Subgroups — C₁₃₁×#36614 #45722498

Order 33536.

7538 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#525×C₁₃₁	C₂	1	3	yes	maximal, complemented
3	#2849×C₁₃₁	C₂	1	6	yes	maximal, complemented
4	#2848×C₁₃₁	C₂	1	4	yes	maximal, complemented
5	#2847×C₁₃₁	C₂	1	4	yes	maximal, complemented
6	#2846×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	C₄×#120×C₁₃₁	C₂	1	8	yes	maximal, complemented
8	#2280×C₁₃₁	C₂	1	3	yes	maximal, complemented
9	C₂⁶×C₁₃₁	C₂²	1	1	yes	characteristic
10	C₂²×#41×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
11	C₂⁴×C₄×C₁₃₁	—	2	24	no	—
12	C₂⁴×C₄×C₁₃₁	C₂²	1	4	yes	—
13	C₂⁴×C₄×C₁₃₁	C₂²	1	4	yes	—
14	C₂⁴×C₄×C₁₃₁	C₂²	1	3	yes	—
15	C₂⁴×C₄×C₁₃₁	C₂²	1	3	yes	—
16	#525×C₁₃₁	—	2	24	no	—
17	C₂×#123×C₁₃₁	C₂²	1	6	yes	complemented
18	C₂×C₂²⋊Q₈×C₁₃₁	C₂²	1	6	yes	complemented
19	C₂×#121×C₁₃₁	C₂²	1	6	yes	complemented
20	C₂×#120×C₁₃₁	C₂²	1	8	yes	—
21	C₂×#120×C₁₃₁	C₂²	1	6	yes	—
22	C₂×C₄×D₄×C₁₃₁	C₂²	1	12	yes	complemented
23	C₂×#117×C₁₃₁	C₂²	1	3	yes	complemented
24	#386×C₁₃₁	C₂²	1	24	yes	complemented
25	#385×C₁₃₁	C₂²	1	24	yes	complemented
26	#381×C₁₃₁	C₂²	1	6	yes	complemented
27	#380×C₁₃₁	C₂²	1	12	yes	complemented
28	#379×C₁₃₁	C₂²	1	6	yes	—
29	#379×C₁₃₁	C₂²	1	8	yes	—
30	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	12	yes	complemented
31	C₂⁵×C₁₃₁	—	2	12	no	—
32	C₂⁵×C₁₃₁	—	2	16	no	—
33	C₂⁵×C₁₃₁	C₂³	1	3	yes	—
34	C₂⁵×C₁₃₁	C₂³	1	4	yes	—
35	C₂×#41×C₁₃₁	—	2	12	no	—
36	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic, complemented
37	C₂²×D₄×C₁₃₁	C₂³	1	12	yes	—
38	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
39	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic, complemented
40	C₂³×C₄×C₁₃₁	—	2	128	no	—
41	C₂³×C₄×C₁₃₁	—	2	12	no	—
42	C₂³×C₄×C₁₃₁	—	2	48	no	—
43	C₂³×C₄×C₁₃₁	—	2	48	no	—
44	C₂³×C₄×C₁₃₁	—	2	24	no	—
45	C₂³×C₄×C₁₃₁	—	2	24	no	—
46	C₂³×C₄×C₁₃₁	D₄	1	24	yes	complemented
47	C₂³×C₄×C₁₃₁	C₂³	1	12	yes	—
48	C₂³×C₄×C₁₃₁	C₂³	1	6	yes	—
49	C₂³×C₄×C₁₃₁	C₂³	1	3	yes	—
50	C₂³×C₄×C₁₃₁	C₂³	1	6	yes	—
51	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	complemented
53	#123×C₁₃₁	—	2	24	no	—
54	C₂²⋊Q₈×C₁₃₁	—	2	24	no	—
55	#121×C₁₃₁	—	2	24	no	—
56	#120×C₁₃₁	—	2	24	no	—
57	#120×C₁₃₁	—	2	32	no	—
58	C₄×D₄×C₁₃₁	—	2	48	no	—
59	#117×C₁₃₁	—	2	12	no	—
