Subgroups — C₁₃₁×#23202 #45709086

Order 33536.

960 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#496×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2949×C₁₃₁	C₂	1	2	yes	maximal, complemented
3	#2948×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	#1978×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#1977×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#1888×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#1887×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#1885×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#1773×C₁₃₁	C₂	1	2	yes	maximal, complemented
10	C₂²×SD₁₆×C₁₃₁	C₂²	1	2	yes	—
11	C₂²×D₈×C₁₃₁	C₂²	1	2	yes	—
12	C₂×#127×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂×#124×C₁₃₁	C₂²	1	1	yes	characteristic
14	#519×C₁₃₁	C₂²	1	1	yes	characteristic
15	#518×C₁₃₁	C₂²	1	1	yes	characteristic
16	#518×C₁₃₁	C₂²	1	2	yes	—
17	#496×C₁₃₁	C₄	1	8	yes	complemented
18	#442×C₁₃₁	—	2	4	no	—
19	#440×C₁₃₁	—	2	4	no	—
20	C₄×SD₁₆×C₁₃₁	—	2	4	no	—
21	C₄×D₈×C₁₃₁	—	2	4	no	—
22	C₂×#108×C₁₃₁	C₂²	1	2	yes	—
23	#427×C₁₃₁	C₂²	1	2	yes	—
24	#419×C₁₃₁	C₂²	1	2	yes	—
25	#418×C₁₃₁	C₂²	1	2	yes	—
26	#418×C₁₃₁	C₂²	1	2	yes	—
27	#418×C₁₃₁	C₂²	1	2	yes	—
28	C₂×#101×C₁₃₁	C₂²	1	1	yes	characteristic
29	C₂×#100×C₁₃₁	C₂²	1	2	yes	—
30	C₂×#100×C₁₃₁	C₂²	1	1	yes	characteristic
31	#405×C₁₃₁	C₂²	1	2	yes	—
32	#405×C₁₃₁	C₂²	1	2	yes	—
33	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
34	#339×C₁₃₁	C₂²	1	2	yes	—
35	#339×C₁₃₁	C₂²	1	2	yes	—
36	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
37	C₂²×D₄×C₁₃₁	—	4	1	no	—
38	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
39	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
40	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
41	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
42	C₂×SD₁₆×C₁₃₁	—	2	4	no	—
43	C₂×SD₁₆×C₁₃₁	C₂×C₄	1	8	yes	complemented
44	C₂×D₈×C₁₃₁	—	2	2	no	—
45	C₂×D₈×C₁₃₁	—	2	2	no	—
46	C₂×D₈×C₁₃₁	—	2	4	no	—
47	C₂×D₈×C₁₃₁	C₂×C₄	1	8	yes	complemented
48	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
49	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
51	#127×C₁₃₁	—	4	1	no	—
52	#127×C₁₃₁	C₂×C₄	1	4	yes	complemented
53	#124×C₁₃₁	—	4	1	no	—
54	#124×C₁₃₁	C₂×C₄	1	4	yes	complemented
55	C₄×Q₈×C₁₃₁	—	2	4	no	—
56	C₄×D₄×C₁₃₁	—	2	4	no	—
57	C₄×D₄×C₁₃₁	—	2	4	no	—
58	C₄×D₄×C₁₃₁	—	2	4	no	—
59	#117×C₁₃₁	—	4	1	no	—
60	#117×C₁₃₁	C₂³	1	2	yes	—
61	#117×C₁₃₁	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₃₁	—	4	1	no	—
63	C₂×C₂²⋊C₄×C₁₃₁	—	4	2	no	—
64	C₂×C₂²⋊C₄×C₁₃₁	—	4	1	no	—
65	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
