	—
98	C₄⋊C₄×C₁₃₁	—	2	4	no	—
99	C₄⋊C₄×C₁₃₁	—	2	2	no	—
100	C₄⋊C₄×C₁₃₁	—	2	2	no	—
101	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
102	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
103	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
104	C₄²×C₁₃₁	—	2	4	no	—
105	C₄²×C₁₃₁	—	2	2	no	—
106	C₄²×C₁₃₁	—	2	2	no	—
107	C₄²×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
111	C₂³×C₁₃₁	C₂×#41	1	1	yes	characteristic
112	Q₈×C₁₃₁	—	4	4	no	—
113	Q₈×C₁₃₁	—	8	2	no	—
114	C₂×C₄×C₁₃₁	—	2	2	no	—
115	C₂×C₄×C₁₃₁	—	2	4	no	—
116	C₂×C₄×C₁₃₁	—	2	4	no	—
117	C₂×C₄×C₁₃₁	—	2	4	no	—
118	C₂×C₄×C₁₃₁	—	4	1	no	—
119	C₂×C₄×C₁₃₁	—	4	2	no	—
120	C₂×C₄×C₁₃₁	—	4	2	no	—
121	C₂×C₄×C₁₃₁	C₄×D₄	1	1	yes	characteristic
122	C₂×C₄×C₁₃₁	C₄×D₄	1	1	yes	characteristic
123	C₂×C₄×C₁₃₁	C₄×D₄	1	1	yes	characteristic
124	C₂×C₄×C₁₃₁	C₄×D₄	1	1	yes	characteristic
125	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
126	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
127	C₂×C₄×C₁₃₁	C₂²×Q₈	1	1	yes	characteristic
128	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
129	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
130	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
131	C₈×C₁₃₁	—	2	1	no	—
132	C₈×C₁₃₁	—	2	1	no	—
133	C₈×C₁₃₁	—	2	2	no	—
134	C₈×C₁₃₁	—	2	2	no	—
135	C₈×C₁₃₁	—	2	4	no	—
136	C₈×C₁₃₁	—	4	2	no	—
137	C₈×C₁₃₁	C₄×Q₈	1	2	yes	—
138	C₈×C₁₃₁	C₄×Q₈	1	2	yes	—
139	C₂²×C₁₃₁	—	2	1	no	—
140	C₂²×C₁₃₁	—	2	1	no	—
141	C₂²×C₁₃₁	C₂×C₄×D₄	1	1	yes	characteristic
142	C₂²×C₁₃₁	#556	1	1	yes	characteristic
143	C₂²×C₁₃₁	#557	1	1	yes	characteristic
144	C₄×C₁₃₁	—	2	1	no	—
145	C₄×C₁₃₁	—	2	1	no	—
146	C₄×C₁₃₁	—	2	1	no	—
147	C₄×C₁₃₁	—	4	4	no	—
148	C₄×C₁₃₁	—	4	4	no	—
149	C₄×C₁₃₁	—	4	4	no	—
150	C₄×C₁₃₁	#443	1	2	yes	—
151	C₄×C₁₃₁	C₂×C₄×Q₈	1	1	yes	characteristic
152	C₄×C₁₃₁	#519	1	1	yes	characteristic
153	C₄×C₁₃₁	#547	1	1	yes	characteristic
154	C₄×C₁₃₁	D₄×Q₈	1	1	yes	characteristic
155	C₂×C₁₃₁	—	2	1	no	—
156	C₂×C₁₃₁	—	2	1	no	—
157	C₂×C₁₃₁	#2365	1	1	yes	characteristic
158	C₂×C₁₃₁	C₂×#443	1	1	yes	characteristic
159	C₂×C₁₃₁	#2957	1	1	yes	characteristic
160	#23170	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₁₃₁	#23170	1	1	yes	characteristic, direct product factor, Sylow
162	#3160	C₂×C₁₃₁	1	1	yes	characteristic
163	#2962	C₂×C₁₃₁	1	2	yes	—
164	#1986	C₂×C₁₃₁	1	2	yes	—
165	#1945	C₂×C₁₃₁	1	2	yes	—
166	#1922	C₂×C₁₃₁	1	4	yes	—
167	C₄×#108	C₂×C₁₃₁	1	1	yes	characteristic
168	#1772	C₂×C₁₃₁	1	2	yes	—
169	C₈×C₄⋊C₄	C₂×C₁₃₁	1	1	yes	characteristic
170	#533	C₂²×C₁₃₁	1	2	yes	—
171	#500	C₄×C₁₃₁	1	1	yes	characteristic, complemented
172	#500	C₄×C₁₃₁	1	1	yes	characteristic, complemented
173	#499	C₄×C₁₃₁	1	2	yes	complemented
174	#499	C₄×C₁₃₁	1	2	yes	complemented
175	#498	C₄×C₁₃₁	1	2	yes	complemented
176	#446	—	2	4	no	—
177	#446	—	2	2	no	—
178	C₈×Q₈	—	2	2	no	—
179	C₂×#108	C₂²×C₁₃₁	1	1	yes	characteristic
180	C₂×#108	C₂²×C₁₃₁	1	1	yes	characteristic
