Subgroups — C₁₃₁×#33221 #45719105

Order 33536.

706 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	C₂×#499×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#3080×C₁₃₁	C₂	1	2	yes	maximal
3	C₄×#131×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	#1998×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#1952×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#1951×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#1848×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1816×C₁₃₁	C₂	1	2	yes	maximal
9	#1815×C₁₃₁	C₂	1	2	yes	maximal
10	C₂×#131×C₁₃₁	C₂²	1	1	yes	characteristic
11	C₂×#131×C₁₃₁	C₂²	1	1	yes	characteristic
12	C₂×#125×C₁₃₁	C₂²	1	2	yes	—
13	C₄×#41×C₁₃₁	C₂²	1	1	yes	characteristic
14	#499×C₁₃₁	—	2	1	no	—
15	#499×C₁₃₁	—	2	1	no	—
16	#499×C₁₃₁	—	2	1	no	—
17	#499×C₁₃₁	—	2	1	no	—
18	#479×C₁₃₁	—	2	4	no	—
19	#478×C₁₃₁	—	2	4	no	—
20	C₂×#108×C₁₃₁	C₂²	1	2	yes	—
21	C₂×#108×C₁₃₁	C₂²	1	2	yes	—
22	#428×C₁₃₁	C₂²	1	4	yes	—
23	C₂×#107×C₁₃₁	C₂²	1	2	yes	—
24	C₂×#106×C₁₃₁	C₂²	1	2	yes	—
25	#423×C₁₃₁	C₂²	1	2	yes	—
26	#417×C₁₃₁	C₂²	1	4	yes	—
27	#405×C₁₃₁	—	2	1	no	—
28	#405×C₁₃₁	—	2	1	no	—
29	#405×C₁₃₁	C₂²	1	1	yes	characteristic
30	#405×C₁₃₁	C₂²	1	1	yes	characteristic
31	C₄×M₁₆×C₁₃₁	—	2	1	no	—
32	C₄×M₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₁₃₁	—	2	1	no	—
34	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
35	#343×C₁₃₁	C₂²	1	4	yes	—
36	#343×C₁₃₁	C₂²	1	4	yes	—
37	C₂×#41×C₁₃₁	C₂³	1	1	yes	characteristic
38	#131×C₁₃₁	—	2	2	no	—
39	#131×C₁₃₁	—	2	2	no	—
40	#131×C₁₃₁	Q₈	1	4	yes	—
41	#131×C₁₃₁	Q₈	1	4	yes	—
42	C₂×M₁₆×C₁₃₁	—	2	1	no	—
43	C₂×M₁₆×C₁₃₁	—	2	1	no	—
44	C₂×M₁₆×C₁₃₁	C₂³	1	4	yes	—
45	C₂×M₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃₁	—	2	1	no	—
48	C₂²×C₈×C₁₃₁	—	2	1	no	—
49	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
51	#125×C₁₃₁	—	2	4	no	—
52	#125×C₁₃₁	—	2	2	no	—
53	#125×C₁₃₁	—	2	2	no	—
54	C₄×Q₈×C₁₃₁	D₄	1	2	yes	—
55	C₄×D₄×C₁₃₁	—	2	2	no	—
56	C₄×D₄×C₁₃₁	D₄	1	2	yes	—
57	#117×C₁₃₁	—	2	1	no	—
58	#117×C₁₃₁	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
60	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
61	C₂×C₄²×C₁₃₁	—	2	1	no	—
62	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
63	#108×C₁₃₁	—	2	4	no	—
64	#108×C₁₃₁	—	2	4	no	—
65	#107×C₁₃₁	—	2	2	no	—
66	#107×C₁₃₁	—	2	2	no	—
67	#107×C₁₃₁	—	2	4	no	—
68	#106×C₁₃₁	—	2	2	no	—
69	#106×C₁₃₁	—	2	2	no	—
70	#106×C₁₃₁	—	2	4	no	—
71	C₄⋊C₈×C₁₃₁	—	2	4	no	—