60	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	6	yes	complemented
61	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	12	yes	complemented
62	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	6	yes	—
63	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	12	yes	—
64	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	24	yes	—
65	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	12	yes	complemented
66	C₂×C₄²×C₁₃₁	C₂³	1	6	yes	complemented
67	#95×C₁₃₁	C₂³	1	24	yes	complemented
68	C₂⁴×C₁₃₁	—	2	32	no	—
69	C₂⁴×C₁₃₁	—	2	192	no	—
70	C₂⁴×C₁₃₁	—	2	24	no	—
71	C₂⁴×C₁₃₁	—	2	12	no	—
72	C₂⁴×C₁₃₁	—	2	24	no	—
73	C₂⁴×C₁₃₁	—	2	24	no	—
74	C₂⁴×C₁₃₁	C₂×D₄	1	12	yes	—
75	C₂⁴×C₁₃₁	#41	1	16	yes	complemented
76	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
77	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
78	C₂⁴×C₁₃₁	C₂⁴	1	6	yes	—
79	#41×C₁₃₁	—	4	16	no	—
80	C₂×Q₈×C₁₃₁	—	2	6	no	—
81	C₂×D₄×C₁₃₁	—	2	24	no	—
82	C₂×D₄×C₁₃₁	—	2	12	no	—
83	C₂×D₄×C₁₃₁	—	2	48	no	—
84	C₂×D₄×C₁₃₁	—	2	6	no	—
85	C₂²×C₄×C₁₃₁	—	2	96	no	—
86	C₂²×C₄×C₁₃₁	—	2	128	no	—
87	C₂²×C₄×C₁₃₁	—	2	128	no	—
88	C₂²×C₄×C₁₃₁	—	2	24	no	—
89	C₂²×C₄×C₁₃₁	—	2	12	no	—
90	C₂²×C₄×C₁₃₁	—	2	96	no	—
91	C₂²×C₄×C₁₃₁	—	2	48	no	—
92	C₂²×C₄×C₁₃₁	—	2	24	no	—
93	C₂²×C₄×C₁₃₁	—	2	24	no	—
94	C₂²×C₄×C₁₃₁	—	2	12	no	—
95	C₂²×C₄×C₁₃₁	C₂×D₄	1	24	yes	—
96	C₂²×C₄×C₁₃₁	C₂×D₄	1	24	yes	—
97	C₂²×C₄×C₁₃₁	C₂×D₄	1	12	yes	—
98	C₂²×C₄×C₁₃₁	C₂×D₄	1	12	yes	—
99	C₂²×C₄×C₁₃₁	C₂⁴	1	12	yes	—
100	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
101	C₂²×C₄×C₁₃₁	C₂⁴	1	6	yes	—
102	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
103	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
104	C₄⋊C₄×C₁₃₁	—	2	12	no	—
105	C₄⋊C₄×C₁₃₁	—	2	24	no	—
106	C₂²⋊C₄×C₁₃₁	—	2	12	no	—
107	C₂²⋊C₄×C₁₃₁	—	2	24	no	—
108	C₂²⋊C₄×C₁₃₁	—	2	48	no	—
109	C₂²⋊C₄×C₁₃₁	—	2	24	no	—
110	C₄²×C₁₃₁	—	2	12	no	—
111	C₂³×C₁₃₁	—	2	32	no	—
112	C₂³×C₁₃₁	—	2	256	no	—
113	C₂³×C₁₃₁	—	2	96	no	—
114	C₂³×C₁₃₁	—	2	96	no	—
115	C₂³×C₁₃₁	—	2	24	no	—
116	C₂³×C₁₃₁	—	2	48	no	—
117	C₂³×C₁₃₁	—	2	96	no	—
118	C₂³×C₁₃₁	—	2	12	no	—
119	C₂³×C₁₃₁	—	2	4	no	—
120	C₂³×C₁₃₁	—	2	12	no	—
121	C₂³×C₁₃₁	—	2	6	no	—
122	C₂³×C₁₃₁	—	2	8	no	—
123	C₂³×C₁₃₁	C₂²×D₄	1	6	yes	—
124	C₂³×C₁₃₁	C₂²×D₄	1	12	yes	—
125	C₂³×C₁₃₁	C₂×#41	1	24	yes	—
