Subgroups — C₁₃₁×#21369 #45707253

Order 33536.

826 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×#433×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2314×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#2274×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	#1949×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#1948×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#1854×C₁₃₁	C₂	1	2	yes	maximal
7	#1853×C₁₃₁	C₂	1	2	yes	maximal
8	#1776×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	C₄×#106×C₁₃₁	C₂	1	2	yes	maximal, complemented
10	C₂×#117×C₁₃₁	C₂²	1	1	yes	characteristic
11	C₂×#117×C₁₃₁	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
13	#433×C₁₃₁	C₄	1	8	yes	complemented
14	C₂×#107×C₁₃₁	C₂²	1	2	yes	—
15	C₂×#106×C₁₃₁	C₂²	1	2	yes	—
16	C₂×#106×C₁₃₁	C₂²	1	2	yes	—
17	C₂×#106×C₁₃₁	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	2	yes	—
19	C₂×C₂²⋊C₈×C₁₃₁	C₂²	1	2	yes	—
20	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
22	#388×C₁₃₁	—	2	2	no	—
23	#387×C₁₃₁	—	2	2	no	—
24	#384×C₁₃₁	C₂²	1	1	yes	characteristic
25	#382×C₁₃₁	C₂²	1	1	yes	characteristic
26	#380×C₁₃₁	C₂²	1	2	yes	—
27	C₄×C₄⋊C₄×C₁₃₁	—	2	2	no	—
28	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
30	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
31	C₄×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
32	#340×C₁₃₁	C₂²	1	2	yes	—
33	#340×C₁₃₁	C₂²	1	2	yes	—
34	#340×C₁₃₁	C₂²	1	2	yes	—
35	#340×C₁₃₁	C₂²	1	2	yes	—
36	C₂³×C₄×C₁₃₁	—	2	1	no	—
37	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
39	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
40	#117×C₁₃₁	—	2	4	no	—
41	#117×C₁₃₁	C₂×C₄	1	4	yes	—
42	#117×C₁₃₁	Q₈	1	4	yes	—
43	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
44	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
45	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₃₁	D₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
48	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
49	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
50	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
51	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
52	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
53	C₂×C₂²⋊C₄×C₁₃₁	D₄	1	2	yes	—
54	C₂×C₄²×C₁₃₁	—	2	1	no	—
55	C₂×C₄²×C₁₃₁	—	2	2	no	—
56	C₂×C₄²×C₁₃₁	—	2	2	no	—
57	C₂×C₄²×C₁₃₁	—	2	2	no	—
