Subgroups — C₁₃₁×#19284 #45705168

Order 33536.

662 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3170×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#3110×C₁₃₁	C₂	1	2	yes	maximal
3	C₂×#436×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	#1699×C₁₃₁	C₂	1	4	yes	maximal, complemented
5	#1693×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#1689×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#1568×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1552×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	C₂²×M₁₆×C₁₃₁	—	2	1	no	—
10	#533×C₁₃₁	C₂²	1	2	yes	—
11	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
12	#500×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
13	#494×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
14	#487×C₁₃₁	C₂²	1	2	yes	complemented
15	#484×C₁₃₁	—	2	2	no	—
16	#474×C₁₃₁	C₂²	1	4	yes	—
17	#467×C₁₃₁	—	2	1	no	—
18	#467×C₁₃₁	—	2	1	no	—
19	#461×C₁₃₁	C₂²	1	4	yes	—
20	#450×C₁₃₁	—	2	2	no	—
21	#440×C₁₃₁	—	2	4	no	—
22	C₄×Q₁₆×C₁₃₁	—	2	1	no	—
23	C₄×Q₁₆×C₁₃₁	—	2	1	no	—
24	#436×C₁₃₁	—	2	1	no	—
25	#436×C₁₃₁	—	2	1	no	—
26	#436×C₁₃₁	C₂²	1	2	yes	—
27	#436×C₁₃₁	C₂²	1	2	yes	—
28	#432×C₁₃₁	C₂²	1	2	yes	—
29	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₈×C₁₃₁	—	2	1	no	—
31	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
32	#335×C₁₃₁	C₂²	1	2	yes	complemented
33	#334×C₁₃₁	C₂²	1	2	yes	complemented
34	#332×C₁₃₁	C₂²	1	4	yes	complemented
35	#332×C₁₃₁	C₂²	1	4	yes	complemented
36	C₂²×D₄×C₁₃₁	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₃₁	—	2	1	no	—
38	C₂×Q₁₆×C₁₃₁	—	2	1	no	—
39	C₂×Q₁₆×C₁₃₁	—	2	1	no	—
40	C₂×SD₁₆×C₁₃₁	—	2	4	no	—
41	C₂×M₁₆×C₁₃₁	—	2	2	no	—
42	C₂×M₁₆×C₁₃₁	—	2	2	no	—
43	C₂×M₁₆×C₁₃₁	—	4	4	no	—
44	C₂²×C₈×C₁₃₁	—	2	1	no	—
45	C₂²×C₈×C₁₃₁	D₄	1	1	yes	characteristic
46	C₂²×C₈×C₁₃₁	D₄	1	1	yes	characteristic
47	C₄⋊Q₈×C₁₃₁	C₂³	1	2	yes	—
48	C₄⋊Q₈×C₁₃₁	C₂³	1	2	yes	—
49	#125×C₁₃₁	—	2	2	no	—
50	C₂²⋊Q₈×C₁₃₁	—	2	2	no	—
51	C₂²⋊Q₈×C₁₃₁	—	2	2	no	—
52	C₄×Q₈×C₁₃₁	—	2	2	no	—
53	C₄×Q₈×C₁₃₁	—	2	2	no	—
54	C₄×D₄×C₁₃₁	—	2	1	no	—
55	C₄×D₄×C₁₃₁	—	2	1	no	—
56	C₄×D₄×C₁₃₁	D₄	1	2	yes	—
57	C₄×D₄×C₁₃₁	C₂³	1	2	yes	—
58	#117×C₁₃₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
60	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
61	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
62	#107×C₁₃₁	—	2	1	no	—
63	#107×C₁₃₁	—	2	1	no	—
64	#107×C₁₃₁	—	2	4	no	—
65	C₄⋊C₈×C₁₃₁	—	2	1	no	—
66	C₄⋊C₈×C₁₃₁	C₂³	1	2	yes	—
67	C₄⋊C₈×C₁₃₁	C₂³	1	4	yes	—
