Subgroups — C₁₃₁×#24677 #45710561

Order 33536.

870 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#476×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×D₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#2563×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2354×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#2073×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2054×C₁₃₁	C₂	1	2	yes	maximal
7	#1990×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1949×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	#1939×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1926×C₁₃₁	C₂	1	2	yes	maximal, complemented
11	#1802×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
16	C₂×#117×C₁₃₁	—	2	1	no	—
17	#476×C₁₃₁	—	2	4	no	—
18	C₄×D₈×C₁₃₁	—	2	4	no	—
19	C₂×#107×C₁₃₁	C₂²	1	1	yes	characteristic
20	C₂×#106×C₁₃₁	C₂²	1	2	yes	—
21	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	2	yes	—
23	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
24	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
25	C₂×#102×C₁₃₁	C₂²	1	1	yes	characteristic
26	C₂×#102×C₁₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
28	#393×C₁₃₁	—	2	2	no	—
29	#390×C₁₃₁	C₂²	1	2	yes	—
30	#390×C₁₃₁	C₂²	1	2	yes	—
31	#388×C₁₃₁	—	2	2	no	—
32	#384×C₁₃₁	C₂²	1	1	yes	characteristic
33	#382×C₁₃₁	C₂²	1	2	yes	—
34	#380×C₁₃₁	—	2	1	no	—
35	#380×C₁₃₁	—	2	1	no	—
36	#380×C₁₃₁	—	2	1	no	—
37	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
38	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
39	#340×C₁₃₁	C₂²	1	2	yes	—
40	#340×C₁₃₁	C₂²	1	2	yes	—
41	#340×C₁₃₁	C₂²	1	2	yes	—
42	#336×C₁₃₁	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃₁	—	2	1	no	—
44	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃₁	—	2	1	no	—
47	C₂³×C₄×C₁₃₁	—	2	1	no	—
48	C₂×D₈×C₁₃₁	—	2	2	no	—
49	C₂×D₈×C₁₃₁	—	2	2	no	—
50	C₂×D₈×C₁₃₁	—	2	2	no	—
51	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
54	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
55	C₄⋊Q₈×C₁₃₁	—	2	2	no	—
56	C₄×D₄×C₁₃₁	—	2	2	no	—
57	C₄×D₄×C₁₃₁	—	2	2	no	—
58	C₄×D₄×C₁₃₁	—	2	2	no	—
59	C₄×D₄×C₁₃₁	D₄	1	4	yes	—
60	#117×C₁₃₁	—	4	4	no	—
61	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₃₁	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
76	C₂×C₄²×C₁₃₁	—	2	2	no	—
77	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
78	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
79	#107×C₁₃₁	—	2	2	no	—
80	#106×C₁₃₁	—	2	4	no	—
81	C₄⋊C₈×C₁₃₁	—	2	4	no	—
82	C₄⋊C₈×C₁₃₁	—	2	2	no	—
