Subgroups — C₁₃₁×#19713 #45705597

Order 33536.

806 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3228×C₁₃₁	C₂	1	2	yes	maximal, complemented
2	#3208×C₁₃₁	C₂	1	2	yes	maximal, complemented
3	#3185×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#3151×C₁₃₁	C₂	1	1	yes	maximal, characteristic
5	#1722×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#1717×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#1715×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1714×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	#1709×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1705×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#1453×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₁₃₁	—	2	2	no	—
13	#533×C₁₃₁	C₂²	1	2	yes	—
14	#532×C₁₃₁	C₂²	1	1	yes	characteristic
15	C₂×#127×C₁₃₁	C₂²	1	1	yes	characteristic
16	#500×C₁₃₁	C₂²	1	2	yes	complemented
17	#498×C₁₃₁	C₂²	1	2	yes	complemented
18	#498×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
19	#496×C₁₃₁	—	2	2	no	—
20	#494×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
21	#493×C₁₃₁	C₂²	1	1	yes	characteristic
22	#493×C₁₃₁	C₂²	1	1	yes	characteristic
23	#492×C₁₃₁	C₂²	1	2	yes	—
24	#492×C₁₃₁	C₂²	1	1	yes	characteristic
25	#492×C₁₃₁	C₂²	1	1	yes	characteristic
26	#492×C₁₃₁	C₂²	1	2	yes	—
27	#487×C₁₃₁	C₂²	1	2	yes	complemented
28	#486×C₁₃₁	C₂²	1	2	yes	—
29	#486×C₁₃₁	C₂²	1	2	yes	—
30	#486×C₁₃₁	C₂²	1	2	yes	complemented
31	#486×C₁₃₁	C₂²	1	2	yes	complemented
32	#482×C₁₃₁	—	2	4	no	—
33	#478×C₁₃₁	—	2	4	no	—
34	#470×C₁₃₁	—	2	2	no	—
35	#460×C₁₃₁	—	2	4	no	—
36	#450×C₁₃₁	—	2	4	no	—
37	#441×C₁₃₁	—	2	2	no	—
38	#431×C₁₃₁	C₂²	1	2	yes	—
39	C₄×M₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
40	#322×C₁₃₁	C₂²	1	2	yes	complemented
41	#322×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
42	C₈²×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
43	C₂×#41×C₁₃₁	—	2	1	no	—
44	C₂²×D₄×C₁₃₁	—	2	1	no	—
45	C₂²×D₄×C₁₃₁	—	2	2	no	—
46	AGL(1,ℤ/8)×C₁₃₁	—	4	8	no	—
47	C₂×Q₁₆×C₁₃₁	—	2	2	no	—
48	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
49	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
50	C₂×SD₁₆×C₁₃₁	—	2	4	no	—
51	C₂×SD₁₆×C₁₃₁	—	2	4	no	—
52	C₂×D₈×C₁₃₁	—	2	2	no	—
53	C₂×D₈×C₁₃₁	—	2	2	no	—
54	C₂×M₁₆×C₁₃₁	D₄	1	2	yes	—
55	C₄⋊Q₈×C₁₃₁	C₂³	1	2	yes	—
56	C₄⋊Q₈×C₁₃₁	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
58	#127×C₁₃₁	—	2	2	no	—
59	#127×C₁₃₁	—	2	1	no	—
60	#127×C₁₃₁	C₂³	1	1	yes	characteristic
61	#127×C₁₃₁	C₂³	1	1	yes	characteristic
62	#127×C₁₃₁	C₂³	1	1	yes	characteristic
63	#125×C₁₃₁	—	2	2	no	—
64	#124×C₁₃₁	—	2	1	no	—
65	C₂²⋊Q₈×C₁₃₁	—	2	2	no	—
