Subgroups — C₁₃₁×#7560 #45693444

Order 33536.

538 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2293×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊C₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#1744×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#1271×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#1270×C₁₃₁	C₂	1	2	yes	maximal
6	C₂×C₄×D₄×C₁₃₁	C₄	1	1	yes	characteristic
7	C₂×#117×C₁₃₁	—	2	1	no	—
8	C₂×C₄⋊C₈×C₁₃₁	—	2	1	no	—
9	C₂×C₄×C₈×C₁₃₁	—	2	1	no	—
10	C₂×C₄×C₈×C₁₃₁	—	2	1	no	—
11	#390×C₁₃₁	C₄	1	1	yes	characteristic
12	#390×C₁₃₁	C₂²	1	1	yes	characteristic
13	#389×C₁₃₁	C₄	1	1	yes	characteristic
14	#389×C₁₃₁	C₂²	1	1	yes	characteristic
15	#388×C₁₃₁	—	2	1	no	—
16	#388×C₁₃₁	—	2	1	no	—
17	C₄×C₄⋊C₄×C₁₃₁	C₄	1	1	yes	characteristic
18	C₄×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
19	C₄³×C₁₃₁	C₂²	1	1	yes	characteristic
20	#336×C₁₃₁	—	2	1	no	—
21	#336×C₁₃₁	C₂²	1	2	yes	—
22	#336×C₁₃₁	C₂²	1	2	yes	—
23	C₂²×D₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₃₁	—	2	1	no	—
25	C₂²×C₈×C₁₃₁	—	2	2	no	—
26	C₂²×C₈×C₁₃₁	—	2	2	no	—
27	C₄×D₄×C₁₃₁	—	2	2	no	—
28	C₄×D₄×C₁₃₁	C₈	1	4	yes	complemented
29	#117×C₁₃₁	—	4	2	no	—
30	#117×C₁₃₁	—	4	2	no	—
31	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
32	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
33	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
36	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
37	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
38	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
39	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
40	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
41	C₂×C₄²×C₁₃₁	—	2	1	no	—
42	C₂×C₄²×C₁₃₁	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₃₁	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
49	C₄⋊C₈×C₁₃₁	—	2	4	no	—
50	C₄×C₈×C₁₃₁	—	2	4	no	—
51	C₄×C₈×C₁₃₁	—	4	2	no	—
52	#95×C₁₃₁	—	2	1	no	—
53	#95×C₁₃₁	—	2	1	no	—
54	#95×C₁₃₁	—	2	1	no	—
55	C₂⁴×C₁₃₁	—	2	1	no	—
56	C₂×D₄×C₁₃₁	—	2	1	no	—
57	C₂×D₄×C₁₃₁	—	4	1	no	—
58	C₂×D₄×C₁₃₁	—	4	1	no	—
59	C₂×D₄×C₁₃₁	C₂×C₈	1	2	yes	—
60	C₂²×C₄×C₁₃₁	—	2	1	no	—
61	C₂²×C₄×C₁₃₁	—	2	4	no	—
62	C₂²×C₄×C₁₃₁	—	2	1	no	—
63	C₂²×C₄×C₁₃₁	—	2	1	no	—
64	C₂²×C₄×C₁₃₁	—	4	2	no	—
65	C₂²×C₄×C₁₃₁	—	4	2	no	—
