Subgroups — C₁₃₁×#8952 #45694836

Order 33536.

560 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#446×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×SD₁₆×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#1954×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈⋊C₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄⋊C₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic
6	#1277×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#1273×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×SD₁₆×C₁₃₁	C₄	1	1	yes	characteristic
9	C₂×C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
11	#446×C₁₃₁	—	2	2	no	—
12	#446×C₁₃₁	—	2	2	no	—
13	C₄×SD₁₆×C₁₃₁	—	2	2	no	—
14	C₄×SD₁₆×C₁₃₁	—	2	2	no	—
15	C₂×#106×C₁₃₁	C₄	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₁₃₁	—	2	1	no	—
17	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
19	C₂×#103×C₁₃₁	C₄	1	1	yes	characteristic
20	C₂×#102×C₁₃₁	C₄	1	1	yes	characteristic
21	C₂×C₂²⋊C₈×C₁₃₁	—	2	1	no	—
22	C₂×C₂²⋊C₈×C₁₃₁	—	2	1	no	—
23	C₂×#97×C₁₃₁	—	2	1	no	—
24	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
27	Q₈⋊C₈×C₁₃₁	—	2	2	no	—
28	D₄⋊C₈×C₁₃₁	—	2	2	no	—
29	C₂²×Q₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
30	C₂²×D₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₃₁	—	2	1	no	—
32	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
33	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
34	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
35	C₂²×C₈×C₁₃₁	—	2	1	no	—
36	C₂²×C₈×C₁₃₁	—	2	1	no	—
37	C₂²×C₈×C₁₃₁	—	2	1	no	—
38	C₂²×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₁₃₁	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₁₃₁	D₄	1	1	yes	characteristic
42	C₄×Q₈×C₁₃₁	—	2	1	no	—
43	C₄×Q₈×C₁₃₁	—	2	1	no	—
44	C₄×Q₈×C₁₃₁	D₄	1	2	yes	—
45	C₄×Q₈×C₁₃₁	D₄	1	2	yes	—
46	C₄×D₄×C₁₃₁	—	2	1	no	—
47	C₄×D₄×C₁₃₁	—	2	1	no	—
48	C₄×D₄×C₁₃₁	—	2	1	no	—
49	C₄×D₄×C₁₃₁	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
54	C₂×C₄²×C₁₃₁	—	2	1	no	—
55	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
56	#106×C₁₃₁	—	2	2	no	—
57	C₄⋊C₈×C₁₃₁	—	2	4	no	—
58	C₄⋊C₈×C₁₃₁	—	2	1	no	—
59	C₄⋊C₈×C₁₃₁	—	2	1	no	—
60	C₄⋊C₈×C₁₃₁	—	2	1	no	—
61	C₄⋊C₈×C₁₃₁	D₄	1	2	yes	—
62	#103×C₁₃₁	—	2	2	no	—
63	#102×C₁₃₁	—	2	2	no	—
64	C₂²⋊C₈×C₁₃₁	—	4	2	no	—
65	C₂²⋊C₈×C₁₃₁	—	4	2	no	—
66	#97×C₁₃₁	—	2	4	no	—
67	C₄×C₈×C₁₃₁	—	2	1	no	—
68	C₄×C₈×C₁₃₁	—	2	1	no	—
69	C₄×C₈×C₁₃₁	—	2	1	no	—
70	C₄×C₈×C₁₃₁	—	2	1	no	—
71	C₄×C₈×C₁₃₁	—	2	1	no	—
72	C₄×C₈×C₁₃₁	—	2	1	no	—
73	C₂⁴×C₁₃₁	—	2	1	no	—
74	C₂×Q₈×C₁₃₁	—	2	1	no	—
75	C₂×Q₈×C₁₃₁	—	2	1	no	—
76	C₂×Q₈×C₁₃₁	—	2	1	no	—
77	C₂×Q₈×C₁₃₁	—	2	1	no	—
78	C₂×Q₈×C₁₃₁	—	2	1	no	—
79	C₂×Q₈×C₁₃₁	C₂²⋊C₄	1	2	yes	—
80	C₂×D₄×C₁₃₁	—	2	1	no	—
81	C₂×D₄×C₁₃₁	—	2	1	no	—