66	C₂²⋊Q₈×C₁₃₁	—	2	2	no	—
67	#121×C₁₃₁	—	2	2	no	—
68	C₄×Q₈×C₁₃₁	—	2	2	no	—
69	C₄×Q₈×C₁₃₁	—	2	2	no	—
70	C₄×D₄×C₁₃₁	—	2	2	no	—
71	#117×C₁₃₁	—	2	2	no	—
72	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
73	#107×C₁₃₁	—	2	4	no	—
74	#106×C₁₃₁	—	2	2	no	—
75	#106×C₁₃₁	—	2	4	no	—
76	C₄⋊C₈×C₁₃₁	D₄	1	4	yes	—
77	#103×C₁₃₁	—	2	4	no	—
78	#102×C₁₃₁	—	2	4	no	—
79	#102×C₁₃₁	—	2	4	no	—
80	#102×C₁₃₁	—	2	4	no	—
81	#102×C₁₃₁	—	2	4	no	—
82	C₂²⋊C₈×C₁₃₁	D₄	1	4	yes	—
83	#97×C₁₃₁	D₄	1	2	yes	—
84	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
85	C₄×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
86	C₄×C₈×C₁₃₁	C₂³	1	2	yes	—
87	C₄×C₈×C₁₃₁	C₂³	1	2	yes	—
88	C₂⁴×C₁₃₁	—	4	1	no	—
89	#41×C₁₃₁	—	4	4	no	—
90	C₂×Q₈×C₁₃₁	—	2	2	no	—
91	C₂×Q₈×C₁₃₁	—	2	2	no	—
92	C₂×Q₈×C₁₃₁	—	2	1	no	—
93	C₂×D₄×C₁₃₁	—	2	2	no	—
94	C₂×D₄×C₁₃₁	—	2	2	no	—
95	C₂×D₄×C₁₃₁	—	2	2	no	—
96	C₂×D₄×C₁₃₁	—	2	1	no	—
97	C₂×D₄×C₁₃₁	—	2	1	no	—
98	C₂×D₄×C₁₃₁	—	2	1	no	—
99	C₂×D₄×C₁₃₁	—	4	4	no	—
100	C₂×D₄×C₁₃₁	—	4	1	no	—
101	C₂×D₄×C₁₃₁	—	4	2	no	—
102	C₂×D₄×C₁₃₁	—	4	1	no	—
103	C₂×D₄×C₁₃₁	—	8	4	no	—
104	C₂²×C₄×C₁₃₁	—	4	1	no	—
105	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
107	Q₁₆×C₁₃₁	—	4	4	no	—
108	SD₁₆×C₁₃₁	—	4	4	no	—
109	SD₁₆×C₁₃₁	—	4	4	no	—
110	SD₁₆×C₁₃₁	—	8	4	no	—
111	SD₁₆×C₁₃₁	—	8	4	no	—
112	D₈×C₁₃₁	—	4	4	no	—
113	D₈×C₁₃₁	—	4	4	no	—
114	M₁₆×C₁₃₁	—	2	4	no	—
115	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₁₃₁	C₂×D₄	1	4	yes	—
117	C₂×C₈×C₁₃₁	C₂×D₄	1	4	yes	—
118	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
119	C₄⋊C₄×C₁₃₁	—	2	2	no	—
120	C₄⋊C₄×C₁₃₁	—	2	2	no	—
121	C₄⋊C₄×C₁₃₁	—	2	2	no	—
122	C₄⋊C₄×C₁₃₁	—	2	2	no	—
123	C₄⋊C₄×C₁₃₁	—	2	2	no	—
124	C₄⋊C₄×C₁₃₁	—	4	2	no	—
125	C₄⋊C₄×C₁₃₁	—	4	2	no	—
126	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
127	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
128	C₄²×C₁₃₁	—	4	2	no	—
129	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₃₁	C₂×D₄	1	2	yes	—
131	C₄²×C₁₃₁	C₂⁴	1	1	yes	characteristic
132	C₂³×C₁₃₁	—	4	1	no	—
133	C₂³×C₁₃₁	—	4	1	no	—
134	C₂³×C₁₃₁	—	4	1	no	—
135	C₂³×C₁₃₁	—	8	2	no	—
136	C₂³×C₁₃₁	—	8	4	no	—
137	C₂³×C₁₃₁	#127	1	1	yes	characteristic
138	Q₈×C₁₃₁	—	4	2	no	—
139	Q₈×C₁₃₁	—	4	4	no	—
140	Q₈×C₁₃₁	—	4	4	no	—
141	D₄×C₁₃₁	—	4	2	no	—
142	D₄×C₁₃₁	—	4	2	no	—
143	D₄×C₁₃₁	—	4	2	no	—
144	D₄×C₁₃₁	—	4	4	no	—
145	D₄×C₁₃₁	—	4	4	no	—
146	D₄×C₁₃₁	—	4	4	no	—
147	D₄×C₁₃₁	—	8	2	no	—
148	D₄×C₁₃₁	—	8	4	no	—
149	D₄×C₁₃₁	—	8	2	no	—
150	C₂×C₄×C₁₃₁	—	2	2	no	—
151	C₂×C₄×C₁₃₁	—	2	4	no	—
152	C₂×C₄×C₁₃₁	—	4	2	no	—
153	C₂×C₄×C₁₃₁	—	4	2	no	—
154	C₂×C₄×C₁₃₁	—	4	1	no	—
155	C₂×C₄×C₁₃₁	—	8	2	no	—
156	C₂×C₄×C₁₃₁	#127	1	2	yes	—