72	#103×C₁₃₁	—	2	4	no	—
73	#102×C₁₃₁	—	2	4	no	—
74	#97×C₁₃₁	—	2	1	no	—
75	#97×C₁₃₁	—	2	1	no	—
76	#97×C₁₃₁	—	2	1	no	—
77	C₄×C₈×C₁₃₁	—	2	1	no	—
78	C₄×C₈×C₁₃₁	—	2	1	no	—
79	C₄×C₈×C₁₃₁	—	2	1	no	—
80	C₄×C₈×C₁₃₁	D₄	1	1	yes	characteristic
81	C₄×C₈×C₁₃₁	D₄	1	1	yes	characteristic
82	C₄×C₈×C₁₃₁	D₄	1	1	yes	characteristic
83	C₄×C₈×C₁₃₁	D₄	1	1	yes	characteristic
84	#41×C₁₃₁	—	2	1	no	—
85	#41×C₁₃₁	—	2	1	no	—
86	#41×C₁₃₁	C₂×Q₈	1	2	yes	—
87	#41×C₁₃₁	C₂×Q₈	1	2	yes	—
88	C₂×Q₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
89	C₂×D₄×C₁₃₁	—	2	1	no	—
90	C₂×D₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃₁	—	2	1	no	—
92	C₂²×C₄×C₁₃₁	—	2	2	no	—
93	C₂²×C₄×C₁₃₁	—	2	4	no	—
94	C₂²×C₄×C₁₃₁	#41	1	2	yes	—
95	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
96	M₁₆×C₁₃₁	—	2	1	no	—
97	M₁₆×C₁₃₁	—	2	1	no	—
98	M₁₆×C₁₃₁	—	2	4	no	—
99	M₁₆×C₁₃₁	—	2	4	no	—
100	M₁₆×C₁₃₁	—	2	4	no	—
101	M₁₆×C₁₃₁	—	2	4	no	—
102	M₁₆×C₁₃₁	C₂×Q₈	1	2	yes	—
103	M₁₆×C₁₃₁	C₂×Q₈	1	2	yes	—
104	C₂×C₈×C₁₃₁	—	2	1	no	—
105	C₂×C₈×C₁₃₁	—	2	1	no	—
106	C₂×C₈×C₁₃₁	—	2	4	no	—
107	C₂×C₈×C₁₃₁	—	2	4	no	—
108	C₂×C₈×C₁₃₁	—	2	4	no	—
109	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
110	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃₁	C₂×Q₈	1	2	yes	—
114	C₂×C₈×C₁₃₁	C₂×Q₈	1	2	yes	—
115	C₂×C₈×C₁₃₁	#41	1	2	yes	—
116	C₂×C₈×C₁₃₁	#41	1	2	yes	—
117	C₄⋊C₄×C₁₃₁	—	2	2	no	—
118	C₄⋊C₄×C₁₃₁	—	2	4	no	—
119	C₄⋊C₄×C₁₃₁	—	2	4	no	—
120	C₄⋊C₄×C₁₃₁	—	4	4	no	—
121	C₄⋊C₄×C₁₃₁	—	4	4	no	—
122	C₄⋊C₄×C₁₃₁	C₂×D₄	1	2	yes	—
123	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
124	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
125	C₄²×C₁₃₁	—	2	2	no	—
126	C₄²×C₁₃₁	—	2	1	no	—
127	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₁₃₁	C₂×D₄	1	2	yes	—
130	C₂³×C₁₃₁	—	2	1	no	—
131	C₂³×C₁₃₁	C₂×#41	1	1	yes	characteristic
132	Q₈×C₁₃₁	—	2	1	no	—
133	Q₈×C₁₃₁	C₄⋊Q₈	1	2	yes	—
134	D₄×C₁₃₁	—	2	2	no	—
135	D₄×C₁₃₁	—	2	2	no	—
136	D₄×C₁₃₁	—	2	1	no	—
137	D₄×C₁₃₁	C₄⋊Q₈	1	2	yes	—
138	C₂×C₄×C₁₃₁	—	2	1	no	—
139	C₂×C₄×C₁₃₁	—	2	2	no	—
140	C₂×C₄×C₁₃₁	—	2	2	no	—
141	C₂×C₄×C₁₃₁	—	2	2	no	—
142	C₂×C₄×C₁₃₁	—	4	2	no	—
143	C₂×C₄×C₁₃₁	—	4	4	no	—
144	C₂×C₄×C₁₃₁	—	4	4	no	—
145	C₂×C₄×C₁₃₁	—	8	4	no	—
146	C₂×C₄×C₁₃₁	#121	1	2	yes	—
147	C₂×C₄×C₁₃₁	#121	1	2	yes	—
148	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
150	C₂×C₄×C₁₃₁	C₂²×Q₈	1	1	yes	characteristic
151	C₂×C₄×C₁₃₁	C₂²×Q₈	1	1	yes	characteristic
152	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