126	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
127	Q₈×C₁₃₁	—	4	4	no	—
128	D₄×C₁₃₁	—	4	8	no	—
129	D₄×C₁₃₁	—	4	48	no	—
130	D₄×C₁₃₁	—	4	4	no	—
131	C₂×C₄×C₁₃₁	—	2	96	no	—
132	C₂×C₄×C₁₃₁	—	2	24	no	—
133	C₂×C₄×C₁₃₁	—	2	12	no	—
134	C₂×C₄×C₁₃₁	—	2	48	no	—
135	C₂×C₄×C₁₃₁	—	2	48	no	—
136	C₂×C₄×C₁₃₁	—	2	12	no	—
137	C₂×C₄×C₁₃₁	—	2	6	no	—
138	C₂×C₄×C₁₃₁	—	2	24	no	—
139	C₂×C₄×C₁₃₁	—	4	8	no	—
140	C₂×C₄×C₁₃₁	#120	1	16	yes	complemented
141	C₂×C₄×C₁₃₁	C₂²×D₄	1	12	yes	—
142	C₂×C₄×C₁₃₁	C₂²×D₄	1	6	yes	—
143	C₂×C₄×C₁₃₁	C₂²×D₄	1	6	yes	—
144	C₂²×C₁₃₁	—	2	96	no	—
145	C₂²×C₁₃₁	—	2	128	no	—
146	C₂²×C₁₃₁	—	2	12	no	—
147	C₂²×C₁₃₁	—	2	12	no	—
148	C₂²×C₁₃₁	—	2	12	no	—
149	C₂²×C₁₃₁	—	2	48	no	—
150	C₂²×C₁₃₁	—	4	2	no	—
151	C₂²×C₁₃₁	—	4	12	no	—
152	C₂²×C₁₃₁	C₂×#120	1	4	yes	—
153	C₂²×C₁₃₁	#525	1	24	yes	complemented
154	C₂²×C₁₃₁	C₂³×D₄	1	3	yes	—
155	C₂²×C₁₃₁	C₂²×#41	1	4	yes	—
156	C₄×C₁₃₁	—	2	12	no	—
157	C₄×C₁₃₁	—	4	2	no	—
158	C₄×C₁₃₁	—	4	12	no	—
159	C₄×C₁₃₁	C₂×#120	1	4	yes	—
160	C₄×C₁₃₁	C₂×#120	1	4	yes	—
161	C₂×C₁₃₁	—	2	4	no	—
162	C₂×C₁₃₁	—	2	24	no	—
163	C₂×C₁₃₁	—	8	2	no	—
164	C₂×C₁₃₁	C₂²×#120	1	1	yes	characteristic
165	C₂×C₁₃₁	C₂×#525	1	6	yes	—
166	#36614	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₁₃₁	#36614	1	1	yes	characteristic, direct product factor, Sylow
168	C₂⁵×C₄	C₂×C₁₃₁	1	1	yes	characteristic, complemented
169	C₂×#525	C₂×C₁₃₁	1	3	yes	complemented
170	#2849	C₂×C₁₃₁	1	6	yes	complemented
171	#2848	C₂×C₁₃₁	1	4	yes	complemented
172	#2847	C₂×C₁₃₁	1	4	yes	complemented
173	#2846	C₂×C₁₃₁	1	2	yes	complemented
174	C₄×#120	C₂×C₁₃₁	1	8	yes	complemented
175	#2280	C₂×C₁₃₁	1	3	yes	complemented
176	C₂⁶	C₂²×C₁₃₁	1	1	yes	characteristic
177	C₂²×#41	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
178	C₂⁴×C₄	—	2	24	no	—
179	C₂⁴×C₄	C₂²×C₁₃₁	1	4	yes	—
180	C₂⁴×C₄	C₂²×C₁₃₁	1	3	yes	—
181	C₂⁴×C₄	C₂²×C₁₃₁	1	4	yes	—
182	C₂⁴×C₄	C₂²×C₁₃₁	1	3	yes	—
183	#525	—	2	24	no	—
184	C₂×#123	C₂²×C₁₃₁	1	6	yes	complemented
185	C₂×C₂²⋊Q₈	C₂²×C₁₃₁	1	6	yes	complemented
186	C₂×#121	C₂²×C₁₃₁	1	6	yes	complemented
187	C₂×#120	C₂²×C₁₃₁	1	8	yes	—
188	C₂×#120	C₂²×C₁₃₁	1	6	yes	—
189	C₂×C₄×D₄	C₂²×C₁₃₁	1	12	yes	complemented
190	C₂×#117	C₂²×C₁₃₁	1	3	yes	complemented
191	#386	C₂²×C₁₃₁	1	24	yes	complemented
192	#385	C₂²×C₁₃₁	1	24	yes	complemented
