Subgroups — C₁₃₁×#29353 #45715237

Order 33536.

684 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	#2861×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₄×#125×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2074×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2073×C₁₃₁	C₂	1	1	yes	maximal, characteristic
5	#2026×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#2025×C₁₃₁	C₂	1	1	yes	maximal, characteristic
7	#1989×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#1983×C₁₃₁	C₂	1	2	yes	maximal
9	#1936×C₁₃₁	C₂	1	2	yes	maximal
10	#1935×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	#1767×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#125×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂×#125×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂×#124×C₁₃₁	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	2	yes	—
16	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
17	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
18	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
19	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
20	C₂×#97×C₁₃₁	C₂²	1	2	yes	—
21	#391×C₁₃₁	C₂²	1	1	yes	characteristic
22	#391×C₁₃₁	C₂²	1	1	yes	characteristic
23	#390×C₁₃₁	C₂²	1	1	yes	characteristic
24	#390×C₁₃₁	C₂²	1	1	yes	characteristic
25	#389×C₁₃₁	C₂²	1	2	yes	—
26	#388×C₁₃₁	—	2	2	no	—
27	#388×C₁₃₁	—	2	2	no	—
28	#387×C₁₃₁	—	2	2	no	—
29	#382×C₁₃₁	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊C₄×C₁₃₁	—	2	2	no	—
31	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
32	C₄³×C₁₃₁	C₂²	1	1	yes	characteristic
33	#340×C₁₃₁	C₂²	1	2	yes	—
34	#340×C₁₃₁	C₂²	1	2	yes	—
35	#340×C₁₃₁	C₂²	1	2	yes	—
36	#340×C₁₃₁	C₂²	1	2	yes	—
37	#336×C₁₃₁	C₂²	1	1	yes	characteristic
38	#336×C₁₃₁	C₂²	1	1	yes	characteristic
39	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
43	#125×C₁₃₁	—	2	4	no	—
44	#125×C₁₃₁	—	2	4	no	—
45	#124×C₁₃₁	—	2	4	no	—
46	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
47	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
48	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
49	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
51	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
54	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
57	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
58	C₂×C₄²×C₁₃₁	—	2	2	no	—
59	C₂×C₄²×C₁₃₁	D₄	1	2	yes	—
60	C₂×C₄²×C₁₃₁	D₄	1	2	yes	—
61	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
64	C₄⋊C₈×C₁₃₁	—	2	4	no	—
65	#103×C₁₃₁	—	2	4	no	—
66	#103×C₁₃₁	—	4	2	no	—
67	#102×C₁₃₁	—	2	4	no	—
68	#102×C₁₃₁	—	4	2	no	—
69	#97×C₁₃₁	—	4	2	no	—
70	#95×C₁₃₁	—	2	2	no	—
71	#95×C₁₃₁	—	2	2	no	—
72	#95×C₁₃₁	—	2	2	no	—
73	#95×C₁₃₁	—	2	2	no	—
74	#95×C₁₃₁	—	2	2	no	—
75	C₂⁴×C₁₃₁	—	2	1	no	—
76	C₂×Q₈×C₁₃₁	—	2	2	no	—
77	C₂×Q₈×C₁₃₁	—	2	2	no	—
78	C₂×Q₈×C₁₃₁	—	2	1	no	—
79	C₂×Q₈×C₁₃₁	—	2	1	no	—
80	C₂×D₄×C₁₃₁	—	2	2	no	—
81	C₂×D₄×C₁₃₁	—	2	2	no	—
82	C₂×D₄×C₁₃₁	—	2	1	no	—
