Subgroups — C₁₃₁×#29870 #45715754

Order 33536.

758 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#478×C₁₃₁	C₂	1	2	yes	maximal
2	#2859×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2293×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	#2085×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2084×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#2083×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#2073×C₁₃₁	C₂	1	2	yes	maximal
8	#2071×C₁₃₁	C₂	1	1	yes	maximal, characteristic
9	#2071×C₁₃₁	C₂	1	1	yes	maximal, characteristic
10	#1989×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	#1831×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#125×C₁₃₁	C₂²	1	2	yes	—
13	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂×#117×C₁₃₁	—	2	1	no	—
15	#478×C₁₃₁	—	2	8	no	—
16	C₂×#107×C₁₃₁	C₂²	1	2	yes	—
17	C₂×#106×C₁₃₁	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	2	yes	—
19	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
20	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
21	#390×C₁₃₁	C₂²	1	1	yes	characteristic
22	#390×C₁₃₁	C₂²	1	1	yes	characteristic
23	#389×C₁₃₁	—	2	1	no	—
24	#389×C₁₃₁	—	2	1	no	—
25	#389×C₁₃₁	—	2	1	no	—
26	#389×C₁₃₁	—	2	1	no	—
27	#389×C₁₃₁	C₂²	1	1	yes	characteristic
28	#389×C₁₃₁	C₂²	1	1	yes	characteristic
29	#388×C₁₃₁	—	2	1	no	—
30	#388×C₁₃₁	—	2	1	no	—
31	#384×C₁₃₁	C₂²	1	1	yes	characteristic
32	#384×C₁₃₁	C₂²	1	1	yes	characteristic
33	#382×C₁₃₁	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
35	C₄×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
36	C₄³×C₁₃₁	C₂²	1	1	yes	characteristic
37	#340×C₁₃₁	C₂²	1	2	yes	—
38	#340×C₁₃₁	C₂²	1	2	yes	—
39	#340×C₁₃₁	C₂²	1	2	yes	—
40	#340×C₁₃₁	C₂²	1	2	yes	—
41	#336×C₁₃₁	C₂²	1	1	yes	characteristic
42	#336×C₁₃₁	C₂²	1	1	yes	characteristic
43	#336×C₁₃₁	C₂²	1	2	yes	—
44	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃₁	—	2	1	no	—
46	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
48	#125×C₁₃₁	—	2	4	no	—
49	#125×C₁₃₁	—	2	4	no	—
50	C₄×D₄×C₁₃₁	—	2	2	no	—
51	C₄×D₄×C₁₃₁	D₄	1	4	yes	—
52	#117×C₁₃₁	—	4	4	no	—
53	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
71	C₂×C₄²×C₁₃₁	—	2	1	no	—
72	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₃₁	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
79	#107×C₁₃₁	—	2	4	no	—
80	#106×C₁₃₁	—	2	4	no	—
81	C₄⋊C₈×C₁₃₁	—	2	4	no	—
82	#102×C₁₃₁	—	2	4	no	—
83	#102×C₁₃₁	—	2	4	no	—
84	#95×C₁₃₁	—	2	1	no	—
85	#95×C₁₃₁	—	2	1	no	—
86	#95×C₁₃₁	—	2	1	no	—
87	#95×C₁₃₁	—	2	2	no	—
88	#95×C₁₃₁	—	2	2	no	—