66	C₂²×C₄×C₁₃₁	C₂²⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₃₁	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₃₁	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₃₁	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₁₃₁	—	2	4	no	—
74	C₂×C₈×C₁₃₁	—	2	4	no	—
75	C₂×C₈×C₁₃₁	—	4	2	no	—
76	C₂×C₈×C₁₃₁	—	4	2	no	—
77	C₂×C₈×C₁₃₁	—	4	2	no	—
78	C₂×C₈×C₁₃₁	—	4	2	no	—
79	C₄⋊C₄×C₁₃₁	—	2	1	no	—
80	C₄⋊C₄×C₁₃₁	—	4	1	no	—
81	C₄⋊C₄×C₁₃₁	—	4	1	no	—
82	C₄⋊C₄×C₁₃₁	—	4	2	no	—
83	C₄⋊C₄×C₁₃₁	—	4	1	no	—
84	C₄⋊C₄×C₁₃₁	—	4	1	no	—
85	C₄⋊C₄×C₁₃₁	C₂×C₈	1	2	yes	—
86	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
87	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
88	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
89	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
90	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
91	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
92	C₄²×C₁₃₁	—	2	2	no	—
93	C₄²×C₁₃₁	—	2	2	no	—
94	C₄²×C₁₃₁	—	2	2	no	—
95	C₄²×C₁₃₁	—	4	1	no	—
96	C₄²×C₁₃₁	—	4	1	no	—
97	C₄²×C₁₃₁	—	4	2	no	—
98	C₄²×C₁₃₁	C₂×C₈	1	2	yes	—
99	C₄²×C₁₃₁	M₁₆	1	2	yes	—
100	C₄²×C₁₃₁	D₈	1	2	yes	—
101	C₄²×C₁₃₁	SD₁₆	1	2	yes	—
102	C₂³×C₁₃₁	—	2	2	no	—
103	C₂³×C₁₃₁	—	4	1	no	—
104	C₂³×C₁₃₁	—	4	1	no	—
105	C₂³×C₁₃₁	—	4	1	no	—
106	C₂³×C₁₃₁	—	4	1	no	—
107	C₂³×C₁₃₁	—	4	1	no	—
108	C₂³×C₁₃₁	—	4	1	no	—
109	C₂³×C₁₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
110	D₄×C₁₃₁	—	4	2	no	—
111	D₄×C₁₃₁	—	4	2	no	—
112	C₂×C₄×C₁₃₁	—	2	1	no	—
113	C₂×C₄×C₁₃₁	—	2	1	no	—
114	C₂×C₄×C₁₃₁	—	2	1	no	—
115	C₂×C₄×C₁₃₁	—	2	1	no	—
116	C₂×C₄×C₁₃₁	—	2	1	no	—
117	C₂×C₄×C₁₃₁	—	2	1	no	—
118	C₂×C₄×C₁₃₁	—	2	1	no	—
119	C₂×C₄×C₁₃₁	—	2	1	no	—
120	C₂×C₄×C₁₃₁	—	2	1	no	—
121	C₂×C₄×C₁₃₁	—	2	1	no	—
122	C₂×C₄×C₁₃₁	—	2	1	no	—
123	C₂×C₄×C₁₃₁	—	2	1	no	—
124	C₂×C₄×C₁₃₁	—	2	2	no	—
125	C₂×C₄×C₁₃₁	—	4	1	no	—
126	C₂×C₄×C₁₃₁	—	4	1	no	—
127	C₂×C₄×C₁₃₁	—	4	8	no	—
128	C₂×C₄×C₁₃₁	—	4	1	no	—
129	C₂×C₄×C₁₃₁	—	4	1	no	—
130	C₂×C₄×C₁₃₁	—	4	1	no	—
131	C₂×C₄×C₁₃₁	—	4	1	no	—
132	C₂×C₄×C₁₃₁	—	4	1	no	—
133	C₂×C₄×C₁₃₁	—	4	1	no	—
134	C₂×C₄×C₁₃₁	C₂²⋊C₈	1	2	yes	—
135	C₂×C₄×C₁₃₁	C₂²⋊C₈	1	2	yes	—
136	C₂×C₄×C₁₃₁	#102	1	2	yes	—
137	C₂×C₄×C₁₃₁	#102	1	2	yes	—
138	C₂×C₄×C₁₃₁	#104	1	2	yes	—
139	C₂×C₄×C₁₃₁	#104	1	2	yes	—
140	C₂×C₄×C₁₃₁	C₂²×C₈	1	1	yes	characteristic
141	C₂×C₄×C₁₃₁	C₂×M₁₆	1	1	yes	characteristic
142	C₂×C₄×C₁₃₁	C₂×D₈	1	1	yes	characteristic
143	C₂×C₄×C₁₃₁	C₂×SD₁₆	1	1	yes	characteristic
144	C₂×C₄×C₁₃₁	#135	1	2	yes	—
145	C₈×C₁₃₁	—	4	4	no	—
146	C₈×C₁₃₁	—	4	4	no	—
147	C₂²×C₁₃₁	—	4	2	no	—
