Subgroups — C₁₃₁×#33719 #45719603

Order 33536.

834 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#510×C₁₃₁	C₂	1	2	yes	maximal, complemented
2	C₂×#509×C₁₃₁	C₂	1	2	yes	maximal, complemented
3	#3147×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#495×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#2251×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2250×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2249×C₁₃₁	C₂	1	4	yes	maximal, complemented
8	C₄×M₃₂×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#135×C₁₃₁	—	2	1	no	—
10	C₂×#135×C₁₃₁	C₂²	1	2	yes	—
11	C₂²×Q₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
12	C₂²×SD₁₆×C₁₃₁	—	2	1	no	—
13	C₂²×D₈×C₁₃₁	C₂²	1	1	yes	characteristic
14	#532×C₁₃₁	—	2	1	no	—
15	C₂×#124×C₁₃₁	—	2	1	no	—
16	#510×C₁₃₁	—	2	8	no	—
17	#509×C₁₃₁	—	2	8	no	—
18	C₂×Q₃₂×C₁₃₁	C₂²	1	4	yes	complemented
19	C₂×SD₃₂×C₁₃₁	C₂²	1	4	yes	—
20	C₂×SD₃₂×C₁₃₁	C₂²	1	4	yes	complemented
21	C₂×D₁₆×C₁₃₁	C₂²	1	4	yes	—
22	C₂×M₃₂×C₁₃₁	C₂²	1	2	yes	—
23	#495×C₁₃₁	—	2	1	no	—
24	#495×C₁₃₁	—	2	1	no	—
25	#495×C₁₃₁	—	2	1	no	—
26	#495×C₁₃₁	C₂²	1	2	yes	—
27	#495×C₁₃₁	C₂²	1	2	yes	—
28	#495×C₁₃₁	C₂²	1	2	yes	complemented
29	#494×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
30	#493×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
31	#492×C₁₃₁	—	2	1	no	—
32	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
33	#346×C₁₃₁	C₂²	1	2	yes	complemented
34	C₄×C₁₆×C₁₃₁	C₂²	1	2	yes	complemented
35	C₂×#41×C₁₃₁	—	2	2	no	—
36	C₂²×Q₈×C₁₃₁	—	2	1	no	—
37	C₂²×D₄×C₁₃₁	—	2	1	no	—
38	#135×C₁₃₁	—	2	4	no	—
39	#135×C₁₃₁	—	2	4	no	—
40	#135×C₁₃₁	—	4	4	no	—
41	C₂×Q₁₆×C₁₃₁	—	2	4	no	—
42	C₂×Q₁₆×C₁₃₁	—	2	1	no	—
43	C₂×Q₁₆×C₁₃₁	—	2	1	no	—
44	C₂×Q₁₆×C₁₃₁	C₂³	1	2	yes	—
45	C₂×Q₁₆×C₁₃₁	C₂³	1	2	yes	—
46	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
47	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
48	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
49	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
50	C₂×SD₁₆×C₁₃₁	—	4	4	no	—
51	C₂×D₈×C₁₃₁	—	2	4	no	—
52	C₂×D₈×C₁₃₁	—	2	1	no	—
53	C₂×D₈×C₁₃₁	—	2	1	no	—
54	C₂×D₈×C₁₃₁	C₂³	1	2	yes	—
55	C₂×D₈×C₁₃₁	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₃₁	D₄	1	1	yes	characteristic
57	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
58	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
59	#127×C₁₃₁	—	2	1	no	—
60	#124×C₁₃₁	—	2	2	no	—
61	#124×C₁₃₁	—	2	2	no	—
62	#124×C₁₃₁	—	2	2	no	—
63	#124×C₁₃₁	—	4	2	no	—
64	#121×C₁₃₁	—	4	2	no	—