193	#381	C₂²×C₁₃₁	1	6	yes	complemented
194	#380	C₂²×C₁₃₁	1	12	yes	complemented
195	#379	C₂²×C₁₃₁	1	8	yes	—
196	#379	C₂²×C₁₃₁	1	6	yes	—
197	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	12	yes	complemented
198	C₂⁵	—	2	12	no	—
199	C₂⁵	—	2	16	no	—
200	C₂⁵	C₂³×C₁₃₁	1	3	yes	—
201	C₂⁵	C₂³×C₁₃₁	1	4	yes	—
202	C₂×#41	—	2	12	no	—
203	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic, complemented
204	C₂²×D₄	C₂³×C₁₃₁	1	12	yes	—
205	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
206	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic, complemented
207	C₂³×C₄	—	2	128	no	—
208	C₂³×C₄	—	2	12	no	—
209	C₂³×C₄	—	2	48	no	—
210	C₂³×C₄	—	2	48	no	—
211	C₂³×C₄	—	2	24	no	—
212	C₂³×C₄	—	2	24	no	—
213	C₂³×C₄	D₄×C₁₃₁	1	24	yes	complemented
214	C₂³×C₄	C₂³×C₁₃₁	1	12	yes	—
215	C₂³×C₄	C₂³×C₁₃₁	1	6	yes	—
216	C₂³×C₄	C₂³×C₁₃₁	1	6	yes	—
217	C₂³×C₄	C₂³×C₁₃₁	1	3	yes	—
218	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
219	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	complemented
220	#123	—	2	24	no	—
221	C₂²⋊Q₈	—	2	24	no	—
222	#121	—	2	24	no	—
223	#120	—	2	24	no	—
224	#120	—	2	32	no	—
225	C₄×D₄	—	2	48	no	—
226	#117	—	2	12	no	—
227	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	6	yes	complemented
228	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	12	yes	complemented
229	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	6	yes	—
230	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	12	yes	—
231	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	24	yes	—
232	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	12	yes	complemented
233	C₂×C₄²	C₂³×C₁₃₁	1	6	yes	complemented
234	#95	C₂³×C₁₃₁	1	24	yes	complemented
235	C₂⁴	—	2	32	no	—
236	C₂⁴	—	2	192	no	—
237	C₂⁴	—	2	24	no	—
238	C₂⁴	—	2	12	no	—
239	C₂⁴	—	2	24	no	—
240	C₂⁴	—	2	24	no	—
241	C₂⁴	C₂×D₄×C₁₃₁	1	12	yes	—
242	C₂⁴	#41×C₁₃₁	1	16	yes	complemented
243	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
244	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
245	C₂⁴	C₂⁴×C₁₃₁	1	6	yes	—
246	#41	—	4	16	no	—
247	C₂×Q₈	—	2	6	no	—
248	C₂×D₄	—	2	24	no	—
249	C₂×D₄	—	2	12	no	—
250	C₂×D₄	—	2	48	no	—
251	C₂×D₄	—	2	6	no	—
252	C₂²×C₄	—	2	96	no	—
253	C₂²×C₄	—	2	128	no	—
254	C₂²×C₄	—	2	128	no	—
255	C₂²×C₄	—	2	24	no	—