181	#427	C₂²×C₁₃₁	1	2	yes	—
182	#427	C₂²×C₁₃₁	1	2	yes	—
183	#424	C₂²×C₁₃₁	1	4	yes	—
184	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
185	#405	C₂²×C₁₃₁	1	4	yes	—
186	C₄×M₁₆	C₂²×C₁₃₁	1	2	yes	—
187	C₂×C₄×C₈	C₂²×C₁₃₁	1	2	yes	—
188	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
189	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
190	#341	C₂²×C₁₃₁	1	2	yes	—
191	#339	C₂²×C₁₃₁	1	4	yes	—
192	#339	C₂²×C₁₃₁	1	4	yes	—
193	#336	C₂²×C₁₃₁	1	2	yes	—
194	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
195	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
196	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
197	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
198	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
199	C₄⋊Q₈	C₂×C₄×C₁₃₁	1	2	yes	—
200	C₄⋊Q₈	C₂×C₄×C₁₃₁	1	2	yes	—
201	#125	C₂×C₄×C₁₃₁	1	4	yes	—
202	C₂²⋊Q₈	—	2	2	no	—
203	C₂²⋊Q₈	—	2	2	no	—
204	C₄×Q₈	—	2	2	no	—
205	C₄×Q₈	—	2	2	no	—
206	#117	C₂³×C₁₃₁	1	4	yes	—
207	C₂×C₄⋊C₄	—	2	1	no	—
208	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
209	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
210	#108	—	2	2	no	—
211	#108	Q₈×C₁₃₁	1	4	yes	complemented
212	#107	C₂×C₄×C₁₃₁	1	2	yes	—
213	#107	C₂×C₄×C₁₃₁	1	2	yes	—
214	#107	C₂×C₄×C₁₃₁	1	2	yes	—
215	#107	C₂×C₄×C₁₃₁	1	2	yes	—
216	#106	C₂×C₄×C₁₃₁	1	4	yes	—
217	#106	C₂×C₄×C₁₃₁	1	4	yes	—
218	C₄⋊C₈	—	2	4	no	—
219	C₄⋊C₈	—	2	4	no	—
220	C₄⋊C₈	D₄×C₁₃₁	1	1	yes	characteristic
221	C₄⋊C₈	D₄×C₁₃₁	1	1	yes	characteristic
222	C₄⋊C₈	D₄×C₁₃₁	1	2	yes	—
223	#97	—	2	4	no	—
224	#97	—	2	2	no	—
225	C₄×C₈	—	2	4	no	—
226	C₄×C₈	—	2	4	no	—
227	C₄×C₈	—	2	2	no	—
228	C₄×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
229	C₄×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
230	C₄×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
231	C₄×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
232	#95	—	2	1	no	—
233	C₂×Q₈	—	2	2	no	—
234	C₂×Q₈	—	2	2	no	—
235	C₂²×C₄	—	2	2	no	—
236	C₂²×C₄	#41×C₁₃₁	1	1	yes	characteristic
237	C₂²×C₄	#41×C₁₃₁	1	1	yes	characteristic
238	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
239	M₁₆	—	2	2	no	—
240	M₁₆	—	2	2	no	—
241	M₁₆	—	2	2	no	—
242	M₁₆	C₂×Q₈×C₁₃₁	1	4	yes	—
243	C₂×C₈	—	2	2	no	—
244	C₂×C₈	—	2	2	no	—
245	C₂×C₈	—	2	1	no	—
246	C₂×C₈	—	2	1	no	—
247	C₂×C₈	—	2	2	no	—
248	C₂×C₈	—	2	2	no	—
249	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
250	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
251	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
252	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
253	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
254	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
255	C₂×C₈	C₂×Q₈×C₁₃₁	1	2	yes	—
256	C₂×C₈	#41×C₁₃₁	1	2	yes	—
257	C₄⋊C₄	—	2	4	no	—
258	C₄⋊C₄	—	2	4	no	—
259	C₄⋊C₄	—	2	4	no	—
260	C₄⋊C₄	—	2	2	no	—
261	C₄⋊C₄	—	2	2	no	—