65	C₄×D₄×C₁₃₁	—	4	2	no	—
66	C₂×C₂²⋊C₄×C₁₃₁	—	4	2	no	—
67	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
68	Q₃₂×C₁₃₁	—	2	8	no	—
69	SD₃₂×C₁₃₁	—	2	8	no	—
70	SD₃₂×C₁₃₁	—	2	8	no	—
71	D₁₆×C₁₃₁	—	2	8	no	—
72	M₃₂×C₁₃₁	D₄	1	8	yes	complemented
73	C₂×C₁₆×C₁₃₁	C₂³	1	4	yes	—
74	C₄×C₈×C₁₃₁	D₄	1	1	yes	characteristic
75	C₄×C₈×C₁₃₁	D₄	1	1	yes	characteristic
76	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
77	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
78	C₂⁴×C₁₃₁	—	4	1	no	—
79	#41×C₁₃₁	—	4	4	no	—
80	#41×C₁₃₁	—	4	4	no	—
81	C₂×Q₈×C₁₃₁	—	2	2	no	—
82	C₂×Q₈×C₁₃₁	—	2	2	no	—
83	C₂×Q₈×C₁₃₁	—	4	1	no	—
84	C₂×Q₈×C₁₃₁	—	4	2	no	—
85	C₂×Q₈×C₁₃₁	—	4	2	no	—
86	C₂×D₄×C₁₃₁	—	2	2	no	—
87	C₂×D₄×C₁₃₁	—	2	2	no	—
88	C₂×D₄×C₁₃₁	—	4	2	no	—
89	C₂×D₄×C₁₃₁	—	4	2	no	—
90	C₂×D₄×C₁₃₁	—	4	2	no	—
91	C₂×D₄×C₁₃₁	—	4	2	no	—
92	C₂×D₄×C₁₃₁	—	4	1	no	—
93	C₂²×C₄×C₁₃₁	—	4	1	no	—
94	C₂²×C₄×C₁₃₁	—	4	2	no	—
95	C₂²×C₄×C₁₃₁	D₈	1	2	yes	—
96	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
97	Q₁₆×C₁₃₁	—	2	2	no	—
98	Q₁₆×C₁₃₁	—	2	4	no	—
99	Q₁₆×C₁₃₁	—	2	2	no	—
100	Q₁₆×C₁₃₁	—	4	2	no	—
101	Q₁₆×C₁₃₁	—	4	2	no	—
102	SD₁₆×C₁₃₁	—	4	4	no	—
103	SD₁₆×C₁₃₁	—	4	4	no	—
104	SD₁₆×C₁₃₁	—	4	4	no	—
105	SD₁₆×C₁₃₁	—	4	4	no	—
106	D₈×C₁₃₁	—	2	2	no	—
107	D₈×C₁₃₁	—	2	4	no	—
108	D₈×C₁₃₁	—	2	2	no	—
109	D₈×C₁₃₁	—	4	2	no	—
110	D₈×C₁₃₁	—	4	2	no	—
111	C₂×C₈×C₁₃₁	D₈	1	4	yes	—
112	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃₁	C₂×D₄	1	4	yes	—
114	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₁₃₁	C₂⁴	1	1	yes	characteristic
117	C₄⋊C₄×C₁₃₁	—	4	2	no	—
118	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
119	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
120	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
121	C₄²×C₁₃₁	D₈	1	2	yes	—
122	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
124	C₁₆×C₁₃₁	C₂×D₄	1	8	yes	—
125	C₂³×C₁₃₁	—	4	2	no	—
126	C₂³×C₁₃₁	—	4	2	no	—
127	C₂³×C₁₃₁	—	8	4	no	—
128	C₂³×C₁₃₁	—	8	2	no	—
129	C₂³×C₁₃₁	C₂×D₈	1	1	yes	characteristic
130	Q₈×C₁₃₁	—	4	2	no	—
131	Q₈×C₁₃₁	—	4	2	no	—
132	Q₈×C₁₃₁	—	4	2	no	—
133	Q₈×C₁₃₁	—	4	2	no	—
134	Q₈×C₁₃₁	—	8	2	no	—
135	D₄×C₁₃₁	—	4	2	no	—
136	D₄×C₁₃₁	—	4	2	no	—
137	D₄×C₁₃₁	—	4	2	no	—
138	D₄×C₁₃₁	—	4	2	no	—
139	D₄×C₁₃₁	—	8	4	no	—
140	D₄×C₁₃₁	—	8	4	no	—
141	D₄×C₁₃₁	—	8	2	no	—
142	C₂×C₄×C₁₃₁	—	4	2	no	—
143	C₂×C₄×C₁₃₁	—	4	2	no	—
144	C₂×C₄×C₁₃₁	—	4	2	no	—
145	C₂×C₄×C₁₃₁	—	8	2	no	—
146	C₂×C₄×C₁₃₁	—	8	4	no	—
147	C₂×C₄×C₁₃₁	#127	1	2	yes	—
148	C₂×C₄×C₁₃₁	C₂×D₈	1	2	yes	—
149	C₂×C₄×C₁₃₁	C₂×D₈	1	2	yes	—