157	C₂×C₄×C₁₃₁	#127	1	1	yes	characteristic
158	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
160	C₈×C₁₃₁	—	2	2	no	—
161	C₈×C₁₃₁	—	2	4	no	—
162	C₈×C₁₃₁	—	2	4	no	—
163	C₈×C₁₃₁	AGL(1,ℤ/8)	1	4	yes	—
164	C₂²×C₁₃₁	—	2	1	no	—
165	C₂²×C₁₃₁	—	2	2	no	—
166	C₂²×C₁₃₁	—	8	1	no	—
167	C₂²×C₁₃₁	—	8	1	no	—
168	C₂²×C₁₃₁	—	8	1	no	—
169	C₂²×C₁₃₁	—	8	2	no	—
170	C₂²×C₁₃₁	—	8	2	no	—
171	C₂²×C₁₃₁	—	8	2	no	—
172	C₂²×C₁₃₁	—	16	4	no	—
173	C₂²×C₁₃₁	C₂×#127	1	1	yes	characteristic
174	C₄×C₁₃₁	—	2	1	no	—
175	C₄×C₁₃₁	—	2	2	no	—
176	C₄×C₁₃₁	—	8	1	no	—
177	C₄×C₁₃₁	—	8	2	no	—
178	C₄×C₁₃₁	—	8	2	no	—
179	C₄×C₁₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
180	C₄×C₁₃₁	#577	1	4	yes	—
181	C₂×C₁₃₁	—	4	1	no	—
182	C₂×C₁₃₁	—	16	1	no	—
183	C₂×C₁₃₁	—	16	1	no	—
184	C₂×C₁₃₁	—	16	1	no	—
185	C₂×C₁₃₁	#3151	1	1	yes	characteristic
186	C₂×C₁₃₁	#3154	1	2	yes	—
187	#19713	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₁₃₁	#19713	1	1	yes	characteristic, direct product factor, Sylow
189	#3228	C₂×C₁₃₁	1	2	yes	complemented
190	#3208	C₂×C₁₃₁	1	2	yes	complemented
191	#3185	C₂×C₁₃₁	1	1	yes	characteristic, complemented
192	#3151	C₂×C₁₃₁	1	1	yes	characteristic
193	#1722	C₂×C₁₃₁	1	1	yes	characteristic, complemented
194	#1717	C₂×C₁₃₁	1	2	yes	complemented
195	#1715	C₂×C₁₃₁	1	1	yes	characteristic, complemented
196	#1714	C₂×C₁₃₁	1	2	yes	complemented
197	#1709	C₂×C₁₃₁	1	1	yes	characteristic, complemented
198	#1705	C₂×C₁₃₁	1	1	yes	characteristic, complemented
199	#1453	C₂×C₁₃₁	1	1	yes	characteristic, complemented
200	C₂×AGL(1,ℤ/8)	—	2	2	no	—
201	#533	C₂²×C₁₃₁	1	2	yes	—
202	#532	C₂²×C₁₃₁	1	1	yes	characteristic
203	C₂×#127	C₂²×C₁₃₁	1	1	yes	characteristic
204	#500	C₂²×C₁₃₁	1	2	yes	complemented
205	#498	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
206	#498	C₂²×C₁₃₁	1	2	yes	complemented
207	#496	—	2	2	no	—
208	#494	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
209	#493	C₂²×C₁₃₁	1	1	yes	characteristic
210	#493	C₂²×C₁₃₁	1	1	yes	characteristic
211	#492	C₂²×C₁₃₁	1	1	yes	characteristic
212	#492	C₂²×C₁₃₁	1	1	yes	characteristic
213	#492	C₂²×C₁₃₁	1	2	yes	—
214	#492	C₂²×C₁₃₁	1	2	yes	—
215	#487	C₂²×C₁₃₁	1	2	yes	complemented
216	#486	C₂²×C₁₃₁	1	2	yes	—
217	#486	C₂²×C₁₃₁	1	2	yes	—
218	#486	C₂²×C₁₃₁	1	2	yes	complemented
219	#486	C₂²×C₁₃₁	1	2	yes	complemented
220	#482	—	2	4	no	—
221	#478	—	2	4	no	—
222	#470	—	2	2	no	—
223	#460	—	2	4	no	—
224	#450	—	2	4	no	—
225	#441	—	2	2	no	—
226	#431	C₂²×C₁₃₁	1	2	yes	—
227	C₄×M₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
228	#322	C₂²×C₁₃₁	1	2	yes	complemented
229	#322	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
