Subgroups — #6045

Order 200.

48 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	#1039	C₂	1	2	yes	maximal
3	C₂×C₅²	C₂²	1	1	yes	characteristic
4	Dic₁₀	—	5	6	no	maximal
5	C₅²	Q₈	1	1	yes	characteristic, complemented, Sylow
6	C₄×C₅	D₅	1	6	yes	—
7	Dic₅	—	5	12	no	—
8	C₂×C₅	C₂×D₅	1	6	yes	—
9	Q₈	—	25	1	no	Sylow
10	C₅	Dic₁₀	1	6	yes	complemented
11	C₄	—	25	2	no	—
12	C₄	C₅⋊D₅	1	1	yes	characteristic
13	C₂	C₂×C₅⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×C₅⋊D₅
commutator, socle, prime radical, cosocle	C₂×C₅²	C₂²
Fitting	C₄×C₅²	C₂
hypercenter	C₄	C₅⋊D₅
hypocenter	C₅²	Q₈
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂ ◁ C₄

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

N	H ≅ G/N	type
5. C₅²	Q₈	semidirect
10. C₅	Dic₁₀	semidirect

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