150	C₂×C₄×C₁₃₁	C₂×D₈	1	2	yes	—
151	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
152	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
153	C₈×C₁₃₁	#127	1	2	yes	—
154	C₈×C₁₃₁	C₂×D₈	1	2	yes	—
155	C₈×C₁₃₁	C₂×D₈	1	2	yes	—
156	C₈×C₁₃₁	C₂²×D₄	1	2	yes	—
157	C₂²×C₁₃₁	—	2	2	no	—
158	C₂²×C₁₃₁	—	8	2	no	—
159	C₂²×C₁₃₁	—	8	2	no	—
160	C₂²×C₁₃₁	—	8	4	no	—
161	C₂²×C₁₃₁	—	8	4	no	—
162	C₂²×C₁₃₁	—	16	4	no	—
163	C₂²×C₁₃₁	#493	1	2	yes	—
164	C₂²×C₁₃₁	C₂²×D₈	1	1	yes	characteristic
165	C₄×C₁₃₁	—	2	2	no	—
166	C₄×C₁₃₁	—	2	2	no	—
167	C₄×C₁₃₁	—	8	2	no	—
168	C₄×C₁₃₁	—	8	2	no	—
169	C₄×C₁₃₁	#493	1	2	yes	—
170	C₄×C₁₃₁	C₂×#127	1	1	yes	characteristic
171	C₄×C₁₃₁	C₂²×D₈	1	1	yes	characteristic
172	C₂×C₁₃₁	—	2	2	no	—
173	C₂×C₁₃₁	—	16	2	no	—
174	C₂×C₁₃₁	—	16	2	no	—
175	C₂×C₁₃₁	C₂×#493	1	1	yes	characteristic
176	C₂×C₁₃₁	#3414	1	2	yes	—
177	#33719	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₁₃₁	#33719	1	1	yes	characteristic, direct product factor, Sylow
179	C₂×#510	C₂×C₁₃₁	1	2	yes	complemented
180	C₂×#509	C₂×C₁₃₁	1	2	yes	complemented
181	#3147	C₂×C₁₃₁	1	1	yes	characteristic, complemented
182	C₂×#495	C₂×C₁₃₁	1	1	yes	characteristic, complemented
183	#2251	C₂×C₁₃₁	1	2	yes	complemented
184	#2250	C₂×C₁₃₁	1	2	yes	complemented
185	#2249	C₂×C₁₃₁	1	4	yes	complemented
186	C₄×M₃₂	C₂×C₁₃₁	1	1	yes	characteristic, complemented
187	C₂×#135	—	2	1	no	—
188	C₂×#135	C₂²×C₁₃₁	1	2	yes	—
189	C₂²×Q₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
190	C₂²×SD₁₆	—	2	1	no	—
191	C₂²×D₈	C₂²×C₁₃₁	1	1	yes	characteristic
192	#532	—	2	1	no	—
193	C₂×#124	—	2	1	no	—
194	#510	—	2	8	no	—
195	#509	—	2	8	no	—
196	C₂×Q₃₂	C₂²×C₁₃₁	1	4	yes	complemented
197	C₂×SD₃₂	C₂²×C₁₃₁	1	4	yes	—
198	C₂×SD₃₂	C₂²×C₁₃₁	1	4	yes	complemented
199	C₂×D₁₆	C₂²×C₁₃₁	1	4	yes	—
200	C₂×M₃₂	C₂²×C₁₃₁	1	2	yes	—
201	#495	—	2	1	no	—
202	#495	—	2	1	no	—
203	#495	—	2	1	no	—
204	#495	C₂²×C₁₃₁	1	2	yes	—
205	#495	C₂²×C₁₃₁	1	2	yes	—
206	#495	C₂²×C₁₃₁	1	2	yes	complemented
207	#494	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
208	#493	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
209	#492	—	2	1	no	—
210	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
211	#346	C₂²×C₁₃₁	1	2	yes	complemented
212	C₄×C₁₆	C₂²×C₁₃₁	1	2	yes	complemented
213	C₂×#41	—	2	2	no	—
214	C₂²×Q₈	—	2	1	no	—
215	C₂²×D₄	—	2	1	no	—
216	#135	—	2	4	no	—
217	#135	—	2	4	no	—
218	#135	—	4	4	no	—
219	C₂×Q₁₆	—	2	4	no	—
220	C₂×Q₁₆	—	2	1	no	—
221	C₂×Q₁₆	—	2	1	no	—
222	C₂×Q₁₆	C₂³×C₁₃₁	1	2	yes	—