148	C₂²×C₁₃₁	—	4	2	no	—
149	C₂²×C₁₃₁	—	4	2	no	—
150	C₂²×C₁₃₁	—	8	1	no	—
151	C₂²×C₁₃₁	—	8	1	no	—
152	C₂²×C₁₃₁	—	8	1	no	—
153	C₂²×C₁₃₁	—	8	1	no	—
154	C₂²×C₁₃₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
155	C₂²×C₁₃₁	#410	1	1	yes	characteristic
156	C₂²×C₁₃₁	#413	1	1	yes	characteristic
157	C₂²×C₁₃₁	C₂×#102	1	1	yes	characteristic
158	C₂²×C₁₃₁	#416	1	1	yes	characteristic
159	C₂²×C₁₃₁	C₂×#104	1	1	yes	characteristic
160	C₂²×C₁₃₁	C₂×#104	1	1	yes	characteristic
161	C₄×C₁₃₁	—	2	2	no	—
162	C₄×C₁₃₁	—	2	1	no	—
163	C₄×C₁₃₁	—	2	1	no	—
164	C₄×C₁₃₁	—	2	2	no	—
165	C₄×C₁₃₁	—	2	2	no	—
166	C₄×C₁₃₁	—	2	1	no	—
167	C₄×C₁₃₁	—	2	1	no	—
168	C₄×C₁₃₁	—	2	2	no	—
169	C₄×C₁₃₁	—	4	2	no	—
170	C₄×C₁₃₁	—	8	1	no	—
171	C₄×C₁₃₁	—	8	1	no	—
172	C₄×C₁₃₁	D₄⋊C₈	1	4	yes	—
173	C₂×C₁₃₁	—	8	2	no	—
174	C₂×C₁₃₁	#1458	1	1	yes	characteristic
175	C₂×C₁₃₁	C₂×D₄⋊C₈	1	1	yes	characteristic
176	C₂×C₁₃₁	#1476	1	1	yes	characteristic
177	C₂×C₁₃₁	#1500	1	1	yes	characteristic
178	C₂×C₁₃₁	#1502	1	1	yes	characteristic
179	C₂×C₁₃₁	#1524	1	1	yes	characteristic
180	C₂×C₁₃₁	#1540	1	1	yes	characteristic
181	#7560	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₁₃₁	#7560	1	1	yes	characteristic, direct product factor, Sylow
183	#2293	C₂×C₁₃₁	1	1	yes	characteristic
184	C₄×C₄⋊C₈	C₂×C₁₃₁	1	1	yes	characteristic, complemented
185	#1744	C₂×C₁₃₁	1	1	yes	characteristic, complemented
186	#1271	C₂×C₁₃₁	1	2	yes	complemented
187	#1270	C₂×C₁₃₁	1	2	yes	—
188	C₂×C₄×D₄	C₄×C₁₃₁	1	1	yes	characteristic
189	C₂×#117	—	2	1	no	—
190	C₂×C₄⋊C₈	—	2	1	no	—
191	C₂×C₄×C₈	—	2	1	no	—
192	C₂×C₄×C₈	—	2	1	no	—
193	#390	C₄×C₁₃₁	1	1	yes	characteristic
194	#390	C₂²×C₁₃₁	1	1	yes	characteristic
195	#389	C₄×C₁₃₁	1	1	yes	characteristic
196	#389	C₂²×C₁₃₁	1	1	yes	characteristic
197	#388	—	2	1	no	—
198	#388	—	2	1	no	—
199	C₄×C₄⋊C₄	C₄×C₁₃₁	1	1	yes	characteristic
200	C₄×C₂²⋊C₄	—	2	1	no	—
201	C₄³	C₂²×C₁₃₁	1	1	yes	characteristic
202	#336	—	2	1	no	—
203	#336	C₂²×C₁₃₁	1	2	yes	—
204	#336	C₂²×C₁₃₁	1	2	yes	—
205	C₂²×D₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
206	C₂³×C₄	—	2	1	no	—
207	C₂²×C₈	—	2	2	no	—
208	C₂²×C₈	—	2	2	no	—
209	C₄×D₄	—	2	2	no	—
210	C₄×D₄	C₈×C₁₃₁	1	4	yes	complemented
211	#117	—	4	2	no	—
212	#117	—	4	2	no	—
213	C₂×C₄⋊C₄	—	2	1	no	—
214	C₂×C₄⋊C₄	—	2	1	no	—
215	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
216	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