83	#102×C₁₃₁	—	2	2	no	—
84	#102×C₁₃₁	—	2	4	no	—
85	#102×C₁₃₁	—	2	4	no	—
86	#102×C₁₃₁	—	2	2	no	—
87	C₄×C₈×C₁₃₁	—	2	2	no	—
88	#95×C₁₃₁	—	2	2	no	—
89	#95×C₁₃₁	—	2	2	no	—
90	#95×C₁₃₁	—	2	2	no	—
91	#95×C₁₃₁	D₄	1	2	yes	—
92	C₂⁴×C₁₃₁	—	2	1	no	—
93	C₂⁴×C₁₃₁	—	2	1	no	—
94	C₂×Q₈×C₁₃₁	—	4	2	no	—
95	C₂×Q₈×C₁₃₁	—	8	1	no	—
96	C₂×Q₈×C₁₃₁	—	8	1	no	—
97	C₂×D₄×C₁₃₁	—	2	1	no	—
98	C₂×D₄×C₁₃₁	—	2	1	no	—
99	C₂×D₄×C₁₃₁	—	2	1	no	—
100	C₂×D₄×C₁₃₁	—	2	1	no	—
101	C₂×D₄×C₁₃₁	—	2	1	no	—
102	C₂×D₄×C₁₃₁	—	2	1	no	—
103	C₂×D₄×C₁₃₁	—	2	1	no	—
104	C₂×D₄×C₁₃₁	—	2	1	no	—
105	C₂×D₄×C₁₃₁	—	2	1	no	—
106	C₂×D₄×C₁₃₁	—	2	1	no	—
107	C₂×D₄×C₁₃₁	C₂×D₄	1	2	yes	—
108	C₂×D₄×C₁₃₁	#41	1	2	yes	—
109	C₂²×C₄×C₁₃₁	—	2	1	no	—
110	C₂²×C₄×C₁₃₁	—	2	4	no	—
111	C₂²×C₄×C₁₃₁	—	2	1	no	—
112	C₂²×C₄×C₁₃₁	—	2	2	no	—
113	C₂²×C₄×C₁₃₁	—	2	2	no	—
114	C₂²×C₄×C₁₃₁	—	4	2	no	—
115	C₂²×C₄×C₁₃₁	—	4	2	no	—
116	C₂²×C₄×C₁₃₁	—	4	2	no	—
117	C₂²×C₄×C₁₃₁	—	4	2	no	—
118	C₂²×C₄×C₁₃₁	—	4	2	no	—
119	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
124	D₈×C₁₃₁	—	2	8	no	—
125	C₂×C₈×C₁₃₁	—	2	1	no	—
126	C₂×C₈×C₁₃₁	—	2	1	no	—
127	C₂×C₈×C₁₃₁	—	2	1	no	—
128	C₂×C₈×C₁₃₁	—	2	2	no	—
129	C₂×C₈×C₁₃₁	—	2	2	no	—
130	C₂×C₈×C₁₃₁	—	2	2	no	—
131	C₂×C₈×C₁₃₁	—	2	1	no	—
132	C₂×C₈×C₁₃₁	—	2	1	no	—
133	C₂×C₈×C₁₃₁	#41	1	2	yes	—
134	C₄⋊C₄×C₁₃₁	—	2	2	no	—
135	C₄⋊C₄×C₁₃₁	—	2	2	no	—
136	C₄⋊C₄×C₁₃₁	—	2	1	no	—
137	C₄⋊C₄×C₁₃₁	—	2	2	no	—
138	C₄⋊C₄×C₁₃₁	—	2	1	no	—
139	C₄⋊C₄×C₁₃₁	—	2	2	no	—
140	C₄⋊C₄×C₁₃₁	—	2	1	no	—
141	C₄⋊C₄×C₁₃₁	—	2	2	no	—
142	C₄⋊C₄×C₁₃₁	—	2	2	no	—
143	C₄⋊C₄×C₁₃₁	—	4	2	no	—
144	C₄⋊C₄×C₁₃₁	—	4	2	no	—
145	C₄⋊C₄×C₁₃₁	—	8	1	no	—
146	C₄⋊C₄×C₁₃₁	C₂×D₄	1	2	yes	—
147	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
148	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
149	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
150	C₂²⋊C₄×C₁₃₁	—	8	2	no	—
151	C₂²⋊C₄×C₁₃₁	—	8	2	no	—
152	C₂²⋊C₄×C₁₃₁	—	8	2	no	—
153	C₄²×C₁₃₁	—	2	2	no	—
154	C₄²×C₁₃₁	—	2	2	no	—
155	C₄²×C₁₃₁	—	4	4	no	—
156	C₄²×C₁₃₁	C₂×D₄	1	2	yes	—
157	C₄²×C₁₃₁	#41	1	2	yes	—
158	C₂³×C₁₃₁	—	2	2	no	—
159	C₂³×C₁₃₁	—	2	2	no	—
160	C₂³×C₁₃₁	—	4	1	no	—
161	C₂³×C₁₃₁	—	4	1	no	—
162	C₂³×C₁₃₁	—	4	1	no	—
163	C₂³×C₁₃₁	—	4	1	no	—
164	C₂³×C₁₃₁	—	4	1	no	—
165	C₂³×C₁₃₁	—	4	1	no	—
166	C₂³×C₁₃₁	—	4	1	no	—
167	C₂³×C₁₃₁	—	4	1	no	—
168	C₂³×C₁₃₁	—	4	1	no	—
169	C₂³×C₁₃₁	—	4	1	no	—
170	C₂³×C₁₃₁	—	4	1	no	—
171	C₂³×C₁₃₁	—	4	1	no	—
172	C₂³×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
173	Q₈×C₁₃₁	—	8	4	no	—
174	D₄×C₁₃₁	—	2	2	no	—
175	D₄×C₁₃₁	—	2	2	no	—