68	#103×C₁₃₁	—	2	2	no	—
69	#103×C₁₃₁	—	2	2	no	—
70	#103×C₁₃₁	—	2	4	no	—
71	#102×C₁₃₁	—	2	4	no	—
72	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
73	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
74	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
75	#97×C₁₃₁	—	2	2	no	—
76	C₄×C₈×C₁₃₁	D₄	1	1	yes	characteristic
77	C₄×C₈×C₁₃₁	D₄	1	1	yes	characteristic
78	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
79	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
80	C₂⁴×C₁₃₁	—	2	1	no	—
81	C₂×Q₈×C₁₃₁	—	2	2	no	—
82	C₂×Q₈×C₁₃₁	—	2	2	no	—
83	C₂×D₄×C₁₃₁	—	2	1	no	—
84	C₂×D₄×C₁₃₁	—	4	2	no	—
85	C₂×D₄×C₁₃₁	C₂×D₄	1	2	yes	—
86	C₂²×C₄×C₁₃₁	—	2	1	no	—
87	C₂²×C₄×C₁₃₁	—	2	2	no	—
88	C₂²×C₄×C₁₃₁	—	2	2	no	—
89	C₂²×C₄×C₁₃₁	—	4	2	no	—
90	C₂²×C₄×C₁₃₁	—	4	2	no	—
91	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃₁	#41	1	1	yes	characteristic
94	Q₁₆×C₁₃₁	—	4	2	no	—
95	Q₁₆×C₁₃₁	—	4	2	no	—
96	SD₁₆×C₁₃₁	—	4	8	no	—
97	M₁₆×C₁₃₁	—	4	4	no	—
98	M₁₆×C₁₃₁	—	4	4	no	—
99	C₂×C₈×C₁₃₁	—	2	2	no	—
100	C₂×C₈×C₁₃₁	—	2	4	no	—
101	C₂×C₈×C₁₃₁	—	2	2	no	—
102	C₂×C₈×C₁₃₁	—	4	1	no	—
103	C₂×C₈×C₁₃₁	—	4	2	no	—
104	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
105	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
106	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
107	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
108	C₄⋊C₄×C₁₃₁	—	2	1	no	—
109	C₄⋊C₄×C₁₃₁	—	2	2	no	—
110	C₄⋊C₄×C₁₃₁	—	2	2	no	—
111	C₄⋊C₄×C₁₃₁	—	2	2	no	—
112	C₄⋊C₄×C₁₃₁	—	2	2	no	—
113	C₄⋊C₄×C₁₃₁	—	4	2	no	—
114	C₄⋊C₄×C₁₃₁	—	4	2	no	—
115	C₄⋊C₄×C₁₃₁	C₂×D₄	1	2	yes	—
116	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
117	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
118	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
119	C₄²×C₁₃₁	—	4	2	no	—
120	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₁₃₁	#41	1	1	yes	characteristic
123	C₄²×C₁₃₁	C₂⁴	1	1	yes	characteristic
124	C₂³×C₁₃₁	—	2	2	no	—
125	C₂³×C₁₃₁	—	4	2	no	—
126	C₂³×C₁₃₁	—	4	2	no	—
127	C₂³×C₁₃₁	—	4	2	no	—
128	C₂³×C₁₃₁	#121	1	1	yes	characteristic
129	Q₈×C₁₃₁	—	4	2	no	—
130	Q₈×C₁₃₁	—	4	4	no	—
131	Q₈×C₁₃₁	—	4	2	no	—
132	D₄×C₁₃₁	—	2	4	no	—
133	D₄×C₁₃₁	—	4	2	no	—
134	C₂×C₄×C₁₃₁	—	2	2	no	—
135	C₂×C₄×C₁₃₁	—	2	1	no	—
136	C₂×C₄×C₁₃₁	—	2	1	no	—
137	C₂×C₄×C₁₃₁	—	2	2	no	—
138	C₂×C₄×C₁₃₁	—	2	2	no	—
139	C₂×C₄×C₁₃₁	—	4	4	no	—
140	C₂×C₄×C₁₃₁	—	4	2	no	—
141	C₂×C₄×C₁₃₁	—	4	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	#121	1	1	yes	characteristic
146	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