66	#108×C₁₃₁	—	2	4	no	—
67	#107×C₁₃₁	D₄	1	4	yes	complemented
68	#106×C₁₃₁	D₄	1	4	yes	complemented
69	#103×C₁₃₁	—	2	4	no	—
70	#102×C₁₃₁	—	2	4	no	—
71	#102×C₁₃₁	—	2	4	no	—
72	#102×C₁₃₁	—	2	4	no	—
73	#101×C₁₃₁	—	4	1	no	—
74	#100×C₁₃₁	—	4	1	no	—
75	#100×C₁₃₁	—	4	2	no	—
76	#97×C₁₃₁	—	2	2	no	—
77	#97×C₁₃₁	—	2	2	no	—
78	#97×C₁₃₁	C₂×C₄	1	4	yes	complemented
79	C₄×C₈×C₁₃₁	—	2	2	no	—
80	C₄×C₈×C₁₃₁	—	2	2	no	—
81	C₂⁴×C₁₃₁	—	2	1	no	—
82	C₂⁴×C₁₃₁	—	2	2	no	—
83	C₂×Q₈×C₁₃₁	—	2	1	no	—
84	C₂×Q₈×C₁₃₁	—	2	2	no	—
85	C₂×Q₈×C₁₃₁	—	2	2	no	—
86	C₂×Q₈×C₁₃₁	C₂²×C₄	1	2	yes	—
87	C₂×D₄×C₁₃₁	—	2	2	no	—
88	C₂×D₄×C₁₃₁	—	2	2	no	—
89	C₂×D₄×C₁₃₁	—	2	2	no	—
90	C₂×D₄×C₁₃₁	—	2	2	no	—
91	C₂×D₄×C₁₃₁	—	2	2	no	—
92	C₂×D₄×C₁₃₁	—	2	2	no	—
93	C₂×D₄×C₁₃₁	—	2	1	no	—
94	C₂×D₄×C₁₃₁	—	2	2	no	—
95	C₂×D₄×C₁₃₁	—	4	4	no	—
96	C₂×D₄×C₁₃₁	—	8	4	no	—
97	C₂×D₄×C₁₃₁	C₂²×C₄	1	2	yes	—
98	C₂×D₄×C₁₃₁	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₁₃₁	—	2	1	no	—
100	C₂²×C₄×C₁₃₁	—	2	1	no	—
101	C₂²×C₄×C₁₃₁	—	4	4	no	—
102	C₂²×C₄×C₁₃₁	—	4	2	no	—
103	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
104	SD₁₆×C₁₃₁	—	2	8	no	—
105	SD₁₆×C₁₃₁	—	2	8	no	—
106	D₈×C₁₃₁	—	2	8	no	—
107	D₈×C₁₃₁	—	2	8	no	—
108	M₁₆×C₁₃₁	—	2	2	no	—
109	M₁₆×C₁₃₁	—	2	2	no	—
110	M₁₆×C₁₃₁	—	2	2	no	—
111	M₁₆×C₁₃₁	—	2	2	no	—
112	C₂×C₈×C₁₃₁	—	2	2	no	—
113	C₂×C₈×C₁₃₁	—	2	2	no	—
114	C₂×C₈×C₁₃₁	C₂²×C₄	1	4	yes	—
115	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₁₃₁	#41	1	4	yes	—
118	C₄⋊C₄×C₁₃₁	—	4	2	no	—
119	C₄⋊C₄×C₁₃₁	C₂×D₄	1	4	yes	—
120	C₄⋊C₄×C₁₃₁	C₂×D₄	1	4	yes	—
121	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
122	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
123	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
124	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
125	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
126	C₄²×C₁₃₁	—	2	2	no	—
127	C₄²×C₁₃₁	—	2	2	no	—
128	C₄²×C₁₃₁	—	2	1	no	—
129	C₄²×C₁₃₁	—	4	2	no	—
130	C₄²×C₁₃₁	C₂²×C₄	1	2	yes	—
131	C₂³×C₁₃₁	—	2	2	no	—
132	C₂³×C₁₃₁	—	2	4	no	—
133	C₂³×C₁₃₁	—	4	1	no	—
134	C₂³×C₁₃₁	—	4	2	no	—
135	C₂³×C₁₃₁	—	4	1	no	—
136	C₂³×C₁₃₁	—	4	2	no	—
137	C₂³×C₁₃₁	—	8	4	no	—
138	C₂³×C₁₃₁	—	8	2	no	—
139	C₂³×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
140	Q₈×C₁₃₁	—	2	4	no	—
141	Q₈×C₁₃₁	—	4	2	no	—
142	D₄×C₁₃₁	—	2	4	no	—
143	D₄×C₁₃₁	—	2	4	no	—
144	D₄×C₁₃₁	—	2	4	no	—
145	D₄×C₁₃₁	—	4	2	no	—
146	D₄×C₁₃₁	—	4	2	no	—
147	D₄×C₁₃₁	—	4	2	no	—
148	D₄×C₁₃₁	—	8	8	no	—
149	C₂×C₄×C₁₃₁	—	2	2	no	—
150	C₂×C₄×C₁₃₁	—	2	2	no	—
151	C₂×C₄×C₁₃₁	—	2	4	no	—
152	C₂×C₄×C₁₃₁	—	2	4	no	—
153	C₂×C₄×C₁₃₁	—	4	2	no	—
154	C₂×C₄×C₁₃₁	—	4	1	no	—
155	C₂×C₄×C₁₃₁	—	4	1	no	—