176	D₄×C₁₃₁	—	2	2	no	—
177	D₄×C₁₃₁	—	2	2	no	—
178	D₄×C₁₃₁	—	4	1	no	—
179	D₄×C₁₃₁	—	4	1	no	—
180	D₄×C₁₃₁	—	4	1	no	—
181	D₄×C₁₃₁	—	4	1	no	—
182	C₂×C₄×C₁₃₁	—	2	1	no	—
183	C₂×C₄×C₁₃₁	—	2	1	no	—
184	C₂×C₄×C₁₃₁	—	2	2	no	—
185	C₂×C₄×C₁₃₁	—	2	2	no	—
186	C₂×C₄×C₁₃₁	—	2	2	no	—
187	C₂×C₄×C₁₃₁	—	2	2	no	—
188	C₂×C₄×C₁₃₁	—	2	2	no	—
189	C₂×C₄×C₁₃₁	—	2	2	no	—
190	C₂×C₄×C₁₃₁	—	2	2	no	—
191	C₂×C₄×C₁₃₁	—	4	1	no	—
192	C₂×C₄×C₁₃₁	—	4	1	no	—
193	C₂×C₄×C₁₃₁	—	4	8	no	—
194	C₂×C₄×C₁₃₁	—	4	1	no	—
195	C₂×C₄×C₁₃₁	—	4	2	no	—
196	C₂×C₄×C₁₃₁	—	4	2	no	—
197	C₂×C₄×C₁₃₁	—	4	1	no	—
198	C₂×C₄×C₁₃₁	—	4	2	no	—
199	C₂×C₄×C₁₃₁	—	4	1	no	—
200	C₂×C₄×C₁₃₁	—	4	2	no	—
201	C₂×C₄×C₁₃₁	—	4	2	no	—
202	C₂×C₄×C₁₃₁	—	4	2	no	—
203	C₂×C₄×C₁₃₁	—	8	4	no	—
204	C₂×C₄×C₁₃₁	#121	1	2	yes	—
205	C₂×C₄×C₁₃₁	#121	1	2	yes	—
206	C₂×C₄×C₁₃₁	#135	1	2	yes	—
207	C₂×C₄×C₁₃₁	AGL(1,ℤ/8)	1	2	yes	—
208	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
213	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
214	C₈×C₁₃₁	—	2	2	no	—
215	C₈×C₁₃₁	—	4	2	no	—
216	C₈×C₁₃₁	—	4	1	no	—
217	C₂²×C₁₃₁	—	4	2	no	—
218	C₂²×C₁₃₁	—	4	2	no	—
219	C₂²×C₁₃₁	—	4	2	no	—
220	C₂²×C₁₃₁	—	4	2	no	—
221	C₂²×C₁₃₁	—	4	2	no	—
222	C₂²×C₁₃₁	—	4	2	no	—
223	C₂²×C₁₃₁	—	8	1	no	—
224	C₂²×C₁₃₁	—	8	1	no	—
225	C₂²×C₁₃₁	—	8	1	no	—
226	C₂²×C₁₃₁	—	8	1	no	—
227	C₂²×C₁₃₁	—	8	1	no	—
228	C₂²×C₁₃₁	—	8	1	no	—
229	C₂²×C₁₃₁	—	8	1	no	—
230	C₂²×C₁₃₁	—	8	1	no	—
231	C₂²×C₁₃₁	C₂×#121	1	1	yes	characteristic
232	C₂²×C₁₃₁	#547	1	1	yes	characteristic
233	C₂²×C₁₃₁	#548	1	1	yes	characteristic
234	C₂²×C₁₃₁	C₂×#135	1	1	yes	characteristic
235	C₂²×C₁₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
236	C₂²×C₁₃₁	#576	1	1	yes	characteristic
237	C₂²×C₁₃₁	#577	1	1	yes	characteristic
238	C₄×C₁₃₁	—	2	2	no	—
239	C₄×C₁₃₁	—	4	2	no	—
240	C₄×C₁₃₁	—	4	2	no	—
241	C₄×C₁₃₁	—	4	2	no	—
242	C₄×C₁₃₁	—	8	2	no	—
243	C₄×C₁₃₁	—	8	1	no	—
244	C₄×C₁₃₁	—	8	2	no	—
245	C₄×C₁₃₁	#463	1	4	yes	—
246	C₄×C₁₃₁	#525	1	1	yes	characteristic
247	C₄×C₁₃₁	#536	1	1	yes	characteristic
248	C₄×C₁₃₁	#552	1	1	yes	characteristic
249	C₄×C₁₃₁	#556	1	1	yes	characteristic
250	C₂×C₁₃₁	—	8	2	no	—
251	C₂×C₁₃₁	—	8	2	no	—
252	C₂×C₁₃₁	#2415	1	1	yes	characteristic
253	C₂×C₁₃₁	C₂×#463	1	1	yes	characteristic
254	C₂×C₁₃₁	#3045	1	1	yes	characteristic
255	C₂×C₁₃₁	#3341	1	1	yes	characteristic
256	C₂×C₁₃₁	#3354	1	1	yes	characteristic
257	C₂×C₁₃₁	#3360	1	1	yes	characteristic
258	C₂×C₁₃₁	#3366	1	1	yes	characteristic
259	#24677	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
