Subgroups — H(3,𝔽₅)⋊C₃ #67329

Order 375.

10 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	H(3,𝔽₅)	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₅²	—	3	2	no	—
3	C₃×C₅	—	25	1	no	maximal
4	C₅	—	15	2	no	—
5	C₅	C₅²⋊C₃	1	1	yes	characteristic
6	C₃	—	25	1	no	Sylow

	subgroup	G/H
center, Frattini, socle, hypercenter	C₅	C₅²⋊C₃
commutator, Fitting, cosocle, hypocenter	H(3,𝔽₅)	C₃
LCS	G ▷ H(3,𝔽₅)
UCS	C₁ ◁ C₅

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

N	H ≅ G/N	type
1. H(3,𝔽₅)	C₃	semidirect

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

subgroup	index
H(3,𝔽₅)	3
C₃×C₅	25