156	C₂×C₄×C₁₃₁	—	16	4	no	—
157	C₂×C₄×C₁₃₁	—	16	2	no	—
158	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₃₁	C₂²×D₄	1	2	yes	—
160	C₂×C₄×C₁₃₁	C₂×#41	1	2	yes	—
161	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
162	C₈×C₁₃₁	—	4	2	no	—
163	C₈×C₁₃₁	—	4	2	no	—
164	C₈×C₁₃₁	C₄×D₄	1	4	yes	—
165	C₈×C₁₃₁	C₄×D₄	1	4	yes	—
166	C₂²×C₁₃₁	—	2	2	no	—
167	C₂²×C₁₃₁	—	4	2	no	—
168	C₂²×C₁₃₁	—	4	4	no	—
169	C₂²×C₁₃₁	—	8	4	no	—
170	C₂²×C₁₃₁	—	8	2	no	—
171	C₂²×C₁₃₁	—	8	4	no	—
172	C₂²×C₁₃₁	—	8	2	no	—
173	C₂²×C₁₃₁	—	16	2	no	—
174	C₂²×C₁₃₁	—	16	1	no	—
175	C₂²×C₁₃₁	#518	1	1	yes	characteristic
176	C₂²×C₁₃₁	D₄²	1	1	yes	characteristic
177	C₂²×C₁₃₁	#559	1	1	yes	characteristic
178	C₄×C₁₃₁	—	4	2	no	—
179	C₄×C₁₃₁	—	4	2	no	—
180	C₄×C₁₃₁	—	4	4	no	—
181	C₄×C₁₃₁	—	4	4	no	—
182	C₄×C₁₃₁	C₂×C₄×D₄	1	2	yes	—
183	C₄×C₁₃₁	#550	1	2	yes	—
184	C₂×C₁₃₁	—	2	1	no	—
185	C₂×C₁₃₁	—	2	1	no	—
186	C₂×C₁₃₁	—	8	4	no	—
187	C₂×C₁₃₁	—	8	2	no	—
188	C₂×C₁₃₁	#2366	1	1	yes	characteristic
189	C₂×C₁₃₁	#3288	1	2	yes	—
190	#23202	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₁₃₁	#23202	1	1	yes	characteristic, direct product factor, Sylow
192	C₂×#496	C₂×C₁₃₁	1	1	yes	characteristic
193	#2949	C₂×C₁₃₁	1	2	yes	complemented
194	#2948	C₂×C₁₃₁	1	2	yes	complemented
195	#1978	C₂×C₁₃₁	1	2	yes	complemented
196	#1977	C₂×C₁₃₁	1	2	yes	complemented
197	#1888	C₂×C₁₃₁	1	1	yes	characteristic, complemented
198	#1887	C₂×C₁₃₁	1	2	yes	complemented
199	#1885	C₂×C₁₃₁	1	1	yes	characteristic, complemented
200	#1773	C₂×C₁₃₁	1	2	yes	complemented
201	C₂²×SD₁₆	C₂²×C₁₃₁	1	2	yes	—
202	C₂²×D₈	C₂²×C₁₃₁	1	2	yes	—
203	C₂×#127	C₂²×C₁₃₁	1	1	yes	characteristic
204	C₂×#124	C₂²×C₁₃₁	1	1	yes	characteristic
205	#519	C₂²×C₁₃₁	1	1	yes	characteristic
206	#518	C₂²×C₁₃₁	1	1	yes	characteristic
207	#518	C₂²×C₁₃₁	1	2	yes	—
208	#496	C₄×C₁₃₁	1	8	yes	complemented
209	#442	—	2	4	no	—
210	#440	—	2	4	no	—
211	C₄×SD₁₆	—	2	4	no	—
212	C₄×D₈	—	2	4	no	—
213	C₂×#108	C₂²×C₁₃₁	1	2	yes	—
214	#427	C₂²×C₁₃₁	1	2	yes	—
215	#419	C₂²×C₁₃₁	1	2	yes	—
216	#418	C₂²×C₁₃₁	1	2	yes	—
217	#418	C₂²×C₁₃₁	1	2	yes	—
218	#418	C₂²×C₁₃₁	1	2	yes	—
219	C₂×#101	C₂²×C₁₃₁	1	1	yes	characteristic
220	C₂×#100	C₂²×C₁₃₁	1	1	yes	characteristic
221	C₂×#100	C₂²×C₁₃₁	1	2	yes	—
222	#405	C₂²×C₁₃₁	1	2	yes	—
223	#405	C₂²×C₁₃₁	1	2	yes	—
224	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
225	#339	C₂²×C₁₃₁	1	2	yes	—
226	#339	C₂²×C₁₃₁	1	2	yes	—
227	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
228	C₂²×D₄	—	4	1	no	—
229	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
230	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
231	C₂×SD₁₆	—	2	2	no	—
232	C₂×SD₁₆	—	2	2	no	—