260	C₁₃₁	#24677	1	1	yes	characteristic, direct product factor, Sylow
261	C₂×#476	C₂×C₁₃₁	1	1	yes	characteristic, complemented
262	C₂×C₄×D₈	C₂×C₁₃₁	1	1	yes	characteristic
263	#2563	C₂×C₁₃₁	1	1	yes	characteristic, complemented
264	#2354	C₂×C₁₃₁	1	1	yes	characteristic, complemented
265	#2073	C₂×C₁₃₁	1	2	yes	complemented
266	#2054	C₂×C₁₃₁	1	2	yes	—
267	#1990	C₂×C₁₃₁	1	1	yes	characteristic, complemented
268	#1949	C₂×C₁₃₁	1	2	yes	complemented
269	#1939	C₂×C₁₃₁	1	1	yes	characteristic, complemented
270	#1926	C₂×C₁₃₁	1	2	yes	complemented
271	#1802	C₂×C₁₃₁	1	1	yes	characteristic, complemented
272	C₂²×D₈	C₂²×C₁₃₁	1	1	yes	characteristic
273	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
274	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
275	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
276	C₂×#117	—	2	1	no	—
277	#476	—	2	4	no	—
278	C₄×D₈	—	2	4	no	—
279	C₂×#107	C₂²×C₁₃₁	1	1	yes	characteristic
280	C₂×#106	C₂²×C₁₃₁	1	2	yes	—
281	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	2	yes	—
282	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
283	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
284	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
285	C₂×#102	C₂²×C₁₃₁	1	1	yes	characteristic
286	C₂×#102	C₂²×C₁₃₁	1	1	yes	characteristic
287	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
288	#393	—	2	2	no	—
289	#390	C₂²×C₁₃₁	1	2	yes	—
290	#390	C₂²×C₁₃₁	1	2	yes	—
291	#388	—	2	2	no	—
292	#384	C₂²×C₁₃₁	1	1	yes	characteristic
293	#382	C₂²×C₁₃₁	1	2	yes	—
294	#380	—	2	1	no	—
295	#380	—	2	1	no	—
296	#380	—	2	1	no	—
297	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
298	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
299	#340	C₂²×C₁₃₁	1	2	yes	—
300	#340	C₂²×C₁₃₁	1	2	yes	—
301	#340	C₂²×C₁₃₁	1	2	yes	—
302	#336	C₂²×C₁₃₁	1	2	yes	—
303	C₂²×Q₈	—	2	1	no	—
304	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
305	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
306	C₂³×C₄	—	2	1	no	—
307	C₂³×C₄	—	2	1	no	—
308	C₂×D₈	—	2	2	no	—
309	C₂×D₈	—	2	2	no	—
310	C₂×D₈	—	2	2	no	—
311	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
312	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
313	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
314	C₄⋊Q₈	—	2	2	no	—
315	C₄⋊Q₈	—	2	2	no	—
316	C₄×D₄	—	2	2	no	—
317	C₄×D₄	—	2	2	no	—
318	C₄×D₄	—	2	2	no	—
319	C₄×D₄	D₄×C₁₃₁	1	4	yes	—
320	#117	—	4	4	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
325	C₂×C₄⋊C₄	D₄×C₁₃₁	1	1	yes	characteristic
