Subgroups — C₁₃₁×#20385 #45706269

Order 33536.

1774 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	C₂⁴×C₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#407×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#405×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#2280×C₁₃₁	C₂	1	1	yes	maximal, characteristic
5	#1752×C₁₃₁	C₂	1	4	yes	maximal, complemented
6	C₈×C₂²⋊C₄×C₁₃₁	C₂	1	4	yes	maximal, complemented
7	#1729×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	C₂⁴×C₄×C₁₃₁	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₃₁	C₂²	1	2	yes	—
10	C₂³×C₈×C₁₃₁	—	2	8	no	—
11	C₂³×C₈×C₁₃₁	C₄	1	8	yes	complemented
12	C₂³×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃₁	C₂²	1	2	yes	—
14	C₂³×C₈×C₁₃₁	C₂²	1	2	yes	—
15	C₂³×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
16	C₂×#117×C₁₃₁	C₂²	1	2	yes	—
17	#407×C₁₃₁	C₄	1	8	yes	complemented
18	C₂×C₂²⋊C₈×C₁₃₁	C₂²	1	4	yes	—
19	#405×C₁₃₁	—	2	8	no	—
20	C₂×#97×C₁₃₁	C₂²	1	4	yes	complemented
21	C₂×C₄×C₈×C₁₃₁	C₂²	1	4	yes	complemented
22	#381×C₁₃₁	C₄	1	2	yes	—
23	#380×C₁₃₁	C₄	1	4	yes	—
24	#379×C₁₃₁	C₄	1	2	yes	—
25	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	—
26	#336×C₁₃₁	C₂²	1	8	yes	complemented
27	C₂⁵×C₁₃₁	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₃₁	—	2	4	no	—
29	C₂³×C₄×C₁₃₁	—	2	4	no	—
30	C₂³×C₄×C₁₃₁	C₂×C₄	1	2	yes	—
31	C₂³×C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₃₁	C₂×C₄	1	4	yes	—
33	C₂³×C₄×C₁₃₁	C₂×C₄	1	4	yes	—
34	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
35	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₁₃₁	—	2	4	no	—
37	C₂×M₁₆×C₁₃₁	—	2	4	no	—
38	C₂×M₁₆×C₁₃₁	C₂×C₄	1	8	yes	—
39	C₂²×C₈×C₁₃₁	—	2	4	no	—
40	C₂²×C₈×C₁₃₁	—	2	32	no	—
41	C₂²×C₈×C₁₃₁	—	2	8	no	—
42	C₂²×C₈×C₁₃₁	—	2	8	no	—
43	C₂²×C₈×C₁₃₁	C₂×C₄	1	4	yes	—
44	C₂²×C₈×C₁₃₁	C₂×C₄	1	8	yes	—
45	C₂²×C₈×C₁₃₁	C₂×C₄	1	8	yes	—
46	C₂²×C₈×C₁₃₁	C₂×C₄	1	4	yes	—
47	C₂²×C₈×C₁₃₁	D₄	1	8	yes	—
48	C₂²×C₈×C₁₃₁	C₂³	1	4	yes	—
49	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
52	#117×C₁₃₁	—	2	4	no	—
53	#117×C₁₃₁	—	2	4	no	—
54	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	4	yes	—
55	C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	1	4	yes	—
56	C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	1	8	yes	—
57	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
58	C₂²⋊C₈×C₁₃₁	C₂×C₄	1	16	yes	—
59	#97×C₁₃₁	—	2	8	no	—
60	C₄×C₈×C₁₃₁	—	2	8	no	—
61	#95×C₁₃₁	C₂×C₄	1	8	yes	—
62	C₂⁴×C₁₃₁	—	2	4	no	—
63	C₂⁴×C₁₃₁	—	2	8	no	—
64	C₂⁴×C₁₃₁	C₄²	1	4	yes	—