233	C₂×SD₁₆	—	2	4	no	—
234	C₂×SD₁₆	C₂×C₄×C₁₃₁	1	8	yes	complemented
235	C₂×D₈	—	2	2	no	—
236	C₂×D₈	—	2	2	no	—
237	C₂×D₈	—	2	4	no	—
238	C₂×D₈	C₂×C₄×C₁₃₁	1	8	yes	complemented
239	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
240	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
241	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
242	#127	—	4	1	no	—
243	#127	C₂×C₄×C₁₃₁	1	4	yes	complemented
244	#124	—	4	1	no	—
245	#124	C₂×C₄×C₁₃₁	1	4	yes	complemented
246	C₄×Q₈	—	2	4	no	—
247	C₄×D₄	—	2	4	no	—
248	C₄×D₄	—	2	4	no	—
249	C₄×D₄	—	2	4	no	—
250	#117	—	4	1	no	—
251	#117	C₂³×C₁₃₁	1	2	yes	—
252	#117	C₂³×C₁₃₁	1	2	yes	—
253	C₂×C₂²⋊C₄	—	4	1	no	—
254	C₂×C₂²⋊C₄	—	4	2	no	—
255	C₂×C₂²⋊C₄	—	4	1	no	—
256	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
257	#108	—	2	4	no	—
258	#107	D₄×C₁₃₁	1	4	yes	complemented
259	#106	D₄×C₁₃₁	1	4	yes	complemented
260	#103	—	2	4	no	—
261	#102	—	2	4	no	—
262	#102	—	2	4	no	—
263	#102	—	2	4	no	—
264	#101	—	4	1	no	—
265	#100	—	4	1	no	—
266	#100	—	4	2	no	—
267	#97	—	2	2	no	—
268	#97	—	2	2	no	—
269	#97	C₂×C₄×C₁₃₁	1	4	yes	complemented
270	C₄×C₈	—	2	2	no	—
271	C₄×C₈	—	2	2	no	—
272	C₂⁴	—	2	1	no	—
273	C₂⁴	—	2	2	no	—
274	C₂×Q₈	—	2	1	no	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	C₂²×C₄×C₁₃₁	1	2	yes	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	2	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	2	no	—
286	C₂×D₄	—	4	4	no	—
287	C₂×D₄	—	8	4	no	—
288	C₂×D₄	C₂²×C₄×C₁₃₁	1	2	yes	—
289	C₂×D₄	C₂²×C₄×C₁₃₁	1	4	yes	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	4	4	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
295	SD₁₆	—	2	8	no	—
296	SD₁₆	—	2	8	no	—
297	D₈	—	2	8	no	—
298	D₈	—	2	8	no	—
299	M₁₆	—	2	2	no	—
300	M₁₆	—	2	2	no	—
301	M₁₆	—	2	2	no	—
302	M₁₆	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	C₂²×C₄×C₁₃₁	1	4	yes	—
306	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
307	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
308	C₂×C₈	#41×C₁₃₁	1	4	yes	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	C₂×D₄×C₁₃₁	1	4	yes	—
311	C₄⋊C₄	C₂×D₄×C₁₃₁	1	4	yes	—
312	C₂²⋊C₄	—	2	2	no	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	4	4	no	—
315	C₂²⋊C₄	—	4	4	no	—
316	C₂²⋊C₄	—	4	2	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	1	no	—
320	C₄²	—	4	2	no	—
321	C₄²	C₂²×C₄×C₁₃₁	1	2	yes	—
322	C₂³	—	2	2	no	—
323	C₂³	—	2	4	no	—
324	C₂³	—	4	1	no	—
325	C₂³	—	4	2	no	—
326	C₂³	—	4	1	no	—
327	C₂³	—	4	2	no	—
328	C₂³	—	8	4	no	—
329	C₂³	—	8	2	no	—
330	C₂³	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
331	Q₈	—	2	4	no	—
332	Q₈	—	4	2	no	—
333	D₄	—	2	4	no	—