223	C₂×Q₁₆	C₂³×C₁₃₁	1	2	yes	—
224	C₂×SD₁₆	—	2	2	no	—
225	C₂×SD₁₆	—	2	2	no	—
226	C₂×SD₁₆	—	2	2	no	—
227	C₂×SD₁₆	—	2	2	no	—
228	C₂×SD₁₆	—	4	4	no	—
229	C₂×D₈	—	2	4	no	—
230	C₂×D₈	—	2	1	no	—
231	C₂×D₈	—	2	1	no	—
232	C₂×D₈	C₂³×C₁₃₁	1	2	yes	—
233	C₂×D₈	C₂³×C₁₃₁	1	2	yes	—
234	C₂²×C₈	D₄×C₁₃₁	1	1	yes	characteristic
235	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
236	C₄⋊Q₈	—	2	1	no	—
237	#127	—	2	1	no	—
238	#124	—	2	2	no	—
239	#124	—	2	2	no	—
240	#124	—	2	2	no	—
241	#124	—	4	2	no	—
242	#121	—	4	2	no	—
243	C₄×D₄	—	4	2	no	—
244	C₂×C₂²⋊C₄	—	4	2	no	—
245	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
246	Q₃₂	—	2	8	no	—
247	SD₃₂	—	2	8	no	—
248	SD₃₂	—	2	8	no	—
249	D₁₆	—	2	8	no	—
250	M₃₂	D₄×C₁₃₁	1	8	yes	complemented
251	C₂×C₁₆	C₂³×C₁₃₁	1	4	yes	—
252	C₄×C₈	D₄×C₁₃₁	1	1	yes	characteristic
253	C₄×C₈	D₄×C₁₃₁	1	1	yes	characteristic
254	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
255	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
256	C₂⁴	—	4	1	no	—
257	#41	—	4	4	no	—
258	#41	—	4	4	no	—
259	C₂×Q₈	—	2	2	no	—
260	C₂×Q₈	—	2	2	no	—
261	C₂×Q₈	—	4	1	no	—
262	C₂×Q₈	—	4	2	no	—
263	C₂×Q₈	—	4	2	no	—
264	C₂×D₄	—	2	2	no	—
265	C₂×D₄	—	2	2	no	—
266	C₂×D₄	—	4	2	no	—
267	C₂×D₄	—	4	2	no	—
268	C₂×D₄	—	4	2	no	—
269	C₂×D₄	—	4	2	no	—
270	C₂×D₄	—	4	1	no	—
271	C₂²×C₄	—	4	1	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	D₈×C₁₃₁	1	2	yes	—
274	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
275	Q₁₆	—	2	2	no	—
276	Q₁₆	—	2	4	no	—
277	Q₁₆	—	2	2	no	—
278	Q₁₆	—	4	2	no	—
279	Q₁₆	—	4	2	no	—
280	SD₁₆	—	4	4	no	—
281	SD₁₆	—	4	4	no	—
282	SD₁₆	—	4	4	no	—
283	SD₁₆	—	4	4	no	—
284	D₈	—	2	2	no	—
285	D₈	—	2	4	no	—
286	D₈	—	2	2	no	—
287	D₈	—	4	2	no	—
288	D₈	—	4	2	no	—
289	C₂×C₈	D₈×C₁₃₁	1	4	yes	—
290	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
291	C₂×C₈	C₂×D₄×C₁₃₁	1	4	yes	—
292	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
293	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
294	C₂×C₈	C₂⁴×C₁₃₁	1	1	yes	characteristic
295	C₄⋊C₄	—	4	2	no	—
296	C₂²⋊C₄	—	4	4	no	—
297	C₂²⋊C₄	—	4	4	no	—
298	C₂²⋊C₄	—	4	4	no	—
299	C₄²	D₈×C₁₃₁	1	2	yes	—
300	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
301	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
302	C₁₆	C₂×D₄×C₁₃₁	1	8	yes	—
303	C₂³	—	4	2	no	—
304	C₂³	—	4	2	no	—
305	C₂³	—	8	4	no	—
306	C₂³	—	8	2	no	—
307	C₂³	C₂×D₈×C₁₃₁	1	1	yes	characteristic
308	Q₈	—	4	2	no	—
309	Q₈	—	4	2	no	—
310	Q₈	—	4	2	no	—
311	Q₈	—	4	2	no	—
312	Q₈	—	8	2	no	—
313	D₄	—	4	2	no	—
314	D₄	—	4	2	no	—
