Subgroups — #6039

Order 200.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1039	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₅	C₂	1	2	yes	maximal
3	C₂×C₅²	C₂²	1	1	yes	characteristic
4	Dic₁₀	—	5	2	no	maximal
5	C₅²	Q₈	1	1	yes	characteristic, complemented, Sylow
6	C₄×C₅	—	5	2	no	—
7	Dic₅	—	5	2	no	—
8	Dic₅	—	10	2	no	—
9	Dic₅	D₅	1	2	yes	—
10	C₂×C₅	—	2	2	no	—
11	C₂×C₅	C₂×D₅	1	2	yes	—
12	Q₈	—	25	1	no	Sylow
13	C₅	—	2	2	no	—
14	C₅	Dic₁₀	1	2	yes	complemented
15	C₄	—	5	2	no	—
16	C₄	—	25	1	no	—
17	C₂	D₅²	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅²
commutator, Fitting, socle, prime radical, cosocle	C₂×C₅²	C₂²
hypocenter	C₅²	Q₈
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂

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

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

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