256	C₂²×C₄	—	2	12	no	—
257	C₂²×C₄	—	2	96	no	—
258	C₂²×C₄	—	2	48	no	—
259	C₂²×C₄	—	2	24	no	—
260	C₂²×C₄	—	2	24	no	—
261	C₂²×C₄	—	2	12	no	—
262	C₂²×C₄	C₂×D₄×C₁₃₁	1	24	yes	—
263	C₂²×C₄	C₂×D₄×C₁₃₁	1	24	yes	—
264	C₂²×C₄	C₂×D₄×C₁₃₁	1	12	yes	—
265	C₂²×C₄	C₂×D₄×C₁₃₁	1	12	yes	—
266	C₂²×C₄	C₂⁴×C₁₃₁	1	12	yes	—
267	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
268	C₂²×C₄	C₂⁴×C₁₃₁	1	6	yes	—
269	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
270	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
271	C₄⋊C₄	—	2	12	no	—
272	C₄⋊C₄	—	2	24	no	—
273	C₂²⋊C₄	—	2	12	no	—
274	C₂²⋊C₄	—	2	24	no	—
275	C₂²⋊C₄	—	2	48	no	—
276	C₂²⋊C₄	—	2	24	no	—
277	C₄²	—	2	12	no	—
278	C₂³	—	2	32	no	—
279	C₂³	—	2	256	no	—
280	C₂³	—	2	96	no	—
281	C₂³	—	2	96	no	—
282	C₂³	—	2	24	no	—
283	C₂³	—	2	48	no	—
284	C₂³	—	2	96	no	—
285	C₂³	—	2	12	no	—
286	C₂³	—	2	4	no	—
287	C₂³	—	2	12	no	—
288	C₂³	—	2	6	no	—
289	C₂³	—	2	8	no	—
290	C₂³	C₂²×D₄×C₁₃₁	1	6	yes	—
291	C₂³	C₂²×D₄×C₁₃₁	1	12	yes	—
292	C₂³	C₂×#41×C₁₃₁	1	24	yes	—
293	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
294	Q₈	—	4	4	no	—
295	D₄	—	4	8	no	—
296	D₄	—	4	48	no	—
297	D₄	—	4	4	no	—
298	C₂×C₄	—	2	96	no	—
299	C₂×C₄	—	2	24	no	—
300	C₂×C₄	—	2	12	no	—
301	C₂×C₄	—	2	48	no	—
302	C₂×C₄	—	2	48	no	—
303	C₂×C₄	—	2	12	no	—
304	C₂×C₄	—	2	6	no	—
305	C₂×C₄	—	2	24	no	—
306	C₂×C₄	—	4	8	no	—
307	C₂×C₄	#120×C₁₃₁	1	16	yes	complemented
308	C₂×C₄	C₂²×D₄×C₁₃₁	1	12	yes	—
309	C₂×C₄	C₂²×D₄×C₁₃₁	1	6	yes	—
310	C₂×C₄	C₂²×D₄×C₁₃₁	1	6	yes	—
311	C₂²	—	2	96	no	—
312	C₂²	—	2	128	no	—
313	C₂²	—	2	12	no	—
314	C₂²	—	2	12	no	—
315	C₂²	—	2	12	no	—
316	C₂²	—	2	48	no	—
317	C₂²	—	4	2	no	—
318	C₂²	—	4	12	no	—
319	C₂²	C₂×#120×C₁₃₁	1	4	yes	—
320	C₂²	#525×C₁₃₁	1	24	yes	complemented
321	C₂²	C₂³×D₄×C₁₃₁	1	3	yes	—
322	C₂²	C₂²×#41×C₁₃₁	1	4	yes	—
323	C₄	—	2	12	no	—
324	C₄	—	4	2	no	—
325	C₄	—	4	12	no	—
326	C₄	C₂×#120×C₁₃₁	1	4	yes	—
327	C₄	C₂×#120×C₁₃₁	1	4	yes	—
328	C₂	—	2	4	no	—
329	C₂	—	2	24	no	—
330	C₂	—	8	2	no	—
331	C₂	C₂²×#120×C₁₃₁	1	1	yes	characteristic
332	C₂	C₂×#525×C₁₃₁	1	6	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₁
socle	C₂³×C₁₃₁	C₂⁵
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
1. C₂⁵×C₄×C₁₃₁	C₂	semidirect
2. C₂×#525×C₁₃₁	C₂	semidirect
3. #2849×C₁₃₁	C₂	semidirect