83	C₂×D₄×C₁₃₁	—	2	1	no	—
84	C₂²×C₄×C₁₃₁	—	2	2	no	—
85	C₂²×C₄×C₁₃₁	—	2	2	no	—
86	C₂²×C₄×C₁₃₁	—	2	1	no	—
87	C₂²×C₄×C₁₃₁	—	2	1	no	—
88	C₂²×C₄×C₁₃₁	—	2	1	no	—
89	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
94	C₂×C₈×C₁₃₁	—	2	2	no	—
95	C₂×C₈×C₁₃₁	—	2	2	no	—
96	C₂×C₈×C₁₃₁	—	2	2	no	—
97	C₂×C₈×C₁₃₁	—	2	2	no	—
98	C₂×C₈×C₁₃₁	—	2	2	no	—
99	C₂×C₈×C₁₃₁	—	2	2	no	—
100	C₄⋊C₄×C₁₃₁	—	2	8	no	—
101	C₄⋊C₄×C₁₃₁	—	2	2	no	—
102	C₄⋊C₄×C₁₃₁	—	2	2	no	—
103	C₄⋊C₄×C₁₃₁	—	2	2	no	—
104	C₄⋊C₄×C₁₃₁	—	2	2	no	—
105	C₄⋊C₄×C₁₃₁	—	2	2	no	—
106	C₄⋊C₄×C₁₃₁	—	4	4	no	—
107	C₄⋊C₄×C₁₃₁	—	4	2	no	—
108	C₄⋊C₄×C₁₃₁	—	4	2	no	—
109	C₄⋊C₄×C₁₃₁	#41	1	4	yes	—
110	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
111	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
112	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
113	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
114	C₄²×C₁₃₁	—	2	2	no	—
115	C₄²×C₁₃₁	—	2	1	no	—
116	C₄²×C₁₃₁	—	2	1	no	—
117	C₄²×C₁₃₁	—	4	2	no	—
118	C₄²×C₁₃₁	—	4	2	no	—
119	C₄²×C₁₃₁	—	4	4	no	—
120	C₄²×C₁₃₁	#41	1	4	yes	—
121	C₂³×C₁₃₁	—	4	1	no	—
122	C₂³×C₁₃₁	—	4	1	no	—
123	C₂³×C₁₃₁	—	4	1	no	—
124	C₂³×C₁₃₁	—	4	2	no	—
125	C₂³×C₁₃₁	—	4	2	no	—
126	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
127	Q₈×C₁₃₁	—	4	2	no	—
128	Q₈×C₁₃₁	—	4	2	no	—
129	D₄×C₁₃₁	—	4	2	no	—
130	D₄×C₁₃₁	—	4	2	no	—
131	C₂×C₄×C₁₃₁	—	2	2	no	—
132	C₂×C₄×C₁₃₁	—	2	2	no	—
133	C₂×C₄×C₁₃₁	—	2	2	no	—
134	C₂×C₄×C₁₃₁	—	2	4	no	—
135	C₂×C₄×C₁₃₁	—	2	2	no	—
136	C₂×C₄×C₁₃₁	—	2	2	no	—
137	C₂×C₄×C₁₃₁	—	2	2	no	—
138	C₂×C₄×C₁₃₁	—	2	2	no	—
139	C₂×C₄×C₁₃₁	—	2	2	no	—
140	C₂×C₄×C₁₃₁	—	4	2	no	—
141	C₂×C₄×C₁₃₁	—	4	2	no	—
142	C₂×C₄×C₁₃₁	—	4	1	no	—
143	C₂×C₄×C₁₃₁	—	4	1	no	—
144	C₂×C₄×C₁₃₁	—	4	1	no	—
145	C₂×C₄×C₁₃₁	—	4	1	no	—
146	C₂×C₄×C₁₃₁	—	4	2	no	—
147	C₂×C₄×C₁₃₁	—	4	1	no	—
148	C₂×C₄×C₁₃₁	—	4	2	no	—
149	C₂×C₄×C₁₃₁	—	4	2	no	—
150	C₂×C₄×C₁₃₁	—	4	2	no	—
151	C₂×C₄×C₁₃₁	—	4	2	no	—
152	C₂×C₄×C₁₃₁	#124	1	2	yes	—
153	C₂×C₄×C₁₃₁	#124	1	2	yes	—
154	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
155	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
156	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
157	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
158	C₈×C₁₃₁	—	4	2	no	—
159	C₈×C₁₃₁	—	4	2	no	—
160	C₂²×C₁₃₁	—	8	1	no	—
161	C₂²×C₁₃₁	—	8	2	no	—
162	C₂²×C₁₃₁	—	8	1	no	—
163	C₂²×C₁₃₁	—	8	1	no	—
164	C₂²×C₁₃₁	—	8	2	no	—
165	C₂²×C₁₃₁	#525	1	1	yes	characteristic
166	C₂²×C₁₃₁	C₂×#124	1	1	yes	characteristic
167	C₂²×C₁₃₁	#537	1	1	yes	characteristic
168	C₂²×C₁₃₁	#575	1	2	yes	—
169	C₂²×C₁₃₁	#575	1	2	yes	—
170	C₄×C₁₃₁	—	2	2	no	—
171	C₄×C₁₃₁	—	2	2	no	—
172	C₄×C₁₃₁	—	4	2	no	—
173	C₄×C₁₃₁	—	4	4	no	—
174	C₄×C₁₃₁	—	4	2	no	—
175	C₄×C₁₃₁	—	8	1	no	—
176	C₄×C₁₃₁	—	8	1	no	—
177	C₄×C₁₃₁	—	8	1	no	—
178	C₄×C₁₃₁	—	8	2	no	—
179	C₄×C₁₃₁	#556	1	2	yes	—
180	C₄×C₁₃₁	#559	1	2	yes	—
181	C₂×C₁₃₁	—	16	1	no	—
182	C₂×C₁₃₁	#2592	1	1	yes	characteristic
183	C₂×C₁₃₁	#3111	1	2	yes	—
184	C₂×C₁₃₁	#3135	1	1	yes	characteristic
185	C₂×C₁₃₁	#3142	1	1	yes	characteristic