89	C₂⁴×C₁₃₁	—	2	1	no	—
90	C₂×D₄×C₁₃₁	—	2	1	no	—
91	C₂×D₄×C₁₃₁	—	2	2	no	—
92	C₂×D₄×C₁₃₁	—	2	2	no	—
93	C₂×D₄×C₁₃₁	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₃₁	—	2	1	no	—
95	C₂²×C₄×C₁₃₁	—	2	4	no	—
96	C₂²×C₄×C₁₃₁	—	2	1	no	—
97	C₂²×C₄×C₁₃₁	—	2	1	no	—
98	C₂²×C₄×C₁₃₁	—	2	2	no	—
99	C₂²×C₄×C₁₃₁	—	2	2	no	—
100	C₂²×C₄×C₁₃₁	—	4	2	no	—
101	C₂²×C₄×C₁₃₁	—	4	2	no	—
102	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
109	C₂×C₈×C₁₃₁	—	2	2	no	—
110	C₂×C₈×C₁₃₁	—	2	2	no	—
111	C₂×C₈×C₁₃₁	—	2	2	no	—
112	C₂×C₈×C₁₃₁	—	2	2	no	—
113	C₂×C₈×C₁₃₁	—	2	2	no	—
114	C₂×C₈×C₁₃₁	—	2	2	no	—
115	C₄⋊C₄×C₁₃₁	—	2	1	no	—
116	C₄⋊C₄×C₁₃₁	—	2	2	no	—
117	C₄⋊C₄×C₁₃₁	—	2	2	no	—
118	C₄⋊C₄×C₁₃₁	—	2	2	no	—
119	C₄⋊C₄×C₁₃₁	—	2	2	no	—
120	C₄⋊C₄×C₁₃₁	—	2	2	no	—
121	C₄⋊C₄×C₁₃₁	—	2	2	no	—
122	C₄⋊C₄×C₁₃₁	—	4	2	no	—
123	C₄⋊C₄×C₁₃₁	—	4	2	no	—
124	C₄⋊C₄×C₁₃₁	—	4	2	no	—
125	C₄⋊C₄×C₁₃₁	—	4	4	no	—
126	C₄⋊C₄×C₁₃₁	—	4	4	no	—
127	C₄⋊C₄×C₁₃₁	—	4	2	no	—
128	C₄⋊C₄×C₁₃₁	—	4	2	no	—
129	C₄⋊C₄×C₁₃₁	—	4	2	no	—
130	C₄⋊C₄×C₁₃₁	C₂×D₄	1	2	yes	—
131	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
132	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
133	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
134	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
135	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
136	C₄²×C₁₃₁	—	2	2	no	—
137	C₄²×C₁₃₁	—	2	2	no	—
138	C₄²×C₁₃₁	—	2	2	no	—
139	C₄²×C₁₃₁	—	2	2	no	—
140	C₄²×C₁₃₁	—	4	1	no	—
141	C₄²×C₁₃₁	—	4	1	no	—
142	C₄²×C₁₃₁	—	4	2	no	—
143	C₄²×C₁₃₁	C₂×D₄	1	2	yes	—
144	C₄²×C₁₃₁	#41	1	2	yes	—
145	C₂³×C₁₃₁	—	2	2	no	—
146	C₂³×C₁₃₁	—	4	1	no	—
147	C₂³×C₁₃₁	—	4	1	no	—
148	C₂³×C₁₃₁	—	4	1	no	—
149	C₂³×C₁₃₁	—	4	1	no	—
150	C₂³×C₁₃₁	—	4	1	no	—
151	C₂³×C₁₃₁	—	4	1	no	—
152	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
153	D₄×C₁₃₁	—	2	4	no	—
154	D₄×C₁₃₁	—	4	2	no	—
155	C₂×C₄×C₁₃₁	—	2	1	no	—
156	C₂×C₄×C₁₃₁	—	2	1	no	—
157	C₂×C₄×C₁₃₁	—	2	1	no	—
158	C₂×C₄×C₁₃₁	—	2	1	no	—
159	C₂×C₄×C₁₃₁	—	2	1	no	—
160	C₂×C₄×C₁₃₁	—	2	1	no	—
161	C₂×C₄×C₁₃₁	—	2	1	no	—
162	C₂×C₄×C₁₃₁	—	2	1	no	—
163	C₂×C₄×C₁₃₁	—	2	2	no	—
164	C₂×C₄×C₁₃₁	—	2	1	no	—
165	C₂×C₄×C₁₃₁	—	2	1	no	—
166	C₂×C₄×C₁₃₁	—	2	1	no	—
167	C₂×C₄×C₁₃₁	—	2	1	no	—
168	C₂×C₄×C₁₃₁	—	2	1	no	—
169	C₂×C₄×C₁₃₁	—	2	1	no	—
170	C₂×C₄×C₁₃₁	—	4	8	no	—
171	C₂×C₄×C₁₃₁	—	4	1	no	—
172	C₂×C₄×C₁₃₁	—	4	1	no	—
173	C₂×C₄×C₁₃₁	—	4	2	no	—
174	C₂×C₄×C₁₃₁	—	4	2	no	—
175	C₂×C₄×C₁₃₁	—	4	1	no	—
176	C₂×C₄×C₁₃₁	—	4	1	no	—
177	C₂×C₄×C₁₃₁	—	4	1	no	—
178	C₂×C₄×C₁₃₁	—	4	2	no	—
179	C₂×C₄×C₁₃₁	—	4	1	no	—
180	C₂×C₄×C₁₃₁	—	4	1	no	—
181	C₂×C₄×C₁₃₁	—	4	2	no	—