58	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
60	#107×C₁₃₁	—	2	4	no	—
61	#106×C₁₃₁	—	2	4	no	—
62	#106×C₁₃₁	—	2	4	no	—
63	#106×C₁₃₁	—	2	4	no	—
64	C₄⋊C₈×C₁₃₁	C₂×C₄	1	8	yes	complemented
65	C₂²⋊C₈×C₁₃₁	C₂×C₄	1	8	yes	—
66	#97×C₁₃₁	C₂×C₄	1	4	yes	complemented
67	C₄×C₈×C₁₃₁	C₂×C₄	1	4	yes	complemented
68	#95×C₁₃₁	—	2	2	no	—
69	#95×C₁₃₁	—	2	2	no	—
70	#95×C₁₃₁	—	2	2	no	—
71	#95×C₁₃₁	—	2	2	no	—
72	#95×C₁₃₁	—	2	2	no	—
73	C₂⁴×C₁₃₁	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃₁	—	2	2	no	—
75	C₂²×C₄×C₁₃₁	—	2	2	no	—
76	C₂²×C₄×C₁₃₁	—	2	2	no	—
77	C₂²×C₄×C₁₃₁	—	2	2	no	—
78	C₂²×C₄×C₁₃₁	—	2	4	no	—
79	C₂²×C₄×C₁₃₁	—	2	2	no	—
80	C₂²×C₄×C₁₃₁	—	2	2	no	—
81	C₂²×C₄×C₁₃₁	—	8	2	no	—
82	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
84	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃₁	C₂×Q₈	1	2	yes	—
87	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
88	C₂×C₈×C₁₃₁	—	2	2	no	—
89	C₂×C₈×C₁₃₁	—	2	2	no	—
90	C₂×C₈×C₁₃₁	—	2	2	no	—
91	C₂×C₈×C₁₃₁	—	2	2	no	—
92	C₂×C₈×C₁₃₁	C₂²×C₄	1	4	yes	—
93	C₂×C₈×C₁₃₁	C₂²×C₄	1	4	yes	—
94	C₄⋊C₄×C₁₃₁	—	2	4	no	—
95	C₄⋊C₄×C₁₃₁	—	2	2	no	—
96	C₄⋊C₄×C₁₃₁	—	2	2	no	—
97	C₄⋊C₄×C₁₃₁	—	2	2	no	—
98	C₄⋊C₄×C₁₃₁	—	2	2	no	—
99	C₄⋊C₄×C₁₃₁	—	2	2	no	—
100	C₄⋊C₄×C₁₃₁	—	2	2	no	—
101	C₄⋊C₄×C₁₃₁	—	8	2	no	—
102	C₄⋊C₄×C₁₃₁	C₄⋊C₄	1	8	yes	—
103	C₄⋊C₄×C₁₃₁	#41	1	4	yes	—
104	C₄⋊C₄×C₁₃₁	#41	1	4	yes	—
105	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
106	C₂²⋊C₄×C₁₃₁	—	8	2	no	—
107	C₂²⋊C₄×C₁₃₁	C₄⋊C₄	1	8	yes	—
108	C₄²×C₁₃₁	—	2	4	no	—
109	C₄²×C₁₃₁	—	8	2	no	—
110	C₄²×C₁₃₁	—	8	2	no	—
111	C₄²×C₁₃₁	—	8	2	no	—
112	C₄²×C₁₃₁	C₂²×C₄	1	2	yes	—
113	C₄²×C₁₃₁	C₂²×C₄	1	2	yes	—
114	C₄²×C₁₃₁	C₂×Q₈	1	2	yes	—
115	C₄²×C₁₃₁	C₂×Q₈	1	2	yes	—
116	C₂³×C₁₃₁	—	2	1	no	—
117	C₂³×C₁₃₁	—	2	1	no	—
118	C₂³×C₁₃₁	—	2	2	no	—
119	C₂³×C₁₃₁	—	2	2	no	—
120	C₂³×C₁₃₁	C₂×C₄⋊C₄	1	2	yes	—
121	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
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	—	2	2	no	—
126	C₂×C₄×C₁₃₁	—	2	2	no	—
127	C₂×C₄×C₁₃₁	—	2	2	no	—
128	C₂×C₄×C₁₃₁	—	2	4	no	—
129	C₂×C₄×C₁₃₁	—	2	4	no	—
130	C₂×C₄×C₁₃₁	—	2	4	no	—
131	C₂×C₄×C₁₃₁	—	2	4	no	—
132	C₂×C₄×C₁₃₁	—	4	2	no	—
133	C₂×C₄×C₁₃₁	—	4	2	no	—
134	C₂×C₄×C₁₃₁	—	4	2	no	—
135	C₂×C₄×C₁₃₁	—	4	2	no	—
136	C₂×C₄×C₁₃₁	—	4	2	no	—
137	C₂×C₄×C₁₃₁	—	4	2	no	—
138	C₂×C₄×C₁₃₁	—	4	2	no	—
139	C₂×C₄×C₁₃₁	—	4	2	no	—
140	C₂×C₄×C₁₃₁	—	4	2	no	—
141	C₂×C₄×C₁₃₁	—	4	2	no	—
142	C₂×C₄×C₁₃₁	—	8	4	no	—
143	C₂×C₄×C₁₃₁	C₂×C₄⋊C₄	1	4	yes	—