147	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
148	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
150	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
151	C₈×C₁₃₁	—	2	1	no	—
152	C₈×C₁₃₁	—	2	1	no	—
153	C₈×C₁₃₁	—	2	1	no	—
154	C₈×C₁₃₁	—	4	2	no	—
155	C₈×C₁₃₁	—	4	4	no	—
156	C₈×C₁₃₁	AGL(1,ℤ/8)	1	2	yes	—
157	C₂²×C₁₃₁	—	2	1	no	—
158	C₂²×C₁₃₁	—	2	1	no	—
159	C₂²×C₁₃₁	—	4	2	no	—
160	C₂²×C₁₃₁	—	4	2	no	—
161	C₂²×C₁₃₁	—	4	2	no	—
162	C₂²×C₁₃₁	—	8	4	no	—
163	C₂²×C₁₃₁	#473	1	2	yes	—
164	C₂²×C₁₃₁	C₂×#121	1	1	yes	characteristic
165	C₄×C₁₃₁	—	2	1	no	—
166	C₄×C₁₃₁	—	2	1	no	—
167	C₄×C₁₃₁	—	2	1	no	—
168	C₄×C₁₃₁	—	2	1	no	—
169	C₄×C₁₃₁	—	4	2	no	—
170	C₄×C₁₃₁	—	8	2	no	—
171	C₄×C₁₃₁	—	8	2	no	—
172	C₄×C₁₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
173	C₄×C₁₃₁	#575	1	1	yes	characteristic
174	C₄×C₁₃₁	#575	1	2	yes	—
175	C₂×C₁₃₁	—	2	2	no	—
176	C₂×C₁₃₁	—	8	2	no	—
177	C₂×C₁₃₁	#3036	1	1	yes	characteristic
178	C₂×C₁₃₁	#3054	1	1	yes	characteristic
179	C₂×C₁₃₁	C₂×#473	1	1	yes	characteristic
180	#19284	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₁₃₁	#19284	1	1	yes	characteristic, direct product factor, Sylow
182	#3170	C₂×C₁₃₁	1	1	yes	characteristic, complemented
183	#3110	C₂×C₁₃₁	1	2	yes	—
184	C₂×#436	C₂×C₁₃₁	1	1	yes	characteristic
185	#1699	C₂×C₁₃₁	1	4	yes	complemented
186	#1693	C₂×C₁₃₁	1	2	yes	complemented
187	#1689	C₂×C₁₃₁	1	2	yes	complemented
188	#1568	C₂×C₁₃₁	1	1	yes	characteristic, complemented
189	#1552	C₂×C₁₃₁	1	2	yes	complemented
190	C₂²×M₁₆	—	2	1	no	—
191	#533	C₂²×C₁₃₁	1	2	yes	—
192	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
193	#500	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
194	#494	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
195	#487	C₂²×C₁₃₁	1	2	yes	complemented
196	#484	—	2	2	no	—
197	#474	C₂²×C₁₃₁	1	4	yes	—
198	#467	—	2	1	no	—
199	#467	—	2	1	no	—
200	#461	C₂²×C₁₃₁	1	4	yes	—
201	#450	—	2	2	no	—
202	#440	—	2	4	no	—
203	C₄×Q₁₆	—	2	1	no	—
204	C₄×Q₁₆	—	2	1	no	—
205	#436	—	2	1	no	—
206	#436	—	2	1	no	—
207	#436	C₂²×C₁₃₁	1	2	yes	—
208	#436	C₂²×C₁₃₁	1	2	yes	—
209	#432	C₂²×C₁₃₁	1	2	yes	—
210	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
211	C₂×C₂²⋊C₈	—	2	1	no	—
212	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
213	#335	C₂²×C₁₃₁	1	2	yes	complemented
214	#334	C₂²×C₁₃₁	1	2	yes	complemented
215	#332	C₂²×C₁₃₁	1	4	yes	complemented
216	#332	C₂²×C₁₃₁	1	4	yes	complemented
217	C₂²×D₄	D₄×C₁₃₁	1	1	yes	characteristic