82	C₂×D₄×C₁₃₁	—	2	1	no	—
83	C₂×D₄×C₁₃₁	—	2	1	no	—
84	C₂×D₄×C₁₃₁	—	2	1	no	—
85	C₂×D₄×C₁₃₁	M₁₆	1	2	yes	—
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	—	4	1	no	—
90	C₂²×C₄×C₁₃₁	—	4	1	no	—
91	C₂²×C₄×C₁₃₁	—	4	1	no	—
92	C₂²×C₄×C₁₃₁	—	4	1	no	—
93	C₂²×C₄×C₁₃₁	—	4	1	no	—
94	C₂²×C₄×C₁₃₁	—	4	1	no	—
95	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃₁	#41	1	1	yes	characteristic
98	SD₁₆×C₁₃₁	—	2	8	no	—
99	C₂×C₈×C₁₃₁	—	2	1	no	—
100	C₂×C₈×C₁₃₁	—	2	1	no	—
101	C₂×C₈×C₁₃₁	—	2	1	no	—
102	C₂×C₈×C₁₃₁	—	2	1	no	—
103	C₂×C₈×C₁₃₁	—	2	2	no	—
104	C₂×C₈×C₁₃₁	—	2	1	no	—
105	C₂×C₈×C₁₃₁	—	2	1	no	—
106	C₂×C₈×C₁₃₁	—	2	2	no	—
107	C₂×C₈×C₁₃₁	—	2	1	no	—
108	C₂×C₈×C₁₃₁	—	2	1	no	—
109	C₂×C₈×C₁₃₁	—	2	1	no	—
110	C₂×C₈×C₁₃₁	—	2	1	no	—
111	C₂×C₈×C₁₃₁	—	4	1	no	—
112	C₂×C₈×C₁₃₁	—	4	1	no	—
113	C₂×C₈×C₁₃₁	—	4	1	no	—
114	C₂×C₈×C₁₃₁	—	4	1	no	—
115	C₂×C₈×C₁₃₁	—	4	1	no	—
116	C₂×C₈×C₁₃₁	—	4	1	no	—
117	C₂×C₈×C₁₃₁	—	4	1	no	—
118	C₂×C₈×C₁₃₁	M₁₆	1	2	yes	—
119	C₂×C₈×C₁₃₁	SD₁₆	1	2	yes	complemented
120	C₄⋊C₄×C₁₃₁	—	2	1	no	—
121	C₄⋊C₄×C₁₃₁	—	2	2	no	—
122	C₄⋊C₄×C₁₃₁	—	2	2	no	—
123	C₄⋊C₄×C₁₃₁	—	2	1	no	—
124	C₄⋊C₄×C₁₃₁	—	2	1	no	—
125	C₄⋊C₄×C₁₃₁	C₂²⋊C₄	1	2	yes	—
126	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
127	C₂²⋊C₄×C₁₃₁	—	4	1	no	—
128	C₄²×C₁₃₁	—	2	2	no	—
129	C₄²×C₁₃₁	—	2	2	no	—
130	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₁₃₁	#41	1	1	yes	characteristic
134	C₂³×C₁₃₁	—	2	2	no	—
135	C₂³×C₁₃₁	—	4	1	no	—
136	C₂³×C₁₃₁	—	4	1	no	—
137	C₂³×C₁₃₁	—	4	1	no	—
138	C₂³×C₁₃₁	—	4	1	no	—
139	C₂³×C₁₃₁	—	4	1	no	—
140	C₂³×C₁₃₁	—	4	1	no	—
141	C₂³×C₁₃₁	C₄×D₄	1	1	yes	characteristic
142	Q₈×C₁₃₁	—	2	2	no	—
143	Q₈×C₁₃₁	—	2	2	no	—
144	Q₈×C₁₃₁	—	4	1	no	—
145	Q₈×C₁₃₁	—	4	1	no	—
146	D₄×C₁₃₁	—	2	2	no	—
147	D₄×C₁₃₁	—	2	2	no	—
148	D₄×C₁₃₁	—	4	1	no	—
149	D₄×C₁₃₁	—	4	1	no	—
150	C₂×C₄×C₁₃₁	—	2	1	no	—
151	C₂×C₄×C₁₃₁	—	2	1	no	—
152	C₂×C₄×C₁₃₁	—	2	2	no	—
153	C₂×C₄×C₁₃₁	—	2	2	no	—
154	C₂×C₄×C₁₃₁	—	4	1	no	—
155	C₂×C₄×C₁₃₁	—	4	1	no	—
156	C₂×C₄×C₁₃₁	—	4	1	no	—
157	C₂×C₄×C₁₃₁	—	4	1	no	—
158	C₂×C₄×C₁₃₁	—	4	1	no	—
159	C₂×C₄×C₁₃₁	—	4	1	no	—
160	C₂×C₄×C₁₃₁	—	4	1	no	—
161	C₂×C₄×C₁₃₁	—	8	1	no	—
162	C₂×C₄×C₁₃₁	—	8	1	no	—
163	C₂×C₄×C₁₃₁	—	8	1	no	—
164	C₂×C₄×C₁₃₁	—	8	1	no	—
165	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₃₁	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₁₃₁	#120	1	1	yes	characteristic
168	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
169	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
170	C₂×C₄×C₁₃₁	#123	1	1	yes	characteristic
171	C₂×C₄×C₁₃₁	C₂×M₁₆	1	1	yes	characteristic
172	C₂×C₄×C₁₃₁	C₂×M₁₆	1	1	yes	characteristic
173	C₂×C₄×C₁₃₁	#131	1	1	yes	characteristic
174	C₂×C₄×C₁₃₁	#131	1	1	yes	characteristic
175	C₂×C₄×C₁₃₁	C₂×SD₁₆	1	1	yes	characteristic