217	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
218	C₂×C₂²⋊C₄	—	2	1	no	—
219	C₂×C₂²⋊C₄	—	2	1	no	—
220	C₂×C₂²⋊C₄	—	2	1	no	—
221	C₂×C₂²⋊C₄	—	2	1	no	—
222	C₂×C₂²⋊C₄	—	2	1	no	—
223	C₂×C₄²	—	2	1	no	—
224	C₂×C₄²	C₂×C₄×C₁₃₁	1	1	yes	characteristic
225	C₂×C₄²	C₂×C₄×C₁₃₁	1	1	yes	characteristic
226	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
227	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
228	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
229	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
230	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
231	C₄⋊C₈	—	2	4	no	—
232	C₄×C₈	—	2	4	no	—
233	C₄×C₈	—	4	2	no	—
234	#95	—	2	1	no	—
235	#95	—	2	1	no	—
236	#95	—	2	1	no	—
237	C₂⁴	—	2	1	no	—
238	C₂×D₄	—	2	1	no	—
239	C₂×D₄	—	4	1	no	—
240	C₂×D₄	—	4	1	no	—
241	C₂×D₄	C₂×C₈×C₁₃₁	1	2	yes	—
242	C₂²×C₄	—	2	1	no	—
243	C₂²×C₄	—	2	4	no	—
244	C₂²×C₄	—	2	1	no	—
245	C₂²×C₄	—	2	1	no	—
246	C₂²×C₄	—	4	2	no	—
247	C₂²×C₄	—	4	2	no	—
248	C₂²×C₄	C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
249	C₂²×C₄	C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
250	C₂²×C₄	C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
251	C₂²×C₄	C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
252	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
253	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
254	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
255	C₂×C₈	—	2	4	no	—
256	C₂×C₈	—	2	4	no	—
257	C₂×C₈	—	4	2	no	—
258	C₂×C₈	—	4	2	no	—
259	C₂×C₈	—	4	2	no	—
260	C₂×C₈	—	4	2	no	—
261	C₄⋊C₄	—	2	1	no	—
262	C₄⋊C₄	—	4	1	no	—
263	C₄⋊C₄	—	4	1	no	—
264	C₄⋊C₄	—	4	2	no	—
265	C₄⋊C₄	—	4	1	no	—
266	C₄⋊C₄	—	4	1	no	—
267	C₄⋊C₄	C₂×C₈×C₁₃₁	1	2	yes	—
268	C₂²⋊C₄	—	2	4	no	—
269	C₂²⋊C₄	—	4	2	no	—
270	C₂²⋊C₄	—	4	2	no	—
271	C₂²⋊C₄	—	4	1	no	—
272	C₂²⋊C₄	—	4	1	no	—
273	C₂²⋊C₄	—	4	2	no	—
274	C₄²	—	2	2	no	—
275	C₄²	—	2	2	no	—
276	C₄²	—	2	2	no	—
277	C₄²	—	4	1	no	—
278	C₄²	—	4	1	no	—
279	C₄²	—	4	2	no	—
280	C₄²	C₂×C₈×C₁₃₁	1	2	yes	—
281	C₄²	M₁₆×C₁₃₁	1	2	yes	—
282	C₄²	D₈×C₁₃₁	1	2	yes	—
283	C₄²	SD₁₆×C₁₃₁	1	2	yes	—
284	C₂³	—	2	2	no	—
285	C₂³	—	4	1	no	—
286	C₂³	—	4	1	no	—
287	C₂³	—	4	1	no	—
288	C₂³	—	4	1	no	—
289	C₂³	—	4	1	no	—
290	C₂³	—	4	1	no	—
291	C₂³	C₂×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
292	D₄	—	4	2	no	—
293	D₄	—	4	2	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	4	1	no	—
308	C₂×C₄	—	4	1	no	—
309	C₂×C₄	—	4	8	no	—