334	D₄	—	2	4	no	—
335	D₄	—	2	4	no	—
336	D₄	—	4	2	no	—
337	D₄	—	4	2	no	—
338	D₄	—	4	2	no	—
339	D₄	—	8	8	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	16	2	no	—
348	C₂×C₄	—	16	4	no	—
349	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
350	C₂×C₄	C₂²×D₄×C₁₃₁	1	2	yes	—
351	C₂×C₄	C₂×#41×C₁₃₁	1	2	yes	—
352	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
353	C₈	—	4	2	no	—
354	C₈	—	4	2	no	—
355	C₈	C₄×D₄×C₁₃₁	1	4	yes	—
356	C₈	C₄×D₄×C₁₃₁	1	4	yes	—
357	C₂²	—	2	2	no	—
358	C₂²	—	4	2	no	—
359	C₂²	—	4	4	no	—
360	C₂²	—	8	4	no	—
361	C₂²	—	8	2	no	—
362	C₂²	—	8	4	no	—
363	C₂²	—	8	2	no	—
364	C₂²	—	16	2	no	—
365	C₂²	—	16	1	no	—
366	C₂²	#518×C₁₃₁	1	1	yes	characteristic
367	C₂²	D₄²×C₁₃₁	1	1	yes	characteristic
368	C₂²	#559×C₁₃₁	1	1	yes	characteristic
369	C₄	—	4	2	no	—
370	C₄	—	4	4	no	—
371	C₄	—	4	4	no	—
372	C₄	—	4	2	no	—
373	C₄	C₂×C₄×D₄×C₁₃₁	1	2	yes	—
374	C₄	#550×C₁₃₁	1	2	yes	—
375	C₂	—	2	1	no	—
376	C₂	—	2	1	no	—
377	C₂	—	8	4	no	—
378	C₂	—	8	2	no	—
379	C₂	#2366×C₁₃₁	1	1	yes	characteristic
380	C₂	#3288×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃₁	D₄²
commutator	C₂×C₄	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂×#496×C₁₃₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₁ ◁ C₂²×C₄×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2949×C₁₃₁	C₂	semidirect
3. #2948×C₁₃₁	C₂	semidirect
4. #1978×C₁₃₁	C₂	semidirect
5. #1977×C₁₃₁	C₂	semidirect
6. #1888×C₁₃₁	C₂	semidirect
7. #1887×C₁₃₁	C₂	semidirect
8. #1885×C₁₃₁	C₂	semidirect
9. #1773×C₁₃₁	C₂	semidirect
17. #496×C₁₃₁	C₄	semidirect
43. C₂×SD₁₆×C₁₃₁	C₂×C₄	semidirect
47. C₂×D₈×C₁₃₁	C₂×C₄	semidirect
52. #127×C₁₃₁	C₂×C₄	semidirect
54. #124×C₁₃₁	C₂×C₄	semidirect
67. #107×C₁₃₁	D₄	semidirect
68. #106×C₁₃₁	D₄	semidirect
78. #97×C₁₃₁	C₂×C₄	semidirect
190. #23202	C₁₃₁	direct (N × H)
191. C₁₃₁	#23202	direct (N × H)
193. #2949	C₂×C₁₃₁	semidirect
194. #2948	C₂×C₁₃₁	semidirect
195. #1978	C₂×C₁₃₁	semidirect
196. #1977	C₂×C₁₃₁	semidirect
197. #1888	C₂×C₁₃₁	semidirect
198. #1887	C₂×C₁₃₁	semidirect
199. #1885	C₂×C₁₃₁	semidirect
200. #1773	C₂×C₁₃₁	semidirect
208. #496	C₄×C₁₃₁	semidirect
234. C₂×SD₁₆	C₂×C₄×C₁₃₁	semidirect
238. C₂×D₈	C₂×C₄×C₁₃₁	semidirect
243. #127	C₂×C₄×C₁₃₁	semidirect
245. #124	C₂×C₄×C₁₃₁	semidirect
258. #107	D₄×C₁₃₁	semidirect
259. #106	D₄×C₁₃₁	semidirect
269. #97	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×#496×C₁₃₁	2
#2949×C₁₃₁	2
#2948×C₁₃₁	2
#1978×C₁₃₁	2
#1977×C₁₃₁	2
#1888×C₁₃₁	2
#1887×C₁₃₁	2
#1885×C₁₃₁	2
#1773×C₁₃₁	2
#23202	131

Subgroups — C131×#23202 #45709086

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#23202 #45709086