Subgroups — #6029

Order 200.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅²	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅²	C₄	1	1	yes	characteristic
3	#168	—	5	6	no	maximal
4	C₅²	C₈	1	1	yes	characteristic, complemented, Sylow
5	C₄×C₅	D₅	1	6	yes	—
6	C₂×C₅	Dic₅	1	6	yes	—
7	C₈	—	25	1	no	Sylow
8	C₅	#168	1	6	yes	complemented
9	C₄	C₅⋊D₅	1	1	yes	characteristic
10	C₂	#1039	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₄	C₅⋊D₅
commutator, hypocenter	C₅²	C₈
Fitting, cosocle	C₄×C₅²	C₂
socle, prime radical	C₂×C₅²	C₄
LCS	G ▷ C₅²
UCS	C₁ ◁ C₄

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

N	H ≅ G/N	type
4. C₅²	C₈	semidirect
8. C₅	#168	semidirect

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

subgroup	index
C₄×C₅²	2
#168	5