65	C₂⁴×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
66	C₂⁴×C₁₃₁	C₂²×C₄	1	2	yes	—
67	C₂²×C₄×C₁₃₁	—	2	4	no	—
68	C₂²×C₄×C₁₃₁	—	2	8	no	—
69	C₂²×C₄×C₁₃₁	—	2	8	no	—
70	C₂²×C₄×C₁₃₁	—	2	8	no	—
71	C₂²×C₄×C₁₃₁	—	2	16	no	—
72	C₂²×C₄×C₁₃₁	—	2	4	no	—
73	C₂²×C₄×C₁₃₁	—	2	4	no	—
74	C₂²×C₄×C₁₃₁	C₄²	1	4	yes	—
75	C₂²×C₄×C₁₃₁	C₄²	1	8	yes	—
76	C₂²×C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
77	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
78	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
79	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
80	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₁₃₁	C₂×D₄	1	4	yes	—
84	C₂²×C₄×C₁₃₁	#41	1	4	yes	—
85	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
86	M₁₆×C₁₃₁	—	2	16	no	—
87	C₂×C₈×C₁₃₁	—	2	8	no	—
88	C₂×C₈×C₁₃₁	—	2	4	no	—
89	C₂×C₈×C₁₃₁	—	2	4	no	—
90	C₂×C₈×C₁₃₁	—	2	4	no	—
91	C₂×C₈×C₁₃₁	—	2	16	no	—
92	C₂×C₈×C₁₃₁	—	2	16	no	—
93	C₂×C₈×C₁₃₁	C₂²⋊C₄	1	16	yes	complemented
94	C₂×C₈×C₁₃₁	C₂²×C₄	1	8	yes	—
95	C₂×C₈×C₁₃₁	C₂²×C₄	1	4	yes	—
96	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
97	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
98	C₂×C₈×C₁₃₁	C₂×D₄	1	4	yes	—
99	C₂×C₈×C₁₃₁	C₂×D₄	1	4	yes	—
100	C₄⋊C₄×C₁₃₁	—	2	8	no	—
101	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
102	C₂²⋊C₄×C₁₃₁	—	2	16	no	—
103	C₄²×C₁₃₁	—	2	4	no	—
104	C₄²×C₁₃₁	—	2	4	no	—
105	C₂³×C₁₃₁	—	2	32	no	—
106	C₂³×C₁₃₁	—	2	4	no	—
107	C₂³×C₁₃₁	—	2	4	no	—
108	C₂³×C₁₃₁	—	2	4	no	—
109	C₂³×C₁₃₁	—	2	8	no	—
110	C₂³×C₁₃₁	—	2	16	no	—
111	C₂³×C₁₃₁	C₂×C₄²	1	2	yes	—
112	C₂³×C₁₃₁	C₂×C₄²	1	4	yes	—
113	C₂³×C₁₃₁	C₄×D₄	1	4	yes	—
114	C₂³×C₁₃₁	#131	1	8	yes	—
115	C₂³×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
116	C₂×C₄×C₁₃₁	—	2	4	no	—
117	C₂×C₄×C₁₃₁	—	2	8	no	—
118	C₂×C₄×C₁₃₁	—	2	4	no	—
119	C₂×C₄×C₁₃₁	—	2	4	no	—
120	C₂×C₄×C₁₃₁	—	2	8	no	—
121	C₂×C₄×C₁₃₁	—	2	16	no	—
122	C₂×C₄×C₁₃₁	—	2	8	no	—
123	C₂×C₄×C₁₃₁	—	2	16	no	—
124	C₂×C₄×C₁₃₁	C₂×C₄²	1	4	yes	—
125	C₂×C₄×C₁₃₁	C₂×C₄²	1	2	yes	—
126	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	4	yes	—
127	C₂×C₄×C₁₃₁	#117	1	4	yes	—
128	C₂×C₄×C₁₃₁	C₄×D₄	1	8	yes	—
129	C₂×C₄×C₁₃₁	C₄×D₄	1	4	yes	—
130	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
131	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
132	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
133	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
134	C₈×C₁₃₁	—	2	4	no	—
135	C₈×C₁₃₁	—	2	8	no	—
136	C₈×C₁₃₁	C₂×C₂²⋊C₄	1	4	yes	—
137	C₈×C₁₃₁	C₂×C₂²⋊C₄	1	4	yes	—
138	C₂²×C₁₃₁	—	2	32	no	—
139	C₂²×C₁₃₁	—	2	4	no	—