218	C₂³×C₄	—	2	1	no	—
219	C₂×Q₁₆	—	2	1	no	—
220	C₂×Q₁₆	—	2	1	no	—
221	C₂×SD₁₆	—	2	4	no	—
222	C₂×M₁₆	—	2	2	no	—
223	C₂×M₁₆	—	2	2	no	—
224	C₂×M₁₆	—	4	4	no	—
225	C₂²×C₈	—	2	1	no	—
226	C₂²×C₈	D₄×C₁₃₁	1	1	yes	characteristic
227	C₂²×C₈	D₄×C₁₃₁	1	1	yes	characteristic
228	C₄⋊Q₈	C₂³×C₁₃₁	1	2	yes	—
229	C₄⋊Q₈	C₂³×C₁₃₁	1	2	yes	—
230	#125	—	2	2	no	—
231	C₂²⋊Q₈	—	2	2	no	—
232	C₂²⋊Q₈	—	2	2	no	—
233	C₄×Q₈	—	2	2	no	—
234	C₄×Q₈	—	2	2	no	—
235	C₄×D₄	—	2	1	no	—
236	C₄×D₄	—	2	1	no	—
237	C₄×D₄	D₄×C₁₃₁	1	2	yes	—
238	C₄×D₄	C₂³×C₁₃₁	1	2	yes	—
239	#117	—	2	2	no	—
240	C₂×C₄⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
241	C₂×C₂²⋊C₄	—	2	1	no	—
242	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
243	#107	—	2	1	no	—
244	#107	—	2	1	no	—
245	#107	—	2	4	no	—
246	C₄⋊C₈	—	2	1	no	—
247	C₄⋊C₈	C₂³×C₁₃₁	1	2	yes	—
248	C₄⋊C₈	C₂³×C₁₃₁	1	4	yes	—
249	#103	—	2	2	no	—
250	#103	—	2	2	no	—
251	#103	—	2	4	no	—
252	#102	—	2	4	no	—
253	C₂²⋊C₈	—	2	2	no	—
254	C₂²⋊C₈	—	2	2	no	—
255	C₂²⋊C₈	—	2	2	no	—
256	#97	—	2	2	no	—
257	C₄×C₈	D₄×C₁₃₁	1	1	yes	characteristic
258	C₄×C₈	D₄×C₁₃₁	1	1	yes	characteristic
259	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
260	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
261	C₂⁴	—	2	1	no	—
262	C₂×Q₈	—	2	2	no	—
263	C₂×Q₈	—	2	2	no	—
264	C₂×D₄	—	2	1	no	—
265	C₂×D₄	—	4	2	no	—
266	C₂×D₄	C₂×D₄×C₁₃₁	1	2	yes	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	4	2	no	—
271	C₂²×C₄	—	4	2	no	—
272	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
274	C₂²×C₄	#41×C₁₃₁	1	1	yes	characteristic
275	Q₁₆	—	4	2	no	—
276	Q₁₆	—	4	2	no	—
277	SD₁₆	—	4	8	no	—
278	M₁₆	—	4	4	no	—
279	M₁₆	—	4	4	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	4	1	no	—
284	C₂×C₈	—	4	2	no	—
285	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
286	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
287	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
288	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
289	C₄⋊C₄	—	2	1	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	4	2	no	—
295	C₄⋊C₄	—	4	2	no	—
296	C₄⋊C₄	C₂×D₄×C₁₃₁	1	2	yes	—
297	C₂²⋊C₄	—	2	2	no	—
298	C₂²⋊C₄	—	2	2	no	—
299	C₂²⋊C₄	—	4	2	no	—
300	C₄²	—	4	2	no	—
301	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
302	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
303	C₄²	#41×C₁₃₁	1	1	yes	characteristic
304	C₄²	C₂⁴×C₁₃₁	1	1	yes	characteristic
305	C₂³	—	2	2	no	—
306	C₂³	—	4	2	no	—
307	C₂³	—	4	2	no	—
308	C₂³	—	4	2	no	—