4. #2848×C₁₃₁	C₂	semidirect
5. #2847×C₁₃₁	C₂	semidirect
6. #2846×C₁₃₁	C₂	semidirect
7. C₄×#120×C₁₃₁	C₂	semidirect
8. #2280×C₁₃₁	C₂	semidirect
10. C₂²×#41×C₁₃₁	C₂²	semidirect
17. C₂×#123×C₁₃₁	C₂²	semidirect
18. C₂×C₂²⋊Q₈×C₁₃₁	C₂²	semidirect
19. C₂×#121×C₁₃₁	C₂²	semidirect
22. C₂×C₄×D₄×C₁₃₁	C₂²	semidirect
23. C₂×#117×C₁₃₁	C₂²	semidirect
24. #386×C₁₃₁	C₂²	semidirect
25. #385×C₁₃₁	C₂²	semidirect
26. #381×C₁₃₁	C₂²	semidirect
27. #380×C₁₃₁	C₂²	semidirect
30. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
36. C₂²×Q₈×C₁₃₁	C₂³	semidirect
39. C₂²×D₄×C₁₃₁	C₂³	semidirect
46. C₂³×C₄×C₁₃₁	D₄	semidirect
52. C₂³×C₄×C₁₃₁	C₂³	semidirect
60. C₂×C₄⋊C₄×C₁₃₁	C₂³	semidirect
61. C₂×C₄⋊C₄×C₁₃₁	C₂³	semidirect
65. C₂×C₂²⋊C₄×C₁₃₁	C₂³	semidirect
66. C₂×C₄²×C₁₃₁	C₂³	semidirect
67. #95×C₁₃₁	C₂³	semidirect
75. C₂⁴×C₁₃₁	#41	semidirect
140. C₂×C₄×C₁₃₁	#120	semidirect
153. C₂²×C₁₃₁	#525	semidirect
166. #36614	C₁₃₁	direct (N × H)
167. C₁₃₁	#36614	direct (N × H)
168. C₂⁵×C₄	C₂×C₁₃₁	semidirect
169. C₂×#525	C₂×C₁₃₁	semidirect
170. #2849	C₂×C₁₃₁	semidirect
171. #2848	C₂×C₁₃₁	semidirect
172. #2847	C₂×C₁₃₁	semidirect
173. #2846	C₂×C₁₃₁	semidirect
174. C₄×#120	C₂×C₁₃₁	semidirect
175. #2280	C₂×C₁₃₁	semidirect
177. C₂²×#41	C₂²×C₁₃₁	semidirect
184. C₂×#123	C₂²×C₁₃₁	semidirect
185. C₂×C₂²⋊Q₈	C₂²×C₁₃₁	semidirect
186. C₂×#121	C₂²×C₁₃₁	semidirect
189. C₂×C₄×D₄	C₂²×C₁₃₁	semidirect
190. C₂×#117	C₂²×C₁₃₁	semidirect
191. #386	C₂²×C₁₃₁	semidirect
192. #385	C₂²×C₁₃₁	semidirect
193. #381	C₂²×C₁₃₁	semidirect
194. #380	C₂²×C₁₃₁	semidirect
197. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
203. C₂²×Q₈	C₂³×C₁₃₁	semidirect
206. C₂²×D₄	C₂³×C₁₃₁	semidirect
213. C₂³×C₄	D₄×C₁₃₁	semidirect
219. C₂³×C₄	C₂³×C₁₃₁	semidirect
227. C₂×C₄⋊C₄	C₂³×C₁₃₁	semidirect
228. C₂×C₄⋊C₄	C₂³×C₁₃₁	semidirect
232. C₂×C₂²⋊C₄	C₂³×C₁₃₁	semidirect
233. C₂×C₄²	C₂³×C₁₃₁	semidirect
234. #95	C₂³×C₁₃₁	semidirect
242. C₂⁴	#41×C₁₃₁	semidirect
307. C₂×C₄	#120×C₁₃₁	semidirect
320. C₂²	#525×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂⁵×C₄×C₁₃₁	2
C₂×#525×C₁₃₁	2
#2849×C₁₃₁	2
#2848×C₁₃₁	2
#2847×C₁₃₁	2
#2846×C₁₃₁	2
C₄×#120×C₁₃₁	2
#2280×C₁₃₁	2
#36614	131

Subgroups — C131×#36614 #45722498

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#36614 #45722498