140	C₂²×C₁₃₁	—	2	4	no	—
141	C₂²×C₁₃₁	—	2	8	no	—
142	C₂²×C₁₃₁	—	2	16	no	—
143	C₂²×C₁₃₁	—	2	4	no	—
144	C₂²×C₁₃₁	C₄×C₂²⋊C₄	1	4	yes	—
145	C₂²×C₁₃₁	#405	1	8	yes	complemented
146	C₂²×C₁₃₁	C₂²×C₄²	1	1	yes	characteristic
147	C₂²×C₁₃₁	C₂×C₄×D₄	1	2	yes	—
148	C₂²×C₁₃₁	C₂×#131	1	4	yes	—
149	C₄×C₁₃₁	—	2	4	no	—
150	C₄×C₁₃₁	—	4	8	no	—
151	C₄×C₁₃₁	C₄×C₂²⋊C₄	1	4	yes	—
152	C₄×C₁₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
153	C₄×C₁₃₁	C₂×#117	1	1	yes	characteristic
154	C₄×C₁₃₁	C₂×C₄×D₄	1	2	yes	—
155	C₂×C₁₃₁	—	2	4	no	—
156	C₂×C₁₃₁	—	2	8	no	—
157	C₂×C₁₃₁	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₁₃₁	C₂×#405	1	2	yes	—
159	C₂×C₁₃₁	#2929	1	4	yes	—
160	#20385	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₁₃₁	#20385	1	1	yes	characteristic, direct product factor, Sylow
162	C₂⁴×C₈	C₂×C₁₃₁	1	1	yes	characteristic
163	C₂×#407	C₂×C₁₃₁	1	1	yes	characteristic
164	C₂×#405	C₂×C₁₃₁	1	2	yes	complemented
165	#2280	C₂×C₁₃₁	1	1	yes	characteristic
166	#1752	C₂×C₁₃₁	1	4	yes	complemented
167	C₈×C₂²⋊C₄	C₂×C₁₃₁	1	4	yes	complemented
168	#1729	C₂×C₁₃₁	1	2	yes	complemented
169	C₂⁴×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
170	C₂²×M₁₆	C₂²×C₁₃₁	1	2	yes	—
171	C₂³×C₈	—	2	8	no	—
172	C₂³×C₈	C₄×C₁₃₁	1	8	yes	complemented
173	C₂³×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
174	C₂³×C₈	C₂²×C₁₃₁	1	2	yes	—
175	C₂³×C₈	C₂²×C₁₃₁	1	2	yes	—
176	C₂³×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
177	C₂×#117	C₂²×C₁₃₁	1	2	yes	—
178	#407	C₄×C₁₃₁	1	8	yes	complemented
179	C₂×C₂²⋊C₈	C₂²×C₁₃₁	1	4	yes	—
180	#405	—	2	8	no	—
181	C₂×#97	C₂²×C₁₃₁	1	4	yes	complemented
182	C₂×C₄×C₈	C₂²×C₁₃₁	1	4	yes	complemented
183	#381	C₄×C₁₃₁	1	2	yes	—
184	#380	C₄×C₁₃₁	1	4	yes	—
185	#379	C₄×C₁₃₁	1	2	yes	—
186	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	—
187	#336	C₂²×C₁₃₁	1	8	yes	complemented
188	C₂⁵	C₂×C₄×C₁₃₁	1	1	yes	characteristic
189	C₂³×C₄	—	2	4	no	—
190	C₂³×C₄	—	2	4	no	—
191	C₂³×C₄	C₂×C₄×C₁₃₁	1	2	yes	—
192	C₂³×C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
193	C₂³×C₄	C₂×C₄×C₁₃₁	1	4	yes	—
194	C₂³×C₄	C₂×C₄×C₁₃₁	1	4	yes	—
195	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
196	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
197	C₂×M₁₆	—	2	4	no	—
198	C₂×M₁₆	—	2	4	no	—
199	C₂×M₁₆	C₂×C₄×C₁₃₁	1	8	yes	—
200	C₂²×C₈	—	2	4	no	—
201	C₂²×C₈	—	2	32	no	—
202	C₂²×C₈	—	2	8	no	—
203	C₂²×C₈	—	2	8	no	—
204	C₂²×C₈	C₂×C₄×C₁₃₁	1	4	yes	—
205	C₂²×C₈	C₂×C₄×C₁₃₁	1	8	yes	—
206	C₂²×C₈	C₂×C₄×C₁₃₁	1	8	yes	—
207	C₂²×C₈	C₂×C₄×C₁₃₁	1	4	yes	—
208	C₂²×C₈	D₄×C₁₃₁	1	8	yes	—