309	C₂³	#121×C₁₃₁	1	1	yes	characteristic
310	Q₈	—	4	2	no	—
311	Q₈	—	4	4	no	—
312	Q₈	—	4	2	no	—
313	D₄	—	2	4	no	—
314	D₄	—	4	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
327	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
328	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
329	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
330	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
331	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
332	C₈	—	2	1	no	—
333	C₈	—	2	1	no	—
334	C₈	—	2	1	no	—
335	C₈	—	4	2	no	—
336	C₈	—	4	4	no	—
337	C₈	AGL(1,ℤ/8)×C₁₃₁	1	2	yes	—
338	C₂²	—	2	1	no	—
339	C₂²	—	2	1	no	—
340	C₂²	—	4	2	no	—
341	C₂²	—	4	2	no	—
342	C₂²	—	4	2	no	—
343	C₂²	—	8	4	no	—
344	C₂²	#473×C₁₃₁	1	2	yes	—
345	C₂²	C₂×#121×C₁₃₁	1	1	yes	characteristic
346	C₄	—	2	1	no	—
347	C₄	—	2	1	no	—
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	4	2	no	—
351	C₄	—	8	2	no	—
352	C₄	—	8	2	no	—
353	C₄	C₂×AGL(1,ℤ/8)×C₁₃₁	1	1	yes	characteristic
354	C₄	#575×C₁₃₁	1	1	yes	characteristic
355	C₄	#575×C₁₃₁	1	2	yes	—
356	C₂	—	2	2	no	—
357	C₂	—	8	2	no	—
358	C₂	#3036×C₁₃₁	1	1	yes	characteristic
359	C₂	#3054×C₁₃₁	1	1	yes	characteristic
360	C₂	C₂×#473×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₁
prime radical	C₂²×D₄×C₁₃₁	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₁ ◁ C₂×C₄²×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3170×C₁₃₁	C₂	semidirect
4. #1699×C₁₃₁	C₂	semidirect
5. #1693×C₁₃₁	C₂	semidirect
6. #1689×C₁₃₁	C₂	semidirect
7. #1568×C₁₃₁	C₂	semidirect
8. #1552×C₁₃₁	C₂	semidirect
12. #500×C₁₃₁	C₂²	semidirect
13. #494×C₁₃₁	C₂²	semidirect
14. #487×C₁₃₁	C₂²	semidirect
32. #335×C₁₃₁	C₂²	semidirect
33. #334×C₁₃₁	C₂²	semidirect
34. #332×C₁₃₁	C₂²	semidirect
35. #332×C₁₃₁	C₂²	semidirect
180. #19284	C₁₃₁	direct (N × H)
181. C₁₃₁	#19284	direct (N × H)
182. #3170	C₂×C₁₃₁	semidirect
185. #1699	C₂×C₁₃₁	semidirect
186. #1693	C₂×C₁₃₁	semidirect
187. #1689	C₂×C₁₃₁	semidirect
188. #1568	C₂×C₁₃₁	semidirect
189. #1552	C₂×C₁₃₁	semidirect
193. #500	C₂²×C₁₃₁	semidirect
194. #494	C₂²×C₁₃₁	semidirect
195. #487	C₂²×C₁₃₁	semidirect
213. #335	C₂²×C₁₃₁	semidirect
214. #334	C₂²×C₁₃₁	semidirect
215. #332	C₂²×C₁₃₁	semidirect
216. #332	C₂²×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#3170×C₁₃₁	2
#3110×C₁₃₁	2
C₂×#436×C₁₃₁	2
#1699×C₁₃₁	2
#1693×C₁₃₁	2
#1689×C₁₃₁	2
#1568×C₁₃₁	2
#1552×C₁₃₁	2
#19284	131

Subgroups — C131×#19284 #45705168

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#19284 #45705168