262	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
263	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
264	C₂²⋊C₄	—	2	4	no	—
265	C₄²	—	2	4	no	—
266	C₄²	—	2	2	no	—
267	C₄²	—	2	2	no	—
268	C₄²	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
269	C₄²	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
270	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
271	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
272	C₂³	C₂×#41×C₁₃₁	1	1	yes	characteristic
273	Q₈	—	4	4	no	—
274	Q₈	—	8	2	no	—
275	C₂×C₄	—	2	2	no	—
276	C₂×C₄	—	2	4	no	—
277	C₂×C₄	—	2	4	no	—
278	C₂×C₄	—	2	4	no	—
279	C₂×C₄	—	4	1	no	—
280	C₂×C₄	—	4	2	no	—
281	C₂×C₄	—	4	2	no	—
282	C₂×C₄	C₄×D₄×C₁₃₁	1	1	yes	characteristic
283	C₂×C₄	C₄×D₄×C₁₃₁	1	1	yes	characteristic
284	C₂×C₄	C₄×D₄×C₁₃₁	1	1	yes	characteristic
285	C₂×C₄	C₄×D₄×C₁₃₁	1	1	yes	characteristic
286	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
287	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
288	C₂×C₄	C₂²×Q₈×C₁₃₁	1	1	yes	characteristic
289	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
290	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
291	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
292	C₈	—	2	1	no	—
293	C₈	—	2	1	no	—
294	C₈	—	2	2	no	—
295	C₈	—	2	2	no	—
296	C₈	—	2	4	no	—
297	C₈	—	4	2	no	—
298	C₈	C₄×Q₈×C₁₃₁	1	2	yes	—
299	C₈	C₄×Q₈×C₁₃₁	1	2	yes	—
300	C₂²	—	2	1	no	—
301	C₂²	—	2	1	no	—
302	C₂²	C₂×C₄×D₄×C₁₃₁	1	1	yes	characteristic
303	C₂²	#556×C₁₃₁	1	1	yes	characteristic
304	C₂²	#557×C₁₃₁	1	1	yes	characteristic
305	C₄	—	2	1	no	—
306	C₄	—	2	1	no	—
307	C₄	—	2	1	no	—
308	C₄	—	4	4	no	—
309	C₄	—	4	4	no	—
310	C₄	—	4	4	no	—
311	C₄	#443×C₁₃₁	1	2	yes	—
312	C₄	C₂×C₄×Q₈×C₁₃₁	1	1	yes	characteristic
313	C₄	#519×C₁₃₁	1	1	yes	characteristic
314	C₄	#547×C₁₃₁	1	1	yes	characteristic
315	C₄	D₄×Q₈×C₁₃₁	1	1	yes	characteristic
316	C₂	—	2	1	no	—
317	C₂	—	2	1	no	—
318	C₂	#2365×C₁₃₁	1	1	yes	characteristic
319	C₂	C₂×#443×C₁₃₁	1	1	yes	characteristic
320	C₂	#2957×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
socle	C₂²×C₁₃₁	C₂×C₄×D₄
prime radical	C₂³×C₁₃₁	C₂×#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₁ ◁ C₂×C₄⋊C₈×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
10. #500×C₁₃₁	C₄	semidirect
11. #500×C₁₃₁	C₄	semidirect
12. #499×C₁₃₁	C₄	semidirect
13. #499×C₁₃₁	C₄	semidirect
14. #498×C₁₃₁	C₄	semidirect
50. #108×C₁₃₁	Q₈	semidirect
160. #23170	C₁₃₁	direct (N × H)
161. C₁₃₁	#23170	direct (N × H)
171. #500	C₄×C₁₃₁	semidirect
172. #500	C₄×C₁₃₁	semidirect
173. #499	C₄×C₁₃₁	semidirect
174. #499	C₄×C₁₃₁	semidirect
175. #498	C₄×C₁₃₁	semidirect
211. #108	Q₈×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#3160×C₁₃₁	2
#2962×C₁₃₁	2
#1986×C₁₃₁	2
#1945×C₁₃₁	2
#1922×C₁₃₁	2
C₄×#108×C₁₃₁	2
#1772×C₁₃₁	2
C₈×C₄⋊C₄×C₁₃₁	2
#23170	131

Subgroups — C131×#23170 #45709054

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#23170 #45709054