230	C₈²	C₂²×C₁₃₁	1	1	yes	characteristic, complemented
231	C₂×#41	—	2	1	no	—
232	C₂²×D₄	—	2	1	no	—
233	C₂²×D₄	—	2	2	no	—
234	AGL(1,ℤ/8)	—	4	8	no	—
235	C₂×Q₁₆	—	2	2	no	—
236	C₂×SD₁₆	—	2	2	no	—
237	C₂×SD₁₆	—	2	2	no	—
238	C₂×SD₁₆	—	2	4	no	—
239	C₂×SD₁₆	—	2	4	no	—
240	C₂×D₈	—	2	2	no	—
241	C₂×D₈	—	2	2	no	—
242	C₂×M₁₆	D₄×C₁₃₁	1	2	yes	—
243	C₄⋊Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
244	C₄⋊Q₈	C₂³×C₁₃₁	1	2	yes	—
245	C₄⋊Q₈	C₂³×C₁₃₁	1	2	yes	—
246	#127	—	2	2	no	—
247	#127	—	2	1	no	—
248	#127	C₂³×C₁₃₁	1	1	yes	characteristic
249	#127	C₂³×C₁₃₁	1	1	yes	characteristic
250	#127	C₂³×C₁₃₁	1	1	yes	characteristic
251	#125	—	2	2	no	—
252	#124	—	2	1	no	—
253	C₂²⋊Q₈	—	2	2	no	—
254	C₂²⋊Q₈	—	2	2	no	—
255	#121	—	2	2	no	—
256	C₄×Q₈	—	2	2	no	—
257	C₄×Q₈	—	2	2	no	—
258	C₄×D₄	—	2	2	no	—
259	#117	—	2	2	no	—
260	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
261	#107	—	2	4	no	—
262	#106	—	2	2	no	—
263	#106	—	2	4	no	—
264	C₄⋊C₈	D₄×C₁₃₁	1	4	yes	—
265	#103	—	2	4	no	—
266	#102	—	2	4	no	—
267	#102	—	2	4	no	—
268	#102	—	2	4	no	—
269	#102	—	2	4	no	—
270	C₂²⋊C₈	D₄×C₁₃₁	1	4	yes	—
271	#97	D₄×C₁₃₁	1	2	yes	—
272	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
273	C₄×C₈	C₂³×C₁₃₁	1	2	yes	—
274	C₄×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
275	C₄×C₈	C₂³×C₁₃₁	1	2	yes	—
276	C₂⁴	—	4	1	no	—
277	#41	—	4	4	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	2	1	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	—	2	1	no	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	—	4	4	no	—
288	C₂×D₄	—	4	1	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	—	4	1	no	—
291	C₂×D₄	—	8	4	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
294	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
295	Q₁₆	—	4	4	no	—
296	SD₁₆	—	4	4	no	—
297	SD₁₆	—	4	4	no	—
298	SD₁₆	—	8	4	no	—
299	SD₁₆	—	8	4	no	—
300	D₈	—	4	4	no	—
301	D₈	—	4	4	no	—
302	M₁₆	—	2	4	no	—
303	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
304	C₂×C₈	C₂×D₄×C₁₃₁	1	4	yes	—
305	C₂×C₈	C₂×D₄×C₁₃₁	1	4	yes	—
306	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₂²⋊C₄	—	4	2	no	—
315	C₂²⋊C₄	—	4	2	no	—
316	C₄²	—	4	2	no	—
317	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
318	C₄²	C₂×D₄×C₁₃₁	1	2	yes	—
319	C₄²	C₂⁴×C₁₃₁	1	1	yes	characteristic
320	C₂³	—	4	1	no	—
321	C₂³	—	4	1	no	—
322	C₂³	—	4	1	no	—
323	C₂³	—	8	2	no	—
324	C₂³	—	8	4	no	—
325	C₂³	#127×C₁₃₁	1	1	yes	characteristic
326	Q₈	—	4	2	no	—
327	Q₈	—	4	4	no	—
328	Q₈	—	4	4	no	—
329	D₄	—	4	2	no	—
330	D₄	—	4	2	no	—
331	D₄	—	4	2	no	—
332	D₄	—	4	4	no	—
333	D₄	—	4	4	no	—
334	D₄	—	4	4	no	—
335	D₄	—	8	2	no	—
336	D₄	—	8	4	no	—