326	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
329	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	1	yes	characteristic
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₄²	—	2	2	no	—
337	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
338	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
339	#107	—	2	2	no	—
340	#106	—	2	4	no	—
341	C₄⋊C₈	—	2	4	no	—
342	C₄⋊C₈	—	2	2	no	—
343	#102	—	2	2	no	—
344	#102	—	2	4	no	—
345	#102	—	2	4	no	—
346	#102	—	2	2	no	—
347	C₄×C₈	—	2	2	no	—
348	#95	—	2	2	no	—
349	#95	—	2	2	no	—
350	#95	—	2	2	no	—
351	#95	D₄×C₁₃₁	1	2	yes	—
352	C₂⁴	—	2	1	no	—
353	C₂⁴	—	2	1	no	—
354	C₂×Q₈	—	4	2	no	—
355	C₂×Q₈	—	8	1	no	—
356	C₂×Q₈	—	8	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	C₂×D₄×C₁₃₁	1	2	yes	—
368	C₂×D₄	#41×C₁₃₁	1	2	yes	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	—	4	2	no	—
376	C₂²×C₄	—	4	2	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
381	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
383	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
384	D₈	—	2	8	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	#41×C₁₃₁	1	2	yes	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	4	2	no	—
404	C₄⋊C₄	—	4	2	no	—
405	C₄⋊C₄	—	8	1	no	—
406	C₄⋊C₄	C₂×D₄×C₁₃₁	1	2	yes	—
407	C₂²⋊C₄	—	2	4	no	—
408	C₂²⋊C₄	—	4	4	no	—
409	C₂²⋊C₄	—	4	2	no	—
410	C₂²⋊C₄	—	8	2	no	—
411	C₂²⋊C₄	—	8	2	no	—
412	C₂²⋊C₄	—	8	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	2	2	no	—
415	C₄²	—	4	4	no	—
416	C₄²	C₂×D₄×C₁₃₁	1	2	yes	—
417	C₄²	#41×C₁₃₁	1	2	yes	—
418	C₂³	—	2	2	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	4	1	no	—
421	C₂³	—	4	1	no	—
422	C₂³	—	4	1	no	—
423	C₂³	—	4	1	no	—
424	C₂³	—	4	1	no	—
425	C₂³	—	4	1	no	—
426	C₂³	—	4	1	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	4	1	no	—
429	C₂³	—	4	1	no	—
430	C₂³	—	4	1	no	—
431	C₂³	—	4	1	no	—
432	C₂³	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
433	Q₈	—	8	4	no	—
434	D₄	—	2	2	no	—
435	D₄	—	2	2	no	—
436	D₄	—	2	2	no	—
437	D₄	—	2	2	no	—
438	D₄	—	4	1	no	—
439	D₄	—	4	1	no	—
440	D₄	—	4	1	no	—
441	D₄	—	4	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	8	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	8	4	no	—
464	C₂×C₄	#121×C₁₃₁	1	2	yes	—
465	C₂×C₄	#121×C₁₃₁	1	2	yes	—
466	C₂×C₄	#135×C₁₃₁	1	2	yes	—
467	C₂×C₄	AGL(1,ℤ/8)×C₁₃₁	1	2	yes	—
468	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
469	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
470	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
