Finite Group Databasebeta

← C₅₃⋊(D₆₁⋊C₅) #44568261

Subgroups — C₅₃⋊(D₆₁⋊C₅) #44568261

Order 32330.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×C₆₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₂₃₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅₃×C₆₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	D₆₁⋊C₅	—	53	1	no	maximal, Hall
5	C₅×D₅₃	—	61	1	no	maximal, Hall
6	C₆₁⋊C₅	D₅₃	1	1	yes	characteristic, complemented, Hall
7	C₅×C₅₃	—	61	1	no	Hall
8	D₆₁	—	53	1	no	Hall
9	D₅₃	—	61	1	no	Hall
10	C₆₁	C₅×D₅₃	1	1	yes	characteristic, complemented, Sylow
11	C₅₃	D₆₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₅	—	3233	1	no	Hall
13	C₅	—	61	1	no	Sylow
14	C₂	—	3233	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅₃×C₆₁	C₂×C₅
LCS	G ▷ C₅₃×C₆₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅₃×C₆₁⋊C₅	C₂	semidirect
2. D₃₂₃₃	C₅	semidirect
3. C₅₃×C₆₁	C₂×C₅	semidirect
6. C₆₁⋊C₅	D₅₃	semidirect
10. C₆₁	C₅×D₅₃	semidirect
11. C₅₃	D₆₁⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×C₆₁⋊C₅	2
D₃₂₃₃	5
D₆₁⋊C₅	53
C₅×D₅₃	61