186	C₂×C₁₃₁	#3256	1	2	yes	—
187	#29353	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₁₃₁	#29353	1	1	yes	characteristic, direct product factor, Sylow
189	#2861	C₂×C₁₃₁	1	1	yes	characteristic
190	C₄×#125	C₂×C₁₃₁	1	1	yes	characteristic, complemented
191	#2074	C₂×C₁₃₁	1	1	yes	characteristic, complemented
192	#2073	C₂×C₁₃₁	1	1	yes	characteristic
193	#2026	C₂×C₁₃₁	1	1	yes	characteristic, complemented
194	#2025	C₂×C₁₃₁	1	1	yes	characteristic
195	#1989	C₂×C₁₃₁	1	2	yes	complemented
196	#1983	C₂×C₁₃₁	1	2	yes	—
197	#1936	C₂×C₁₃₁	1	2	yes	—
198	#1935	C₂×C₁₃₁	1	2	yes	complemented
199	#1767	C₂×C₁₃₁	1	1	yes	characteristic, complemented
200	C₂×#125	C₂²×C₁₃₁	1	1	yes	characteristic
201	C₂×#125	C₂²×C₁₃₁	1	1	yes	characteristic
202	C₂×#124	C₂²×C₁₃₁	1	1	yes	characteristic
203	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	2	yes	—
204	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
205	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
206	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
207	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
208	C₂×#97	C₂²×C₁₃₁	1	2	yes	—
209	#391	C₂²×C₁₃₁	1	1	yes	characteristic
210	#391	C₂²×C₁₃₁	1	1	yes	characteristic
211	#390	C₂²×C₁₃₁	1	1	yes	characteristic
212	#390	C₂²×C₁₃₁	1	1	yes	characteristic
213	#389	C₂²×C₁₃₁	1	2	yes	—
214	#388	—	2	2	no	—
215	#388	—	2	2	no	—
216	#387	—	2	2	no	—
217	#382	C₂²×C₁₃₁	1	1	yes	characteristic
218	C₄×C₄⋊C₄	—	2	2	no	—
219	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
220	C₄³	C₂²×C₁₃₁	1	1	yes	characteristic
221	#340	C₂²×C₁₃₁	1	2	yes	—
222	#340	C₂²×C₁₃₁	1	2	yes	—
223	#340	C₂²×C₁₃₁	1	2	yes	—
224	#340	C₂²×C₁₃₁	1	2	yes	—
225	#336	C₂²×C₁₃₁	1	1	yes	characteristic
226	#336	C₂²×C₁₃₁	1	1	yes	characteristic
227	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
228	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
229	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
230	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
231	#125	—	2	4	no	—
232	#125	—	2	4	no	—
233	#124	—	2	4	no	—
234	C₂×C₄⋊C₄	—	2	2	no	—
235	C₂×C₄⋊C₄	—	2	1	no	—
236	C₂×C₄⋊C₄	—	2	1	no	—
237	C₂×C₄⋊C₄	—	2	2	no	—
238	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
239	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
241	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
242	C₂×C₂²⋊C₄	—	2	1	no	—
243	C₂×C₂²⋊C₄	—	2	1	no	—
244	C₂×C₂²⋊C₄	—	2	2	no	—
245	C₂×C₂²⋊C₄	—	2	2	no	—
246	C₂×C₄²	—	2	2	no	—
247	C₂×C₄²	D₄×C₁₃₁	1	2	yes	—
248	C₂×C₄²	D₄×C₁₃₁	1	2	yes	—
249	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
250	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
251	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
252	C₄⋊C₈	—	2	4	no	—
253	#103	—	2	4	no	—
254	#103	—	4	2	no	—
255	#102	—	2	4	no	—
256	#102	—	4	2	no	—
257	#97	—	4	2	no	—
258	#95	—	2	2	no	—
259	#95	—	2	2	no	—
260	#95	—	2	2	no	—
261	#95	—	2	2	no	—
262	#95	—	2	2	no	—
263	C₂⁴	—	2	1	no	—
264	C₂×Q₈	—	2	2	no	—