310	C₂×C₄	—	4	1	no	—
311	C₂×C₄	—	4	1	no	—
312	C₂×C₄	—	4	1	no	—
313	C₂×C₄	—	4	1	no	—
314	C₂×C₄	—	4	1	no	—
315	C₂×C₄	—	4	1	no	—
316	C₂×C₄	C₂²⋊C₈×C₁₃₁	1	2	yes	—
317	C₂×C₄	C₂²⋊C₈×C₁₃₁	1	2	yes	—
318	C₂×C₄	#102×C₁₃₁	1	2	yes	—
319	C₂×C₄	#102×C₁₃₁	1	2	yes	—
320	C₂×C₄	#104×C₁₃₁	1	2	yes	—
321	C₂×C₄	#104×C₁₃₁	1	2	yes	—
322	C₂×C₄	C₂²×C₈×C₁₃₁	1	1	yes	characteristic
323	C₂×C₄	C₂×M₁₆×C₁₃₁	1	1	yes	characteristic
324	C₂×C₄	C₂×D₈×C₁₃₁	1	1	yes	characteristic
325	C₂×C₄	C₂×SD₁₆×C₁₃₁	1	1	yes	characteristic
326	C₂×C₄	#135×C₁₃₁	1	2	yes	—
327	C₈	—	4	4	no	—
328	C₈	—	4	4	no	—
329	C₂²	—	4	2	no	—
330	C₂²	—	4	2	no	—
331	C₂²	—	4	2	no	—
332	C₂²	—	8	1	no	—
333	C₂²	—	8	1	no	—
334	C₂²	—	8	1	no	—
335	C₂²	—	8	1	no	—
336	C₂²	C₂×C₂²⋊C₈×C₁₃₁	1	1	yes	characteristic
337	C₂²	#410×C₁₃₁	1	1	yes	characteristic
338	C₂²	#413×C₁₃₁	1	1	yes	characteristic
339	C₂²	C₂×#102×C₁₃₁	1	1	yes	characteristic
340	C₂²	#416×C₁₃₁	1	1	yes	characteristic
341	C₂²	C₂×#104×C₁₃₁	1	1	yes	characteristic
342	C₂²	C₂×#104×C₁₃₁	1	1	yes	characteristic
343	C₄	—	2	1	no	—
344	C₄	—	2	1	no	—
345	C₄	—	2	2	no	—
346	C₄	—	2	2	no	—
347	C₄	—	2	1	no	—
348	C₄	—	2	1	no	—
349	C₄	—	2	2	no	—
350	C₄	—	2	2	no	—
351	C₄	—	4	2	no	—
352	C₄	—	8	1	no	—
353	C₄	—	8	1	no	—
354	C₄	D₄⋊C₈×C₁₃₁	1	4	yes	—
355	C₂	—	8	2	no	—
356	C₂	#1458×C₁₃₁	1	1	yes	characteristic
357	C₂	C₂×D₄⋊C₈×C₁₃₁	1	1	yes	characteristic
358	C₂	#1476×C₁₃₁	1	1	yes	characteristic
359	C₂	#1500×C₁₃₁	1	1	yes	characteristic
360	C₂	#1502×C₁₃₁	1	1	yes	characteristic
361	C₂	#1524×C₁₃₁	1	1	yes	characteristic
362	C₂	#1540×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃₁	C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₈×C₁₃₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃₁
socle	C₂³×C₁₃₁	C₂×C₂²⋊C₄
prime radical	C₂²×D₄×C₁₃₁	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₁ ◁ C₄³×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₄⋊C₈×C₁₃₁	C₂	semidirect
3. #1744×C₁₃₁	C₂	semidirect
4. #1271×C₁₃₁	C₂	semidirect
28. C₄×D₄×C₁₃₁	C₈	semidirect
181. #7560	C₁₃₁	direct (N × H)
182. C₁₃₁	#7560	direct (N × H)
184. C₄×C₄⋊C₈	C₂×C₁₃₁	semidirect
185. #1744	C₂×C₁₃₁	semidirect
186. #1271	C₂×C₁₃₁	semidirect
210. C₄×D₄	C₈×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#2293×C₁₃₁	2
C₄×C₄⋊C₈×C₁₃₁	2
#1744×C₁₃₁	2
#1271×C₁₃₁	2
#1270×C₁₃₁	2
#7560	131

Subgroups — C131×#7560 #45693444

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#7560 #45693444