144	C₂×C₄×C₁₃₁	C₂×C₄⋊C₄	1	4	yes	—
145	C₂×C₄×C₁₃₁	C₂×C₄⋊C₄	1	2	yes	—
146	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₃₁	C₂²×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
149	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
150	C₈×C₁₃₁	—	2	4	no	—
151	C₈×C₁₃₁	—	2	4	no	—
152	C₂²×C₁₃₁	—	2	4	no	—
153	C₂²×C₁₃₁	—	2	2	no	—
154	C₂²×C₁₃₁	—	4	1	no	—
155	C₂²×C₁₃₁	—	4	2	no	—
156	C₂²×C₁₃₁	—	4	1	no	—
157	C₂²×C₁₃₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
158	C₂²×C₁₃₁	#525	1	1	yes	characteristic
159	C₂²×C₁₃₁	#525	1	1	yes	characteristic
160	C₂²×C₁₃₁	#577	1	2	yes	—
161	C₂²×C₁₃₁	#577	1	2	yes	—
162	C₄×C₁₃₁	—	2	4	no	—
163	C₄×C₁₃₁	—	2	4	no	—
164	C₄×C₁₃₁	—	2	2	no	—
165	C₄×C₁₃₁	—	4	4	no	—
166	C₄×C₁₃₁	—	4	4	no	—
167	C₄×C₁₃₁	—	8	2	no	—
168	C₄×C₁₃₁	—	8	2	no	—
169	C₄×C₁₃₁	C₄×#41	1	2	yes	—
170	C₄×C₁₃₁	#533	1	2	yes	—
171	C₂×C₁₃₁	—	4	2	no	—
172	C₂×C₁₃₁	#2296	1	1	yes	characteristic
173	C₂×C₁₃₁	#2912	1	2	yes	—
174	C₂×C₁₃₁	#3123	1	1	yes	characteristic
175	C₂×C₁₃₁	#3125	1	2	yes	—
176	C₂×C₁₃₁	#3126	1	1	yes	characteristic
177	#21369	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₁₃₁	#21369	1	1	yes	characteristic, direct product factor, Sylow
179	C₂×#433	C₂×C₁₃₁	1	1	yes	characteristic
180	#2314	C₂×C₁₃₁	1	1	yes	characteristic
181	#2274	C₂×C₁₃₁	1	1	yes	characteristic
182	#1949	C₂×C₁₃₁	1	2	yes	complemented
183	#1948	C₂×C₁₃₁	1	2	yes	complemented
184	#1854	C₂×C₁₃₁	1	2	yes	—
185	#1853	C₂×C₁₃₁	1	2	yes	—
186	#1776	C₂×C₁₃₁	1	2	yes	complemented
187	C₄×#106	C₂×C₁₃₁	1	2	yes	complemented
188	C₂×#117	C₂²×C₁₃₁	1	1	yes	characteristic
189	C₂×#117	C₂²×C₁₃₁	1	1	yes	characteristic
190	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
191	#433	C₄×C₁₃₁	1	8	yes	complemented
192	C₂×#107	C₂²×C₁₃₁	1	2	yes	—
193	C₂×#106	C₂²×C₁₃₁	1	2	yes	—
194	C₂×#106	C₂²×C₁₃₁	1	2	yes	—
195	C₂×#106	C₂²×C₁₃₁	1	2	yes	—
196	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	2	yes	—
197	C₂×C₂²⋊C₈	C₂²×C₁₃₁	1	2	yes	—
198	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
199	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
200	#388	—	2	2	no	—
201	#387	—	2	2	no	—
202	#384	C₂²×C₁₃₁	1	1	yes	characteristic
203	#382	C₂²×C₁₃₁	1	1	yes	characteristic
204	#380	C₂²×C₁₃₁	1	2	yes	—
205	C₄×C₄⋊C₄	—	2	2	no	—
206	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
207	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