182	C₂×C₄×C₁₃₁	—	4	1	no	—
183	C₂×C₄×C₁₃₁	—	4	2	no	—
184	C₂×C₄×C₁₃₁	—	4	2	no	—
185	C₂×C₄×C₁₃₁	#121	1	2	yes	—
186	C₂×C₄×C₁₃₁	#121	1	2	yes	—
187	C₂×C₄×C₁₃₁	#135	1	2	yes	—
188	C₂×C₄×C₁₃₁	AGL(1,ℤ/8)	1	2	yes	—
189	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
192	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
193	C₈×C₁₃₁	—	4	2	no	—
194	C₈×C₁₃₁	—	4	2	no	—
195	C₂²×C₁₃₁	—	4	2	no	—
196	C₂²×C₁₃₁	—	4	2	no	—
197	C₂²×C₁₃₁	—	4	2	no	—
198	C₂²×C₁₃₁	—	8	1	no	—
199	C₂²×C₁₃₁	—	8	1	no	—
200	C₂²×C₁₃₁	—	8	1	no	—
201	C₂²×C₁₃₁	—	8	1	no	—
202	C₂²×C₁₃₁	C₂×#121	1	1	yes	characteristic
203	C₂²×C₁₃₁	#536	1	1	yes	characteristic
204	C₂²×C₁₃₁	#536	1	1	yes	characteristic
205	C₂²×C₁₃₁	C₂×#135	1	1	yes	characteristic
206	C₂²×C₁₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
207	C₂²×C₁₃₁	#575	1	1	yes	characteristic
208	C₂²×C₁₃₁	#575	1	1	yes	characteristic
209	C₄×C₁₃₁	—	2	2	no	—
210	C₄×C₁₃₁	—	2	2	no	—
211	C₄×C₁₃₁	—	2	2	no	—
212	C₄×C₁₃₁	—	2	2	no	—
213	C₄×C₁₃₁	—	4	1	no	—
214	C₄×C₁₃₁	—	4	1	no	—
215	C₄×C₁₃₁	—	4	2	no	—
216	C₄×C₁₃₁	—	8	1	no	—
217	C₄×C₁₃₁	—	8	1	no	—
218	C₄×C₁₃₁	—	8	2	no	—
219	C₄×C₁₃₁	—	8	2	no	—
220	C₄×C₁₃₁	#536	1	2	yes	—
221	C₄×C₁₃₁	#541	1	2	yes	—
222	C₂×C₁₃₁	—	8	2	no	—
223	C₂×C₁₃₁	#2621	1	1	yes	characteristic
224	C₂×C₁₃₁	#3035	1	1	yes	characteristic
225	C₂×C₁₃₁	#3036	1	1	yes	characteristic
226	C₂×C₁₃₁	#3228	1	1	yes	characteristic
227	C₂×C₁₃₁	#3232	1	1	yes	characteristic
228	C₂×C₁₃₁	#3234	1	1	yes	characteristic
229	C₂×C₁₃₁	#3240	1	1	yes	characteristic
230	#29870	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₁₃₁	#29870	1	1	yes	characteristic, direct product factor, Sylow
232	C₂×#478	C₂×C₁₃₁	1	2	yes	—
233	#2859	C₂×C₁₃₁	1	1	yes	characteristic, complemented
234	#2293	C₂×C₁₃₁	1	1	yes	characteristic
235	#2085	C₂×C₁₃₁	1	2	yes	complemented
236	#2084	C₂×C₁₃₁	1	1	yes	characteristic, complemented
237	#2083	C₂×C₁₃₁	1	1	yes	characteristic, complemented
238	#2073	C₂×C₁₃₁	1	2	yes	—
239	#2071	C₂×C₁₃₁	1	1	yes	characteristic
240	#2071	C₂×C₁₃₁	1	1	yes	characteristic
241	#1989	C₂×C₁₃₁	1	2	yes	complemented
242	#1831	C₂×C₁₃₁	1	1	yes	characteristic, complemented
243	C₂×#125	C₂²×C₁₃₁	1	2	yes	—
244	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
245	C₂×#117	—	2	1	no	—
246	#478	—	2	8	no	—
247	C₂×#107	C₂²×C₁₃₁	1	2	yes	—
248	C₂×#106	C₂²×C₁₃₁	1	2	yes	—
249	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	2	yes	—
250	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
251	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