176	C₂×C₄×C₁₃₁	#135	1	1	yes	characteristic
177	C₂×C₄×C₁₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
178	C₂×C₄×C₁₃₁	#137	1	1	yes	characteristic
179	C₈×C₁₃₁	—	2	2	no	—
180	C₈×C₁₃₁	—	2	2	no	—
181	C₈×C₁₃₁	—	4	2	no	—
182	C₈×C₁₃₁	—	4	1	no	—
183	C₈×C₁₃₁	—	4	1	no	—
184	C₈×C₁₃₁	—	4	2	no	—
185	C₈×C₁₃₁	—	8	1	no	—
186	C₂²×C₁₃₁	—	4	2	no	—
187	C₂²×C₁₃₁	—	4	2	no	—
188	C₂²×C₁₃₁	—	4	2	no	—
189	C₂²×C₁₃₁	—	8	1	no	—
190	C₂²×C₁₃₁	—	8	1	no	—
191	C₂²×C₁₃₁	—	8	1	no	—
192	C₂²×C₁₃₁	—	8	1	no	—
193	C₂²×C₁₃₁	#386	1	1	yes	characteristic
194	C₂²×C₁₃₁	#435	1	1	yes	characteristic
195	C₂²×C₁₃₁	#436	1	1	yes	characteristic
196	C₂²×C₁₃₁	C₄×SD₁₆	1	1	yes	characteristic
197	C₂²×C₁₃₁	#440	1	1	yes	characteristic
198	C₂²×C₁₃₁	#443	1	1	yes	characteristic
199	C₂²×C₁₃₁	#444	1	1	yes	characteristic
200	C₄×C₁₃₁	—	2	1	no	—
201	C₄×C₁₃₁	—	2	1	no	—
202	C₄×C₁₃₁	—	4	2	no	—
203	C₄×C₁₃₁	—	4	2	no	—
204	C₄×C₁₃₁	—	8	1	no	—
205	C₄×C₁₃₁	#407	1	1	yes	characteristic
206	C₄×C₁₃₁	#408	1	1	yes	characteristic
207	C₄×C₁₃₁	#435	1	1	yes	characteristic
208	C₄×C₁₃₁	#436	1	1	yes	characteristic
209	C₄×C₁₃₁	#448	1	1	yes	characteristic
210	C₄×C₁₃₁	#449	1	1	yes	characteristic
211	C₄×C₁₃₁	#460	1	1	yes	characteristic
212	C₄×C₁₃₁	#464	1	1	yes	characteristic
213	C₂×C₁₃₁	—	8	2	no	—
214	C₂×C₁₃₁	#1582	1	1	yes	characteristic
215	C₂×C₁₃₁	#1585	1	1	yes	characteristic
216	C₂×C₁₃₁	#1590	1	1	yes	characteristic
217	C₂×C₁₃₁	#1592	1	1	yes	characteristic
218	C₂×C₁₃₁	#1870	1	1	yes	characteristic
219	C₂×C₁₃₁	#1876	1	1	yes	characteristic
220	C₂×C₁₃₁	#1880	1	1	yes	characteristic
221	#8952	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₁₃₁	#8952	1	1	yes	characteristic, direct product factor, Sylow
223	C₂×#446	C₂×C₁₃₁	1	1	yes	characteristic, complemented
224	C₂×C₄×SD₁₆	C₂×C₁₃₁	1	1	yes	characteristic
225	#1954	C₂×C₁₃₁	1	1	yes	characteristic
226	C₂×Q₈⋊C₈	C₂×C₁₃₁	1	1	yes	characteristic, complemented
227	C₂×D₄⋊C₈	C₂×C₁₃₁	1	1	yes	characteristic
228	#1277	C₂×C₁₃₁	1	1	yes	characteristic, complemented
229	#1273	C₂×C₁₃₁	1	1	yes	characteristic, complemented
230	C₂²×SD₁₆	C₄×C₁₃₁	1	1	yes	characteristic
231	C₂×C₄×Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
232	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
233	#446	—	2	2	no	—
234	#446	—	2	2	no	—
235	C₄×SD₁₆	—	2	2	no	—
236	C₄×SD₁₆	—	2	2	no	—
237	C₂×#106	C₄×C₁₃₁	1	1	yes	characteristic
238	C₂×C₄⋊C₈	—	2	1	no	—
239	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
240	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
241	C₂×#103	C₄×C₁₃₁	1	1	yes	characteristic
242	C₂×#102	C₄×C₁₃₁	1	1	yes	characteristic
243	C₂×C₂²⋊C₈	—	2	1	no	—
244	C₂×C₂²⋊C₈	—	2	1	no	—
245	C₂×#97	—	2	1	no	—
246	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