471	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
472	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
473	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
474	C₈	—	2	2	no	—
475	C₈	—	4	2	no	—
476	C₈	—	4	1	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	8	1	no	—
484	C₂²	—	8	1	no	—
485	C₂²	—	8	1	no	—
486	C₂²	—	8	1	no	—
487	C₂²	—	8	1	no	—
488	C₂²	—	8	1	no	—
489	C₂²	—	8	1	no	—
490	C₂²	—	8	1	no	—
491	C₂²	C₂×#121×C₁₃₁	1	1	yes	characteristic
492	C₂²	#547×C₁₃₁	1	1	yes	characteristic
493	C₂²	#548×C₁₃₁	1	1	yes	characteristic
494	C₂²	C₂×#135×C₁₃₁	1	1	yes	characteristic
495	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₁	1	1	yes	characteristic
496	C₂²	#576×C₁₃₁	1	1	yes	characteristic
497	C₂²	#577×C₁₃₁	1	1	yes	characteristic
498	C₄	—	2	2	no	—
499	C₄	—	4	2	no	—
500	C₄	—	4	2	no	—
501	C₄	—	4	2	no	—
502	C₄	—	8	1	no	—
503	C₄	—	8	2	no	—
504	C₄	—	8	2	no	—
505	C₄	#463×C₁₃₁	1	4	yes	—
506	C₄	#525×C₁₃₁	1	1	yes	characteristic
507	C₄	#536×C₁₃₁	1	1	yes	characteristic
508	C₄	#552×C₁₃₁	1	1	yes	characteristic
509	C₄	#556×C₁₃₁	1	1	yes	characteristic
510	C₂	—	8	2	no	—
511	C₂	—	8	2	no	—
512	C₂	#2415×C₁₃₁	1	1	yes	characteristic
513	C₂	C₂×#463×C₁₃₁	1	1	yes	characteristic
514	C₂	#3045×C₁₃₁	1	1	yes	characteristic
515	C₂	#3341×C₁₃₁	1	1	yes	characteristic
516	C₂	#3354×C₁₃₁	1	1	yes	characteristic
517	C₂	#3360×C₁₃₁	1	1	yes	characteristic
518	C₂	#3366×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂²×D₈×C₁₃₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ C₄×C₄⋊C₄×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#476×C₁₃₁	C₂	semidirect
3. #2563×C₁₃₁	C₂	semidirect
4. #2354×C₁₃₁	C₂	semidirect
5. #2073×C₁₃₁	C₂	semidirect
7. #1990×C₁₃₁	C₂	semidirect
8. #1949×C₁₃₁	C₂	semidirect
9. #1939×C₁₃₁	C₂	semidirect
10. #1926×C₁₃₁	C₂	semidirect
11. #1802×C₁₃₁	C₂	semidirect
259. #24677	C₁₃₁	direct (N × H)
260. C₁₃₁	#24677	direct (N × H)
261. C₂×#476	C₂×C₁₃₁	semidirect
263. #2563	C₂×C₁₃₁	semidirect
264. #2354	C₂×C₁₃₁	semidirect
265. #2073	C₂×C₁₃₁	semidirect
267. #1990	C₂×C₁₃₁	semidirect
268. #1949	C₂×C₁₃₁	semidirect
269. #1939	C₂×C₁₃₁	semidirect
270. #1926	C₂×C₁₃₁	semidirect
271. #1802	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×#476×C₁₃₁	2
C₂×C₄×D₈×C₁₃₁	2
#2563×C₁₃₁	2
#2354×C₁₃₁	2
#2073×C₁₃₁	2
#2054×C₁₃₁	2
#1990×C₁₃₁	2
#1949×C₁₃₁	2
#1939×C₁₃₁	2
#1926×C₁₃₁	2
#1802×C₁₃₁	2
#24677	131

Subgroups — C131×#24677 #45710561

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#24677 #45710561