252	#390	C₂²×C₁₃₁	1	1	yes	characteristic
253	#390	C₂²×C₁₃₁	1	1	yes	characteristic
254	#389	—	2	1	no	—
255	#389	—	2	1	no	—
256	#389	—	2	1	no	—
257	#389	—	2	1	no	—
258	#389	C₂²×C₁₃₁	1	1	yes	characteristic
259	#389	C₂²×C₁₃₁	1	1	yes	characteristic
260	#388	—	2	1	no	—
261	#388	—	2	1	no	—
262	#384	C₂²×C₁₃₁	1	1	yes	characteristic
263	#384	C₂²×C₁₃₁	1	1	yes	characteristic
264	#382	C₂²×C₁₃₁	1	2	yes	—
265	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
266	C₄×C₂²⋊C₄	—	2	1	no	—
267	C₄³	C₂²×C₁₃₁	1	1	yes	characteristic
268	#340	C₂²×C₁₃₁	1	2	yes	—
269	#340	C₂²×C₁₃₁	1	2	yes	—
270	#340	C₂²×C₁₃₁	1	2	yes	—
271	#340	C₂²×C₁₃₁	1	2	yes	—
272	#336	C₂²×C₁₃₁	1	1	yes	characteristic
273	#336	C₂²×C₁₃₁	1	1	yes	characteristic
274	#336	C₂²×C₁₃₁	1	2	yes	—
275	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
276	C₂³×C₄	—	2	1	no	—
277	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
278	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
279	#125	—	2	4	no	—
280	#125	—	2	4	no	—
281	C₄×D₄	—	2	2	no	—
282	C₄×D₄	D₄×C₁₃₁	1	4	yes	—
283	#117	—	4	4	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	—	2	1	no	—
298	C₂×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₂²⋊C₄	—	2	1	no	—
301	C₂×C₂²⋊C₄	—	2	1	no	—
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
304	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
305	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
306	C₂×C₄²	D₄×C₁₃₁	1	1	yes	characteristic
307	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
308	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
309	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
310	#107	—	2	4	no	—
311	#106	—	2	4	no	—
312	C₄⋊C₈	—	2	4	no	—
313	#102	—	2	4	no	—
314	#102	—	2	4	no	—
315	#95	—	2	1	no	—
316	#95	—	2	1	no	—
317	#95	—	2	1	no	—
318	#95	—	2	2	no	—
319	#95	—	2	2	no	—
320	C₂⁴	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	C₂×D₄×C₁₃₁	1	2	yes	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
339	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	—	4	2	no	—
355	C₄⋊C₄	—	4	2	no	—
356	C₄⋊C₄	—	4	4	no	—
357	C₄⋊C₄	—	4	4	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	—	4	2	no	—
360	C₄⋊C₄	—	4	2	no	—
361	C₄⋊C₄	C₂×D₄×C₁₃₁	1	2	yes	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₂²⋊C₄	—	4	2	no	—
364	C₂²⋊C₄	—	4	2	no	—
365	C₂²⋊C₄	—	4	2	no	—
366	C₂²⋊C₄	—	4	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	4	1	no	—
372	C₄²	—	4	1	no	—
373	C₄²	—	4	2	no	—
374	C₄²	C₂×D₄×C₁₃₁	1	2	yes	—
375	C₄²	#41×C₁₃₁	1	2	yes	—
376	C₂³	—	2	2	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	1	no	—