209	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
210	C₂²×C₈	C₂³×C₁₃₁	1	4	yes	—
211	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
212	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
213	#117	—	2	4	no	—
214	#117	—	2	4	no	—
215	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	4	yes	—
216	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	1	4	yes	—
217	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	1	8	yes	—
218	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
219	C₂²⋊C₈	C₂×C₄×C₁₃₁	1	16	yes	—
220	#97	—	2	8	no	—
221	C₄×C₈	—	2	8	no	—
222	#95	C₂×C₄×C₁₃₁	1	8	yes	—
223	C₂⁴	—	2	4	no	—
224	C₂⁴	—	2	8	no	—
225	C₂⁴	C₄²×C₁₃₁	1	4	yes	—
226	C₂⁴	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
227	C₂⁴	C₂²×C₄×C₁₃₁	1	2	yes	—
228	C₂²×C₄	—	2	4	no	—
229	C₂²×C₄	—	2	8	no	—
230	C₂²×C₄	—	2	8	no	—
231	C₂²×C₄	—	2	8	no	—
232	C₂²×C₄	—	2	16	no	—
233	C₂²×C₄	—	2	4	no	—
234	C₂²×C₄	—	2	4	no	—
235	C₂²×C₄	C₄²×C₁₃₁	1	4	yes	—
236	C₂²×C₄	C₄²×C₁₃₁	1	8	yes	—
237	C₂²×C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
238	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
239	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
240	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
241	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
242	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
243	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
244	C₂²×C₄	C₂×D₄×C₁₃₁	1	4	yes	—
245	C₂²×C₄	#41×C₁₃₁	1	4	yes	—
246	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
247	M₁₆	—	2	16	no	—
248	C₂×C₈	—	2	8	no	—
249	C₂×C₈	—	2	4	no	—
250	C₂×C₈	—	2	4	no	—
251	C₂×C₈	—	2	4	no	—
252	C₂×C₈	—	2	16	no	—
253	C₂×C₈	—	2	16	no	—
254	C₂×C₈	C₂²⋊C₄×C₁₃₁	1	16	yes	complemented
255	C₂×C₈	C₂²×C₄×C₁₃₁	1	8	yes	—
256	C₂×C₈	C₂²×C₄×C₁₃₁	1	4	yes	—
257	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
258	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
259	C₂×C₈	C₂×D₄×C₁₃₁	1	4	yes	—
260	C₂×C₈	C₂×D₄×C₁₃₁	1	4	yes	—
261	C₄⋊C₄	—	2	8	no	—
262	C₂²⋊C₄	—	2	8	no	—
263	C₂²⋊C₄	—	2	16	no	—
264	C₄²	—	2	4	no	—
265	C₄²	—	2	4	no	—
266	C₂³	—	2	32	no	—
267	C₂³	—	2	16	no	—
268	C₂³	—	2	4	no	—
269	C₂³	—	2	4	no	—
270	C₂³	—	2	4	no	—
271	C₂³	—	2	8	no	—
272	C₂³	C₂×C₄²×C₁₃₁	1	4	yes	—
273	C₂³	C₂×C₄²×C₁₃₁	1	2	yes	—
274	C₂³	C₄×D₄×C₁₃₁	1	4	yes	—
275	C₂³	#131×C₁₃₁	1	8	yes	—
276	C₂³	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
277	C₂×C₄	—	2	4	no	—
278	C₂×C₄	—	2	8	no	—
279	C₂×C₄	—	2	4	no	—
280	C₂×C₄	—	2	4	no	—
281	C₂×C₄	—	2	8	no	—
282	C₂×C₄	—	2	16	no	—