315	D₄	—	4	2	no	—
316	D₄	—	4	2	no	—
317	D₄	—	8	4	no	—
318	D₄	—	8	4	no	—
319	D₄	—	8	2	no	—
320	C₂×C₄	—	4	2	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	8	2	no	—
324	C₂×C₄	—	8	4	no	—
325	C₂×C₄	#127×C₁₃₁	1	2	yes	—
326	C₂×C₄	C₂×D₈×C₁₃₁	1	2	yes	—
327	C₂×C₄	C₂×D₈×C₁₃₁	1	2	yes	—
328	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
329	C₂×C₄	C₂×D₈×C₁₃₁	1	2	yes	—
330	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
331	C₈	#127×C₁₃₁	1	2	yes	—
332	C₈	C₂×D₈×C₁₃₁	1	2	yes	—
333	C₈	C₂×D₈×C₁₃₁	1	2	yes	—
334	C₈	C₂²×D₄×C₁₃₁	1	2	yes	—
335	C₂²	—	2	2	no	—
336	C₂²	—	8	2	no	—
337	C₂²	—	8	2	no	—
338	C₂²	—	8	4	no	—
339	C₂²	—	8	4	no	—
340	C₂²	—	16	4	no	—
341	C₂²	#493×C₁₃₁	1	2	yes	—
342	C₂²	C₂²×D₈×C₁₃₁	1	1	yes	characteristic
343	C₄	—	2	2	no	—
344	C₄	—	2	2	no	—
345	C₄	—	8	2	no	—
346	C₄	—	8	2	no	—
347	C₄	#493×C₁₃₁	1	2	yes	—
348	C₄	C₂×#127×C₁₃₁	1	1	yes	characteristic
349	C₄	C₂²×D₈×C₁₃₁	1	1	yes	characteristic
350	C₂	—	2	2	no	—
351	C₂	—	16	2	no	—
352	C₂	—	16	2	no	—
353	C₂	C₂×#493×C₁₃₁	1	1	yes	characteristic
354	C₂	#3414×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₁ ◁ C₂×C₄²×C₁₃₁ ◁ C₂×C₄×C₈×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#510×C₁₃₁	C₂	semidirect
2. C₂×#509×C₁₃₁	C₂	semidirect
3. #3147×C₁₃₁	C₂	semidirect
4. C₂×#495×C₁₃₁	C₂	semidirect
5. #2251×C₁₃₁	C₂	semidirect
6. #2250×C₁₃₁	C₂	semidirect
7. #2249×C₁₃₁	C₂	semidirect
8. C₄×M₃₂×C₁₃₁	C₂	semidirect
18. C₂×Q₃₂×C₁₃₁	C₂²	semidirect
20. C₂×SD₃₂×C₁₃₁	C₂²	semidirect
28. #495×C₁₃₁	C₂²	semidirect
29. #494×C₁₃₁	C₂²	semidirect
30. #493×C₁₃₁	C₂²	semidirect
33. #346×C₁₃₁	C₂²	semidirect
34. C₄×C₁₆×C₁₃₁	C₂²	semidirect
72. M₃₂×C₁₃₁	D₄	semidirect
177. #33719	C₁₃₁	direct (N × H)
178. C₁₃₁	#33719	direct (N × H)
179. C₂×#510	C₂×C₁₃₁	semidirect
180. C₂×#509	C₂×C₁₃₁	semidirect
181. #3147	C₂×C₁₃₁	semidirect
182. C₂×#495	C₂×C₁₃₁	semidirect
183. #2251	C₂×C₁₃₁	semidirect
184. #2250	C₂×C₁₃₁	semidirect
185. #2249	C₂×C₁₃₁	semidirect
186. C₄×M₃₂	C₂×C₁₃₁	semidirect
196. C₂×Q₃₂	C₂²×C₁₃₁	semidirect
198. C₂×SD₃₂	C₂²×C₁₃₁	semidirect
206. #495	C₂²×C₁₃₁	semidirect
207. #494	C₂²×C₁₃₁	semidirect
208. #493	C₂²×C₁₃₁	semidirect
211. #346	C₂²×C₁₃₁	semidirect
212. C₄×C₁₆	C₂²×C₁₃₁	semidirect
250. M₃₂	D₄×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#510×C₁₃₁	2
C₂×#509×C₁₃₁	2
#3147×C₁₃₁	2
C₂×#495×C₁₃₁	2
#2251×C₁₃₁	2
#2250×C₁₃₁	2
#2249×C₁₃₁	2
C₄×M₃₂×C₁₃₁	2
#33719	131

Subgroups — C131×#33719 #45719603

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#33719 #45719603