Subgroups — #564⋊C₅ #65674

Order 320.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#564	C₅	1	1	yes	maximal, characteristic, complemented, Sylow
2	#125	—	5	3	no	—
3	C₂²×C₅	—	16	1	no	maximal
4	C₄⋊C₄	—	5	6	no	—
5	C₄²	—	5	1	no	—
6	C₂×C₅	—	16	3	no	—
7	C₂×C₄	—	5	3	no	—
8	C₅	—	16	1	no	Sylow
9	C₂²	C₂⁴⋊C₅	1	1	yes	characteristic
10	C₄	—	10	3	no	—
11	C₂	2₋¹⁺⁴⋊C₅	1	3	yes	—

	subgroup	G/H
center, Frattini, socle, hypercenter	C₂²	C₂⁴⋊C₅
commutator, Fitting, cosocle, hypocenter	#564	C₅
LCS	G ▷ #564
UCS	C₁ ◁ C₂²

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

N	H ≅ G/N	type
1. #564	C₅	semidirect

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

subgroup	index
#564	5
C₂²×C₅	16