283	C₂×C₄	—	2	8	no	—
284	C₂×C₄	—	2	16	no	—
285	C₂×C₄	C₂×C₄²×C₁₃₁	1	4	yes	—
286	C₂×C₄	C₂×C₄²×C₁₃₁	1	2	yes	—
287	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	4	yes	—
288	C₂×C₄	#117×C₁₃₁	1	4	yes	—
289	C₂×C₄	C₄×D₄×C₁₃₁	1	8	yes	—
290	C₂×C₄	C₄×D₄×C₁₃₁	1	4	yes	—
291	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
292	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
293	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
294	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
295	C₈	—	2	4	no	—
296	C₈	—	2	8	no	—
297	C₈	C₂×C₂²⋊C₄×C₁₃₁	1	4	yes	—
298	C₈	C₂×C₂²⋊C₄×C₁₃₁	1	4	yes	—
299	C₂²	—	2	32	no	—
300	C₂²	—	2	4	no	—
301	C₂²	—	2	4	no	—
302	C₂²	—	2	4	no	—
303	C₂²	—	2	8	no	—
304	C₂²	—	2	16	no	—
305	C₂²	C₄×C₂²⋊C₄×C₁₃₁	1	4	yes	—
306	C₂²	#405×C₁₃₁	1	8	yes	complemented
307	C₂²	C₂²×C₄²×C₁₃₁	1	1	yes	characteristic
308	C₂²	C₂×C₄×D₄×C₁₃₁	1	2	yes	—
309	C₂²	C₂×#131×C₁₃₁	1	4	yes	—
310	C₄	—	2	4	no	—
311	C₄	—	4	8	no	—
312	C₄	C₄×C₂²⋊C₄×C₁₃₁	1	4	yes	—
313	C₄	C₂²×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
314	C₄	C₂×#117×C₁₃₁	1	1	yes	characteristic
315	C₄	C₂×C₄×D₄×C₁₃₁	1	2	yes	—
316	C₂	—	2	8	no	—
317	C₂	—	2	4	no	—
318	C₂	C₂×C₄×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
319	C₂	C₂×#405×C₁₃₁	1	2	yes	—
320	C₂	#2929×C₁₃₁	1	4	yes	—

	subgroup	G/H
center	C₂²×C₈×C₁₃₁	C₂³
commutator	C₂²	C₂²×C₄²×C₁₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
socle	C₂³×C₁₃₁	C₂³×C₄
prime radical	C₂⁵×C₁₃₁	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×#405×C₁₃₁	C₂	semidirect
5. #1752×C₁₃₁	C₂	semidirect
6. C₈×C₂²⋊C₄×C₁₃₁	C₂	semidirect
7. #1729×C₁₃₁	C₂	semidirect
11. C₂³×C₈×C₁₃₁	C₄	semidirect
17. #407×C₁₃₁	C₄	semidirect
20. C₂×#97×C₁₃₁	C₂²	semidirect
21. C₂×C₄×C₈×C₁₃₁	C₂²	semidirect
26. #336×C₁₃₁	C₂²	semidirect
93. C₂×C₈×C₁₃₁	C₂²⋊C₄	semidirect
145. C₂²×C₁₃₁	#405	semidirect
160. #20385	C₁₃₁	direct (N × H)
161. C₁₃₁	#20385	direct (N × H)
164. C₂×#405	C₂×C₁₃₁	semidirect
166. #1752	C₂×C₁₃₁	semidirect
167. C₈×C₂²⋊C₄	C₂×C₁₃₁	semidirect
168. #1729	C₂×C₁₃₁	semidirect
172. C₂³×C₈	C₄×C₁₃₁	semidirect
178. #407	C₄×C₁₃₁	semidirect
181. C₂×#97	C₂²×C₁₃₁	semidirect
182. C₂×C₄×C₈	C₂²×C₁₃₁	semidirect
187. #336	C₂²×C₁₃₁	semidirect
254. C₂×C₈	C₂²⋊C₄×C₁₃₁	semidirect
306. C₂²	#405×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂⁴×C₈×C₁₃₁	2
C₂×#407×C₁₃₁	2
C₂×#405×C₁₃₁	2
#2280×C₁₃₁	2
#1752×C₁₃₁	2
C₈×C₂²⋊C₄×C₁₃₁	2
#1729×C₁₃₁	2
#20385	131

Subgroups — C131×#20385 #45706269

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#20385 #45706269