337	D₄	—	8	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	8	2	no	—
344	C₂×C₄	#127×C₁₃₁	1	2	yes	—
345	C₂×C₄	#127×C₁₃₁	1	1	yes	characteristic
346	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
347	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
348	C₈	—	2	2	no	—
349	C₈	—	2	4	no	—
350	C₈	—	2	4	no	—
351	C₈	AGL(1,ℤ/8)×C₁₃₁	1	4	yes	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	8	1	no	—
355	C₂²	—	8	1	no	—
356	C₂²	—	8	1	no	—
357	C₂²	—	8	2	no	—
358	C₂²	—	8	2	no	—
359	C₂²	—	8	2	no	—
360	C₂²	—	16	4	no	—
361	C₂²	C₂×#127×C₁₃₁	1	1	yes	characteristic
362	C₄	—	2	1	no	—
363	C₄	—	2	2	no	—
364	C₄	—	8	1	no	—
365	C₄	—	8	2	no	—
366	C₄	—	8	2	no	—
367	C₄	C₂×AGL(1,ℤ/8)×C₁₃₁	1	2	yes	—
368	C₄	#577×C₁₃₁	1	4	yes	—
369	C₂	—	4	1	no	—
370	C₂	—	16	1	no	—
371	C₂	—	16	1	no	—
372	C₂	—	16	1	no	—
373	C₂	#3151×C₁₃₁	1	1	yes	characteristic
374	C₂	#3154×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃₁	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₁
prime radical	#3151×C₁₃₁	C₂
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. #3228×C₁₃₁	C₂	semidirect
2. #3208×C₁₃₁	C₂	semidirect
3. #3185×C₁₃₁	C₂	semidirect
5. #1722×C₁₃₁	C₂	semidirect
6. #1717×C₁₃₁	C₂	semidirect
7. #1715×C₁₃₁	C₂	semidirect
8. #1714×C₁₃₁	C₂	semidirect
9. #1709×C₁₃₁	C₂	semidirect
10. #1705×C₁₃₁	C₂	semidirect
11. #1453×C₁₃₁	C₂	semidirect
16. #500×C₁₃₁	C₂²	semidirect
17. #498×C₁₃₁	C₂²	semidirect
18. #498×C₁₃₁	C₂²	semidirect
20. #494×C₁₃₁	C₂²	semidirect
27. #487×C₁₃₁	C₂²	semidirect
30. #486×C₁₃₁	C₂²	semidirect
31. #486×C₁₃₁	C₂²	semidirect
40. #322×C₁₃₁	C₂²	semidirect
41. #322×C₁₃₁	C₂²	semidirect
42. C₈²×C₁₃₁	C₂²	semidirect
187. #19713	C₁₃₁	direct (N × H)
188. C₁₃₁	#19713	direct (N × H)
189. #3228	C₂×C₁₃₁	semidirect
190. #3208	C₂×C₁₃₁	semidirect
191. #3185	C₂×C₁₃₁	semidirect
193. #1722	C₂×C₁₃₁	semidirect
194. #1717	C₂×C₁₃₁	semidirect
195. #1715	C₂×C₁₃₁	semidirect
196. #1714	C₂×C₁₃₁	semidirect
197. #1709	C₂×C₁₃₁	semidirect
198. #1705	C₂×C₁₃₁	semidirect
199. #1453	C₂×C₁₃₁	semidirect
204. #500	C₂²×C₁₃₁	semidirect
205. #498	C₂²×C₁₃₁	semidirect
206. #498	C₂²×C₁₃₁	semidirect
208. #494	C₂²×C₁₃₁	semidirect
215. #487	C₂²×C₁₃₁	semidirect
218. #486	C₂²×C₁₃₁	semidirect
219. #486	C₂²×C₁₃₁	semidirect
228. #322	C₂²×C₁₃₁	semidirect
229. #322	C₂²×C₁₃₁	semidirect
230. C₈²	C₂²×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#3228×C₁₃₁	2
#3208×C₁₃₁	2
#3185×C₁₃₁	2
#3151×C₁₃₁	2
#1722×C₁₃₁	2
#1717×C₁₃₁	2
#1715×C₁₃₁	2
#1714×C₁₃₁	2
#1709×C₁₃₁	2
#1705×C₁₃₁	2
#1453×C₁₃₁	2
#19713	131

Subgroups — C131×#19713 #45705597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#19713 #45705597