265	C₂×Q₈	—	2	2	no	—
266	C₂×Q₈	—	2	1	no	—
267	C₂×Q₈	—	2	1	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	—	2	1	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
278	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
279	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
281	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₄⋊C₄	—	2	8	no	—
289	C₄⋊C₄	—	2	2	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	4	no	—
295	C₄⋊C₄	—	4	2	no	—
296	C₄⋊C₄	—	4	2	no	—
297	C₄⋊C₄	#41×C₁₃₁	1	4	yes	—
298	C₂²⋊C₄	—	4	4	no	—
299	C₂²⋊C₄	—	4	4	no	—
300	C₂²⋊C₄	—	4	2	no	—
301	C₂²⋊C₄	—	4	2	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	2	1	no	—
304	C₄²	—	2	1	no	—
305	C₄²	—	4	2	no	—
306	C₄²	—	4	2	no	—
307	C₄²	—	4	4	no	—
308	C₄²	#41×C₁₃₁	1	4	yes	—
309	C₂³	—	4	1	no	—
310	C₂³	—	4	1	no	—
311	C₂³	—	4	1	no	—
312	C₂³	—	4	2	no	—
313	C₂³	—	4	2	no	—
314	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
315	Q₈	—	4	2	no	—
316	Q₈	—	4	2	no	—
317	D₄	—	4	2	no	—
318	D₄	—	4	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	#124×C₁₃₁	1	2	yes	—
341	C₂×C₄	#124×C₁₃₁	1	2	yes	—
342	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
343	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
344	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
345	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
346	C₈	—	4	2	no	—
347	C₈	—	4	2	no	—
348	C₂²	—	8	2	no	—
349	C₂²	—	8	1	no	—
350	C₂²	—	8	2	no	—
351	C₂²	—	8	1	no	—
352	C₂²	—	8	1	no	—
353	C₂²	#525×C₁₃₁	1	1	yes	characteristic
354	C₂²	C₂×#124×C₁₃₁	1	1	yes	characteristic
355	C₂²	#537×C₁₃₁	1	1	yes	characteristic
356	C₂²	#575×C₁₃₁	1	2	yes	—
357	C₂²	#575×C₁₃₁	1	2	yes	—
358	C₄	—	2	2	no	—
359	C₄	—	2	2	no	—
360	C₄	—	4	2	no	—
361	C₄	—	4	2	no	—
362	C₄	—	4	4	no	—
363	C₄	—	8	2	no	—
364	C₄	—	8	1	no	—
365	C₄	—	8	1	no	—
366	C₄	—	8	1	no	—
367	C₄	#556×C₁₃₁	1	2	yes	—
368	C₄	#559×C₁₃₁	1	2	yes	—
369	C₂	—	16	1	no	—
370	C₂	#2592×C₁₃₁	1	1	yes	characteristic
371	C₂	#3111×C₁₃₁	1	2	yes	—
372	C₂	#3135×C₁₃₁	1	1	yes	characteristic
373	C₂	#3142×C₁₃₁	1	1	yes	characteristic
374	C₂	#3256×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂²×D₄×C₁₃₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ C₄³×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×#125×C₁₃₁	C₂	semidirect
3. #2074×C₁₃₁	C₂	semidirect
5. #2026×C₁₃₁	C₂	semidirect
7. #1989×C₁₃₁	C₂	semidirect
10. #1935×C₁₃₁	C₂	semidirect
11. #1767×C₁₃₁	C₂	semidirect
187. #29353	C₁₃₁	direct (N × H)
188. C₁₃₁	#29353	direct (N × H)
190. C₄×#125	C₂×C₁₃₁	semidirect
191. #2074	C₂×C₁₃₁	semidirect
193. #2026	C₂×C₁₃₁	semidirect
195. #1989	C₂×C₁₃₁	semidirect
198. #1935	C₂×C₁₃₁	semidirect
199. #1767	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#2861×C₁₃₁	2
C₄×#125×C₁₃₁	2
#2074×C₁₃₁	2
#2073×C₁₃₁	2
#2026×C₁₃₁	2
#2025×C₁₃₁	2
#1989×C₁₃₁	2
#1983×C₁₃₁	2
#1936×C₁₃₁	2
#1935×C₁₃₁	2
#1767×C₁₃₁	2
#29353	131

Subgroups — C131×#29353 #45715237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#29353 #45715237