Subgroups — C₃×A₄×C₁₃₁⋊C₅ #37556090

Order 23580.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₁₃₁⋊C₅	C₃	1	1	yes	maximal, characteristic, complemented
2	A₄×C₁₃₁⋊C₅	C₃	1	3	yes	maximal, direct product factor
3	C₃²×C₁₃₁⋊C₅	—	4	1	no	maximal, Hall
4	C₃×A₄×C₁₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₃×C₁₃₁⋊C₅	—	3	1	no	—
6	C₂²×C₁₃₁⋊C₅	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₃₁⋊C₅	—	4	3	no	—
8	C₃×C₁₃₁⋊C₅	A₄	1	1	yes	characteristic, direct product factor
9	C₂²×C₃×C₁₃₁	C₃×C₅	1	1	yes	characteristic, complemented
10	A₄×C₁₃₁	C₃×C₅	1	3	yes	complemented
11	C₂×C₁₃₁⋊C₅	—	3	1	no	—
12	C₃²×C₁₃₁	—	4	1	no	Hall
13	C₂×C₃×C₁₃₁	—	3	1	no	—
14	C₁₃₁⋊C₅	C₃×A₄	1	1	yes	characteristic, direct product factor, Hall
15	C₂²×C₁₃₁	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₃×C₁₃₁	—	4	3	no	—
17	C₃×C₁₃₁	C₅×A₄	1	1	yes	characteristic, complemented
18	C₂×C₁₃₁	—	3	1	no	—
19	C₃×C₅×A₄	—	131	1	no	maximal, Hall
20	C₁₃₁	C₃×C₅×A₄	1	1	yes	characteristic, complemented, Sylow
21	C₂²×C₃×C₅	—	131	1	no	—
22	C₅×A₄	—	131	3	no	—
23	C₃²×C₅	—	524	1	no	Hall
24	C₃×A₄	C₁₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₃×C₅	—	393	1	no	—
26	C₂²×C₅	—	131	1	no	Hall
27	C₃×C₅	—	524	3	no	—
28	C₃×C₅	—	131	1	no	—
29	C₂²×C₃	C₃×C₁₃₁⋊C₅	1	1	yes	characteristic, complemented
30	A₄	C₃×C₁₃₁⋊C₅	1	3	yes	direct product factor
31	C₂×C₅	—	393	1	no	—
32	C₃²	—	4	1	no	Sylow
33	C₂×C₃	—	3	1	no	—
34	C₅	—	131	1	no	Sylow
35	C₂²	C₃²×C₁₃₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
36	C₃	—	4	3	no	—
37	C₃	A₄×C₁₃₁⋊C₅	1	1	yes	characteristic, direct product factor
38	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃	A₄×C₁₃₁⋊C₅
commutator, cosocle, hypocenter	C₂²×C₁₃₁	C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₁₃₁	C₃×C₅
LCS	G ▷ C₂²×C₁₃₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₁₃₁⋊C₅	C₃	semidirect
2. A₄×C₁₃₁⋊C₅	C₃	direct (N × H)
4. C₃×A₄×C₁₃₁	C₅	semidirect
6. C₂²×C₁₃₁⋊C₅	C₃²	semidirect
8. C₃×C₁₃₁⋊C₅	A₄	direct (N × H)
9. C₂²×C₃×C₁₃₁	C₃×C₅	semidirect
10. A₄×C₁₃₁	C₃×C₅	semidirect
14. C₁₃₁⋊C₅	C₃×A₄	direct (N × H)
15. C₂²×C₁₃₁	C₃²×C₅	semidirect
17. C₃×C₁₃₁	C₅×A₄	semidirect
20. C₁₃₁	C₃×C₅×A₄	semidirect
24. C₃×A₄	C₁₃₁⋊C₅	direct (N × H)
29. C₂²×C₃	C₃×C₁₃₁⋊C₅	semidirect
30. A₄	C₃×C₁₃₁⋊C₅	direct (N × H)
35. C₂²	C₃²×C₁₃₁⋊C₅	semidirect
37. C₃	A₄×C₁₃₁⋊C₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₁₃₁⋊C₅	3
A₄×C₁₃₁⋊C₅	3
C₃²×C₁₃₁⋊C₅	4
C₃×A₄×C₁₃₁	5
C₃×C₅×A₄	131

Subgroups — C3×A4×C131⋊C5 #37556090

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×A₄×C₁₃₁⋊C₅ #37556090