153	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
154	C₈×C₁₃₁	—	2	2	no	—
155	C₈×C₁₃₁	—	2	2	no	—
156	C₈×C₁₃₁	—	4	4	no	—
157	C₈×C₁₃₁	C₂²⋊Q₈	1	2	yes	—
158	C₈×C₁₃₁	C₂²⋊Q₈	1	2	yes	—
159	C₈×C₁₃₁	C₂²⋊Q₈	1	2	yes	—
160	C₈×C₁₃₁	C₂²⋊Q₈	1	2	yes	—
161	C₂²×C₁₃₁	—	2	2	no	—
162	C₂²×C₁₃₁	—	2	2	no	—
163	C₂²×C₁₃₁	—	4	2	no	—
164	C₂²×C₁₃₁	C₂×#121	1	1	yes	characteristic
165	C₂²×C₁₃₁	#533	1	1	yes	characteristic
166	C₂²×C₁₃₁	#533	1	1	yes	characteristic
167	C₄×C₁₃₁	—	2	2	no	—
168	C₄×C₁₃₁	—	2	2	no	—
169	C₄×C₁₃₁	—	2	2	no	—
170	C₄×C₁₃₁	—	4	2	no	—
171	C₄×C₁₃₁	—	8	4	no	—
172	C₄×C₁₃₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
173	C₄×C₁₃₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
174	C₄×C₁₃₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
175	C₄×C₁₃₁	#532	1	1	yes	characteristic
176	C₂×C₁₃₁	—	2	1	no	—
177	C₂×C₁₃₁	—	2	1	no	—
178	C₂×C₁₃₁	—	4	2	no	—
179	C₂×C₁₃₁	#2857	1	1	yes	characteristic
180	C₂×C₁₃₁	#3067	1	2	yes	—
181	#33221	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₁₃₁	#33221	1	1	yes	characteristic, direct product factor, Sylow
183	C₂×#499	C₂×C₁₃₁	1	1	yes	characteristic, complemented
184	#3080	C₂×C₁₃₁	1	2	yes	—
185	C₄×#131	C₂×C₁₃₁	1	1	yes	characteristic
186	#1998	C₂×C₁₃₁	1	2	yes	complemented
187	#1952	C₂×C₁₃₁	1	2	yes	complemented
188	#1951	C₂×C₁₃₁	1	2	yes	complemented
189	#1848	C₂×C₁₃₁	1	1	yes	characteristic, complemented
190	#1816	C₂×C₁₃₁	1	2	yes	—
191	#1815	C₂×C₁₃₁	1	2	yes	—
192	C₂×#131	C₂²×C₁₃₁	1	1	yes	characteristic
193	C₂×#131	C₂²×C₁₃₁	1	1	yes	characteristic
194	C₂×#125	C₂²×C₁₃₁	1	2	yes	—
195	C₄×#41	C₂²×C₁₃₁	1	1	yes	characteristic
196	#499	—	2	1	no	—
197	#499	—	2	1	no	—
198	#499	—	2	1	no	—
199	#499	—	2	1	no	—
200	#479	—	2	4	no	—
201	#478	—	2	4	no	—
202	C₂×#108	C₂²×C₁₃₁	1	2	yes	—
203	C₂×#108	C₂²×C₁₃₁	1	2	yes	—
204	#428	C₂²×C₁₃₁	1	4	yes	—
205	C₂×#107	C₂²×C₁₃₁	1	2	yes	—
206	C₂×#106	C₂²×C₁₃₁	1	2	yes	—
207	#423	C₂²×C₁₃₁	1	2	yes	—
208	#417	C₂²×C₁₃₁	1	4	yes	—
209	#405	—	2	1	no	—
210	#405	—	2	1	no	—
211	#405	C₂²×C₁₃₁	1	1	yes	characteristic
212	#405	C₂²×C₁₃₁	1	1	yes	characteristic
213	C₄×M₁₆	—	2	1	no	—
214	C₄×M₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
215	C₂×C₄×C₈	—	2	1	no	—
216	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
217	#343	C₂²×C₁₃₁	1	4	yes	—
218	#343	C₂²×C₁₃₁	1	4	yes	—
219	C₂×#41	C₂³×C₁₃₁	1	1	yes	characteristic
220	#131	—	2	2	no	—
221	#131	—	2	2	no	—
222	#131	Q₈×C₁₃₁	1	4	yes	—
223	#131	Q₈×C₁₃₁	1	4	yes	—