208	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
209	C₄×C₂²⋊C₄	—	2	2	no	—
210	#340	C₂²×C₁₃₁	1	2	yes	—
211	#340	C₂²×C₁₃₁	1	2	yes	—
212	#340	C₂²×C₁₃₁	1	2	yes	—
213	#340	C₂²×C₁₃₁	1	2	yes	—
214	C₂³×C₄	—	2	1	no	—
215	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
216	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
217	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
218	#117	—	2	4	no	—
219	#117	C₂×C₄×C₁₃₁	1	4	yes	—
220	#117	Q₈×C₁₃₁	1	4	yes	—
221	C₂×C₄⋊C₄	—	2	1	no	—
222	C₂×C₄⋊C₄	—	2	4	no	—
223	C₂×C₄⋊C₄	—	2	2	no	—
224	C₂×C₄⋊C₄	D₄×C₁₃₁	1	2	yes	—
225	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
226	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
227	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
228	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
229	C₂×C₂²⋊C₄	—	2	1	no	—
230	C₂×C₂²⋊C₄	—	2	2	no	—
231	C₂×C₂²⋊C₄	D₄×C₁₃₁	1	2	yes	—
232	C₂×C₄²	—	2	1	no	—
233	C₂×C₄²	—	2	2	no	—
234	C₂×C₄²	—	2	2	no	—
235	C₂×C₄²	—	2	2	no	—
236	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
237	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
238	#107	—	2	4	no	—
239	#106	—	2	4	no	—
240	#106	—	2	4	no	—
241	#106	—	2	4	no	—
242	C₄⋊C₈	C₂×C₄×C₁₃₁	1	8	yes	complemented
243	C₂²⋊C₈	C₂×C₄×C₁₃₁	1	8	yes	—
244	#97	C₂×C₄×C₁₃₁	1	4	yes	complemented
245	C₄×C₈	C₂×C₄×C₁₃₁	1	4	yes	complemented
246	#95	—	2	2	no	—
247	#95	—	2	2	no	—
248	#95	—	2	2	no	—
249	#95	—	2	2	no	—
250	#95	—	2	2	no	—
251	C₂⁴	C₂×D₄×C₁₃₁	1	1	yes	characteristic
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	8	2	no	—
260	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
261	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
262	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
263	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
264	C₂²×C₄	C₂×Q₈×C₁₃₁	1	2	yes	—
265	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	C₂²×C₄×C₁₃₁	1	4	yes	—
271	C₂×C₈	C₂²×C₄×C₁₃₁	1	4	yes	—
272	C₄⋊C₄	—	2	4	no	—
273	C₄⋊C₄	—	2	2	no	—
274	C₄⋊C₄	—	2	2	no	—
275	C₄⋊C₄	—	2	2	no	—
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	2	2	no	—
278	C₄⋊C₄	—	2	2	no	—
279	C₄⋊C₄	—	8	2	no	—
280	C₄⋊C₄	C₄⋊C₄×C₁₃₁	1	8	yes	—
281	C₄⋊C₄	#41×C₁₃₁	1	4	yes	—
282	C₄⋊C₄	#41×C₁₃₁	1	4	yes	—
283	C₂²⋊C₄	—	2	4	no	—
284	C₂²⋊C₄	—	8	2	no	—
285	C₂²⋊C₄	C₄⋊C₄×C₁₃₁	1	8	yes	—
286	C₄²	—	2	4	no	—
287	C₄²	—	8	2	no	—
288	C₄²	—	8	2	no	—
289	C₄²	—	8	2	no	—
290	C₄²	C₂²×C₄×C₁₃₁	1	2	yes	—