247	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
248	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
249	Q₈⋊C₈	—	2	2	no	—
250	D₄⋊C₈	—	2	2	no	—
251	C₂²×Q₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
252	C₂²×D₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
253	C₂³×C₄	—	2	1	no	—
254	C₂×SD₁₆	—	2	2	no	—
255	C₂×SD₁₆	—	2	2	no	—
256	C₂×SD₁₆	—	2	2	no	—
257	C₂²×C₈	—	2	1	no	—
258	C₂²×C₈	—	2	1	no	—
259	C₂²×C₈	—	2	1	no	—
260	C₂²×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
261	C₂²×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
262	C₂²×C₈	D₄×C₁₃₁	1	1	yes	characteristic
263	C₂²×C₈	D₄×C₁₃₁	1	1	yes	characteristic
264	C₄×Q₈	—	2	1	no	—
265	C₄×Q₈	—	2	1	no	—
266	C₄×Q₈	D₄×C₁₃₁	1	2	yes	—
267	C₄×Q₈	D₄×C₁₃₁	1	2	yes	—
268	C₄×D₄	—	2	1	no	—
269	C₄×D₄	—	2	1	no	—
270	C₄×D₄	—	2	1	no	—
271	C₄×D₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
275	C₂×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₄²	—	2	1	no	—
277	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
278	#106	—	2	2	no	—
279	C₄⋊C₈	—	2	4	no	—
280	C₄⋊C₈	—	2	1	no	—
281	C₄⋊C₈	—	2	1	no	—
282	C₄⋊C₈	—	2	1	no	—
283	C₄⋊C₈	D₄×C₁₃₁	1	2	yes	—
284	#103	—	2	2	no	—
285	#102	—	2	2	no	—
286	C₂²⋊C₈	—	4	2	no	—
287	C₂²⋊C₈	—	4	2	no	—
288	#97	—	2	4	no	—
289	C₄×C₈	—	2	1	no	—
290	C₄×C₈	—	2	1	no	—
291	C₄×C₈	—	2	1	no	—
292	C₄×C₈	—	2	1	no	—
293	C₄×C₈	—	2	1	no	—
294	C₄×C₈	—	2	1	no	—
295	C₂⁴	—	2	1	no	—
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	—	2	1	no	—
298	C₂×Q₈	—	2	1	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	C₂²⋊C₄×C₁₃₁	1	2	yes	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	M₁₆×C₁₃₁	1	2	yes	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	—	4	1	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	—	4	1	no	—
316	C₂²×C₄	—	4	1	no	—
317	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
319	C₂²×C₄	#41×C₁₃₁	1	1	yes	characteristic
320	SD₁₆	—	2	8	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	4	1	no	—
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	M₁₆×C₁₃₁	1	2	yes	—
341	C₂×C₈	SD₁₆×C₁₃₁	1	2	yes	complemented
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	C₂²⋊C₄×C₁₃₁	1	2	yes	—
348	C₂²⋊C₄	—	4	1	no	—
349	C₂²⋊C₄	—	4	1	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
353	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
354	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
355	C₄²	#41×C₁₃₁	1	1	yes	characteristic
356	C₂³	—	2	2	no	—
357	C₂³	—	4	1	no	—
358	C₂³	—	4	1	no	—
359	C₂³	—	4	1	no	—
360	C₂³	—	4	1	no	—
361	C₂³	—	4	1	no	—
362	C₂³	—	4	1	no	—
363	C₂³	C₄×D₄×C₁₃₁	1	1	yes	characteristic
364	Q₈	—	2	2	no	—
365	Q₈	—	2	2	no	—
366	Q₈	—	4	1	no	—
367	Q₈	—	4	1	no	—
368	D₄	—	2	2	no	—
369	D₄	—	2	2	no	—
370	D₄	—	4	1	no	—