224	C₂×M₁₆	—	2	1	no	—
225	C₂×M₁₆	—	2	1	no	—
226	C₂×M₁₆	C₂³×C₁₃₁	1	4	yes	—
227	C₂×M₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
228	C₂×M₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
229	C₂²×C₈	—	2	1	no	—
230	C₂²×C₈	—	2	1	no	—
231	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
232	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
233	#125	—	2	4	no	—
234	#125	—	2	2	no	—
235	#125	—	2	2	no	—
236	C₄×Q₈	D₄×C₁₃₁	1	2	yes	—
237	C₄×D₄	—	2	2	no	—
238	C₄×D₄	D₄×C₁₃₁	1	2	yes	—
239	#117	—	2	1	no	—
240	#117	C₂³×C₁₃₁	1	1	yes	characteristic
241	C₂×C₄⋊C₄	—	2	4	no	—
242	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
243	C₂×C₄²	—	2	1	no	—
244	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
245	#108	—	2	4	no	—
246	#108	—	2	4	no	—
247	#107	—	2	2	no	—
248	#107	—	2	2	no	—
249	#107	—	2	4	no	—
250	#106	—	2	2	no	—
251	#106	—	2	2	no	—
252	#106	—	2	4	no	—
253	C₄⋊C₈	—	2	4	no	—
254	#103	—	2	4	no	—
255	#102	—	2	4	no	—
256	#97	—	2	1	no	—
257	#97	—	2	1	no	—
258	#97	—	2	1	no	—
259	C₄×C₈	—	2	1	no	—
260	C₄×C₈	—	2	1	no	—
261	C₄×C₈	—	2	1	no	—
262	C₄×C₈	D₄×C₁₃₁	1	1	yes	characteristic
263	C₄×C₈	D₄×C₁₃₁	1	1	yes	characteristic
264	C₄×C₈	D₄×C₁₃₁	1	1	yes	characteristic
265	C₄×C₈	D₄×C₁₃₁	1	1	yes	characteristic
266	#41	—	2	1	no	—
267	#41	—	2	1	no	—
268	#41	C₂×Q₈×C₁₃₁	1	2	yes	—
269	#41	C₂×Q₈×C₁₃₁	1	2	yes	—
270	C₂×Q₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
271	C₂×D₄	—	2	1	no	—
272	C₂×D₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	#41×C₁₃₁	1	2	yes	—
277	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
278	M₁₆	—	2	1	no	—
279	M₁₆	—	2	1	no	—
280	M₁₆	—	2	4	no	—
281	M₁₆	—	2	4	no	—
282	M₁₆	—	2	4	no	—
283	M₁₆	—	2	4	no	—
284	M₁₆	C₂×Q₈×C₁₃₁	1	2	yes	—
285	M₁₆	C₂×Q₈×C₁₃₁	1	2	yes	—
286	C₂×C₈	—	2	1	no	—
287	C₂×C₈	—	2	1	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	—	2	4	no	—
291	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
292	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
293	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
294	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
295	C₂×C₈	C₂×Q₈×C₁₃₁	1	2	yes	—
296	C₂×C₈	C₂×Q₈×C₁₃₁	1	2	yes	—
297	C₂×C₈	#41×C₁₃₁	1	2	yes	—
298	C₂×C₈	#41×C₁₃₁	1	2	yes	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	4	no	—
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	—	4	4	no	—
303	C₄⋊C₄	—	4	4	no	—
304	C₄⋊C₄	C₂×D₄×C₁₃₁	1	2	yes	—
305	C₂²⋊C₄	—	2	1	no	—
306	C₂²⋊C₄	—	2	2	no	—
