Subgroups — (C₃⋊D₃)⋊(D₁₃₁⋊C₅) #37556087

Order 23580.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃×C₁₃₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₃⋊(D₁₃₁⋊C₅)	C₂	1	2	yes	maximal, complemented
3	D₃×D₁₃₁⋊C₅	—	3	2	no	maximal
4	C₃²×C₁₃₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	(C₃⋊D₃)⋊D₁₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	C₃⋊(D₁₃₁⋊C₅)	D₃	1	2	yes	complemented
7	D₃×C₁₃₁⋊C₅	—	3	2	no	—
8	D₃×C₁₃₁⋊C₅	—	6	1	no	—
9	C₃×D₁₃₁⋊C₅	—	3	2	no	—
10	C₂×D₁₃₁⋊C₅	—	9	1	no	Hall
11	C₃⋊D₃×C₁₃₁	C₂×C₅	1	1	yes	characteristic, complemented
12	C₃×D₃₉₃	C₂×C₅	1	2	yes	complemented
13	C₃×C₁₃₁⋊C₅	—	2	1	no	—
14	C₃×C₁₃₁⋊C₅	C₂×D₃	1	2	yes	complemented
15	D₃×D₁₃₁	—	3	2	no	—
16	C₂×C₁₃₁⋊C₅	—	9	1	no	—
17	D₁₃₁⋊C₅	—	3	2	no	—
18	C₃²×C₁₃₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
19	D₃₉₃	C₅×D₃	1	2	yes	complemented
20	C₃×D₁₃₁	—	3	2	no	—
21	D₃×C₁₃₁	—	3	2	no	—
22	D₃×C₁₃₁	—	6	1	no	—
23	C₁₃₁⋊C₅	D₃²	1	1	yes	characteristic, complemented, Hall
24	C₂×D₁₃₁	—	9	1	no	Hall
25	C₃×C₁₃₁	—	2	1	no	—
26	C₃×C₁₃₁	C₂×C₅×D₃	1	2	yes	complemented
27	C₂×C₁₃₁	—	9	1	no	—
28	D₁₃₁	—	3	2	no	—
29	C₅×D₃²	—	131	1	no	maximal, Hall
30	C₁₃₁	C₅×D₃²	1	1	yes	characteristic, complemented, Sylow
31	C₅×C₃⋊D₃	—	131	1	no	—
32	C₃×C₅×D₃	—	131	2	no	—
33	C₂×C₅×D₃	—	393	2	no	—
34	C₃²×C₅	—	131	1	no	Hall
35	D₃²	—	131	1	no	Hall
36	C₂×C₃×C₅	—	393	2	no	—
37	C₅×D₃	—	786	1	no	—
38	C₅×D₃	—	131	2	no	—
39	C₅×D₃	—	393	2	no	—
40	C₂²×C₅	—	1179	1	no	Hall
41	C₃⋊D₃	D₁₃₁⋊C₅	1	1	yes	characteristic, complemented
42	C₃×D₃	—	131	2	no	—
43	C₃×C₅	—	262	1	no	—
44	C₃×C₅	—	131	2	no	—
45	C₂×D₃	—	393	2	no	—
46	C₂×C₅	—	393	2	no	—
47	C₂×C₅	—	1179	1	no	—
48	C₃²	C₂×D₁₃₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₃	—	393	2	no	—
50	D₃	—	3	2	no	—
51	D₃	—	6	1	no	—
52	D₃	—	131	2	no	—
53	C₅	—	131	1	no	Sylow
54	C₂²	—	1179	1	no	Sylow
55	C₃	—	2	1	no	—
56	C₃	D₃×D₁₃₁⋊C₅	1	2	yes	complemented
57	C₂	—	9	1	no	—
58	C₂	—	393	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₃₁	C₂²×C₅
LCS	G ▷ C₃²×C₁₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₃×C₁₃₁⋊C₅	C₂	semidirect
2. C₃×C₃⋊(D₁₃₁⋊C₅)	C₂	semidirect
4. C₃²×C₁₃₁⋊C₅	C₂²	semidirect
5. (C₃⋊D₃)⋊D₁₃₁	C₅	semidirect
6. C₃⋊(D₁₃₁⋊C₅)	D₃	semidirect
11. C₃⋊D₃×C₁₃₁	C₂×C₅	semidirect
12. C₃×D₃₉₃	C₂×C₅	semidirect
14. C₃×C₁₃₁⋊C₅	C₂×D₃	semidirect
18. C₃²×C₁₃₁	C₂²×C₅	semidirect
19. D₃₉₃	C₅×D₃	semidirect
23. C₁₃₁⋊C₅	D₃²	semidirect
26. C₃×C₁₃₁	C₂×C₅×D₃	semidirect
30. C₁₃₁	C₅×D₃²	semidirect
41. C₃⋊D₃	D₁₃₁⋊C₅	semidirect
48. C₃²	C₂×D₁₃₁⋊C₅	semidirect
56. C₃	D₃×D₁₃₁⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊D₃×C₁₃₁⋊C₅	2
C₃×C₃⋊(D₁₃₁⋊C₅)	2
D₃×D₁₃₁⋊C₅	3
(C₃⋊D₃)⋊D₁₃₁	5
C₅×D₃²	131

Subgroups — (C3⋊D3)⋊(D131⋊C5) #37556087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₃⋊D₃)⋊(D₁₃₁⋊C₅) #37556087