371	D₄	—	4	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	8	1	no	—
384	C₂×C₄	—	8	1	no	—
385	C₂×C₄	—	8	1	no	—
386	C₂×C₄	—	8	1	no	—
387	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
388	C₂×C₄	C₄×D₄×C₁₃₁	1	1	yes	characteristic
389	C₂×C₄	#120×C₁₃₁	1	1	yes	characteristic
390	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
391	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
392	C₂×C₄	#123×C₁₃₁	1	1	yes	characteristic
393	C₂×C₄	C₂×M₁₆×C₁₃₁	1	1	yes	characteristic
394	C₂×C₄	C₂×M₁₆×C₁₃₁	1	1	yes	characteristic
395	C₂×C₄	#131×C₁₃₁	1	1	yes	characteristic
396	C₂×C₄	#131×C₁₃₁	1	1	yes	characteristic
397	C₂×C₄	C₂×SD₁₆×C₁₃₁	1	1	yes	characteristic
398	C₂×C₄	#135×C₁₃₁	1	1	yes	characteristic
399	C₂×C₄	AGL(1,ℤ/8)×C₁₃₁	1	1	yes	characteristic
400	C₂×C₄	#137×C₁₃₁	1	1	yes	characteristic
401	C₈	—	2	2	no	—
402	C₈	—	2	2	no	—
403	C₈	—	4	2	no	—
404	C₈	—	4	1	no	—
405	C₈	—	4	1	no	—
406	C₈	—	4	2	no	—
407	C₈	—	8	1	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	8	1	no	—
412	C₂²	—	8	1	no	—
413	C₂²	—	8	1	no	—
414	C₂²	—	8	1	no	—
415	C₂²	#386×C₁₃₁	1	1	yes	characteristic
416	C₂²	#435×C₁₃₁	1	1	yes	characteristic
417	C₂²	#436×C₁₃₁	1	1	yes	characteristic
418	C₂²	C₄×SD₁₆×C₁₃₁	1	1	yes	characteristic
419	C₂²	#440×C₁₃₁	1	1	yes	characteristic
420	C₂²	#443×C₁₃₁	1	1	yes	characteristic
421	C₂²	#444×C₁₃₁	1	1	yes	characteristic
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	8	1	no	—
427	C₄	#407×C₁₃₁	1	1	yes	characteristic
428	C₄	#408×C₁₃₁	1	1	yes	characteristic
429	C₄	#435×C₁₃₁	1	1	yes	characteristic
430	C₄	#436×C₁₃₁	1	1	yes	characteristic
431	C₄	#448×C₁₃₁	1	1	yes	characteristic
432	C₄	#449×C₁₃₁	1	1	yes	characteristic
433	C₄	#460×C₁₃₁	1	1	yes	characteristic
434	C₄	#464×C₁₃₁	1	1	yes	characteristic
435	C₂	—	8	2	no	—
436	C₂	#1582×C₁₃₁	1	1	yes	characteristic
437	C₂	#1585×C₁₃₁	1	1	yes	characteristic
438	C₂	#1590×C₁₃₁	1	1	yes	characteristic
439	C₂	#1592×C₁₃₁	1	1	yes	characteristic
440	C₂	#1870×C₁₃₁	1	1	yes	characteristic
441	C₂	#1876×C₁₃₁	1	1	yes	characteristic
442	C₂	#1880×C₁₃₁	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×#446×C₁₃₁	C₂	semidirect
4. C₂×Q₈⋊C₈×C₁₃₁	C₂	semidirect
6. #1277×C₁₃₁	C₂	semidirect
7. #1273×C₁₃₁	C₂	semidirect
119. C₂×C₈×C₁₃₁	SD₁₆	semidirect
221. #8952	C₁₃₁	direct (N × H)
222. C₁₃₁	#8952	direct (N × H)
223. C₂×#446	C₂×C₁₃₁	semidirect
226. C₂×Q₈⋊C₈	C₂×C₁₃₁	semidirect
228. #1277	C₂×C₁₃₁	semidirect
229. #1273	C₂×C₁₃₁	semidirect
341. C₂×C₈	SD₁₆×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#446×C₁₃₁	2
C₂×C₄×SD₁₆×C₁₃₁	2
#1954×C₁₃₁	2
C₂×Q₈⋊C₈×C₁₃₁	2
C₂×D₄⋊C₈×C₁₃₁	2
#1277×C₁₃₁	2
#1273×C₁₃₁	2
#8952	131

Subgroups — C131×#8952 #45694836

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#8952 #45694836