307	C₄²	—	2	2	no	—
308	C₄²	—	2	1	no	—
309	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
310	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
311	C₄²	C₂×D₄×C₁₃₁	1	2	yes	—
312	C₂³	—	2	1	no	—
313	C₂³	C₂×#41×C₁₃₁	1	1	yes	characteristic
314	Q₈	—	2	1	no	—
315	Q₈	C₄⋊Q₈×C₁₃₁	1	2	yes	—
316	D₄	—	2	2	no	—
317	D₄	—	2	2	no	—
318	D₄	—	2	1	no	—
319	D₄	C₄⋊Q₈×C₁₃₁	1	2	yes	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	8	4	no	—
328	C₂×C₄	#121×C₁₃₁	1	2	yes	—
329	C₂×C₄	#121×C₁₃₁	1	2	yes	—
330	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
331	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
332	C₂×C₄	C₂²×Q₈×C₁₃₁	1	1	yes	characteristic
333	C₂×C₄	C₂²×Q₈×C₁₃₁	1	1	yes	characteristic
334	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
335	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
336	C₈	—	2	2	no	—
337	C₈	—	2	2	no	—
338	C₈	—	4	4	no	—
339	C₈	C₂²⋊Q₈×C₁₃₁	1	2	yes	—
340	C₈	C₂²⋊Q₈×C₁₃₁	1	2	yes	—
341	C₈	C₂²⋊Q₈×C₁₃₁	1	2	yes	—
342	C₈	C₂²⋊Q₈×C₁₃₁	1	2	yes	—
343	C₂²	—	2	2	no	—
344	C₂²	—	2	2	no	—
345	C₂²	—	4	2	no	—
346	C₂²	C₂×#121×C₁₃₁	1	1	yes	characteristic
347	C₂²	#533×C₁₃₁	1	1	yes	characteristic
348	C₂²	#533×C₁₃₁	1	1	yes	characteristic
349	C₄	—	2	2	no	—
350	C₄	—	2	2	no	—
351	C₄	—	2	2	no	—
352	C₄	—	4	2	no	—
353	C₄	—	8	4	no	—
354	C₄	C₂×C₂²⋊Q₈×C₁₃₁	1	1	yes	characteristic
355	C₄	C₂×C₂²⋊Q₈×C₁₃₁	1	1	yes	characteristic
356	C₄	C₂×C₄⋊Q₈×C₁₃₁	1	1	yes	characteristic
357	C₄	#532×C₁₃₁	1	1	yes	characteristic
358	C₂	—	2	1	no	—
359	C₂	—	2	1	no	—
360	C₂	—	4	2	no	—
361	C₂	#2857×C₁₃₁	1	1	yes	characteristic
362	C₂	#3067×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃₁	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂×#41×C₁₃₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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. C₂×#499×C₁₃₁	C₂	semidirect
4. #1998×C₁₃₁	C₂	semidirect
5. #1952×C₁₃₁	C₂	semidirect
6. #1951×C₁₃₁	C₂	semidirect
7. #1848×C₁₃₁	C₂	semidirect
181. #33221	C₁₃₁	direct (N × H)
182. C₁₃₁	#33221	direct (N × H)
183. C₂×#499	C₂×C₁₃₁	semidirect
186. #1998	C₂×C₁₃₁	semidirect
187. #1952	C₂×C₁₃₁	semidirect
188. #1951	C₂×C₁₃₁	semidirect
189. #1848	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#499×C₁₃₁	2
#3080×C₁₃₁	2
C₄×#131×C₁₃₁	2
#1998×C₁₃₁	2
#1952×C₁₃₁	2
#1951×C₁₃₁	2
#1848×C₁₃₁	2
#1816×C₁₃₁	2
#1815×C₁₃₁	2
#33221	131

Subgroups — C131×#33221 #45719105

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#33221 #45719105