291	C₄²	C₂²×C₄×C₁₃₁	1	2	yes	—
292	C₄²	C₂×Q₈×C₁₃₁	1	2	yes	—
293	C₄²	C₂×Q₈×C₁₃₁	1	2	yes	—
294	C₂³	—	2	1	no	—
295	C₂³	—	2	1	no	—
296	C₂³	—	2	2	no	—
297	C₂³	—	2	2	no	—
298	C₂³	C₂×C₄⋊C₄×C₁₃₁	1	2	yes	—
299	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	4	2	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	8	4	no	—
321	C₂×C₄	C₂×C₄⋊C₄×C₁₃₁	1	4	yes	—
322	C₂×C₄	C₂×C₄⋊C₄×C₁₃₁	1	4	yes	—
323	C₂×C₄	C₂×C₄⋊C₄×C₁₃₁	1	2	yes	—
324	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
325	C₂×C₄	C₂²×Q₈×C₁₃₁	1	1	yes	characteristic
326	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
327	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
328	C₈	—	2	4	no	—
329	C₈	—	2	4	no	—
330	C₂²	—	2	2	no	—
331	C₂²	—	2	4	no	—
332	C₂²	—	4	1	no	—
333	C₂²	—	4	2	no	—
334	C₂²	—	4	1	no	—
335	C₂²	C₂²×C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
336	C₂²	#525×C₁₃₁	1	1	yes	characteristic
337	C₂²	#525×C₁₃₁	1	1	yes	characteristic
338	C₂²	#577×C₁₃₁	1	2	yes	—
339	C₂²	#577×C₁₃₁	1	2	yes	—
340	C₄	—	2	2	no	—
341	C₄	—	2	4	no	—
342	C₄	—	2	4	no	—
343	C₄	—	4	4	no	—
344	C₄	—	4	4	no	—
345	C₄	—	8	2	no	—
346	C₄	—	8	2	no	—
347	C₄	C₄×#41×C₁₃₁	1	2	yes	—
348	C₄	#533×C₁₃₁	1	2	yes	—
349	C₂	—	4	2	no	—
350	C₂	#2296×C₁₃₁	1	1	yes	characteristic
351	C₂	#2912×C₁₃₁	1	2	yes	—
352	C₂	#3123×C₁₃₁	1	1	yes	characteristic
353	C₂	#3125×C₁₃₁	1	2	yes	—
354	C₂	#3126×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂⁴×C₁₃₁	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ C₂×#117×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. #1949×C₁₃₁	C₂	semidirect
5. #1948×C₁₃₁	C₂	semidirect
8. #1776×C₁₃₁	C₂	semidirect
9. C₄×#106×C₁₃₁	C₂	semidirect
13. #433×C₁₃₁	C₄	semidirect
64. C₄⋊C₈×C₁₃₁	C₂×C₄	semidirect
66. #97×C₁₃₁	C₂×C₄	semidirect
67. C₄×C₈×C₁₃₁	C₂×C₄	semidirect
177. #21369	C₁₃₁	direct (N × H)
178. C₁₃₁	#21369	direct (N × H)
182. #1949	C₂×C₁₃₁	semidirect
183. #1948	C₂×C₁₃₁	semidirect
186. #1776	C₂×C₁₃₁	semidirect
187. C₄×#106	C₂×C₁₃₁	semidirect
191. #433	C₄×C₁₃₁	semidirect
242. C₄⋊C₈	C₂×C₄×C₁₃₁	semidirect
244. #97	C₂×C₄×C₁₃₁	semidirect
245. C₄×C₈	C₂×C₄×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#433×C₁₃₁	2
#2314×C₁₃₁	2
#2274×C₁₃₁	2
#1949×C₁₃₁	2
#1948×C₁₃₁	2
#1854×C₁₃₁	2
#1853×C₁₃₁	2
#1776×C₁₃₁	2
C₄×#106×C₁₃₁	2
#21369	131

Subgroups — C131×#21369 #45707253

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#21369 #45707253