383	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
384	D₄	—	2	4	no	—
385	D₄	—	4	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	4	8	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	#121×C₁₃₁	1	2	yes	—
417	C₂×C₄	#121×C₁₃₁	1	2	yes	—
418	C₂×C₄	#135×C₁₃₁	1	2	yes	—
419	C₂×C₄	AGL(1,ℤ/8)×C₁₃₁	1	2	yes	—
420	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
421	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
422	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
423	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
424	C₈	—	4	2	no	—
425	C₈	—	4	2	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	8	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	8	1	no	—
432	C₂²	—	8	1	no	—
433	C₂²	C₂×#121×C₁₃₁	1	1	yes	characteristic
434	C₂²	#536×C₁₃₁	1	1	yes	characteristic
435	C₂²	#536×C₁₃₁	1	1	yes	characteristic
436	C₂²	C₂×#135×C₁₃₁	1	1	yes	characteristic
437	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₁	1	1	yes	characteristic
438	C₂²	#575×C₁₃₁	1	1	yes	characteristic
439	C₂²	#575×C₁₃₁	1	1	yes	characteristic
440	C₄	—	2	2	no	—
441	C₄	—	2	2	no	—
442	C₄	—	2	2	no	—
443	C₄	—	2	2	no	—
444	C₄	—	4	2	no	—
445	C₄	—	4	1	no	—
446	C₄	—	4	1	no	—
447	C₄	—	8	2	no	—
448	C₄	—	8	2	no	—
449	C₄	—	8	1	no	—
450	C₄	—	8	1	no	—
451	C₄	#536×C₁₃₁	1	2	yes	—
452	C₄	#541×C₁₃₁	1	2	yes	—
453	C₂	—	8	2	no	—
454	C₂	#2621×C₁₃₁	1	1	yes	characteristic
455	C₂	#3035×C₁₃₁	1	1	yes	characteristic
456	C₂	#3036×C₁₃₁	1	1	yes	characteristic
457	C₂	#3228×C₁₃₁	1	1	yes	characteristic
458	C₂	#3232×C₁₃₁	1	1	yes	characteristic
459	C₂	#3234×C₁₃₁	1	1	yes	characteristic
460	C₂	#3240×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂²×D₄×C₁₃₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ C₄³×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2859×C₁₃₁	C₂	semidirect
4. #2085×C₁₃₁	C₂	semidirect
5. #2084×C₁₃₁	C₂	semidirect
6. #2083×C₁₃₁	C₂	semidirect
10. #1989×C₁₃₁	C₂	semidirect
11. #1831×C₁₃₁	C₂	semidirect
230. #29870	C₁₃₁	direct (N × H)
231. C₁₃₁	#29870	direct (N × H)
233. #2859	C₂×C₁₃₁	semidirect
235. #2085	C₂×C₁₃₁	semidirect
236. #2084	C₂×C₁₃₁	semidirect
237. #2083	C₂×C₁₃₁	semidirect
241. #1989	C₂×C₁₃₁	semidirect
242. #1831	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×#478×C₁₃₁	2
#2859×C₁₃₁	2
#2293×C₁₃₁	2
#2085×C₁₃₁	2
#2084×C₁₃₁	2
#2083×C₁₃₁	2
#2073×C₁₃₁	2
#2071×C₁₃₁	2
#1989×C₁₃₁	2
#1831×C₁₃₁	2
#29870	131

Subgroups — C131×#29870 #45715754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#29870 #45715754