Subgroups — #6037

Order 200.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₅	C₂	1	2	yes	maximal, complemented
2	#1039	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅²	C₂²	1	1	yes	characteristic
4	C₅×D₅	—	2	2	no	—
5	C₂²⋊D₅	—	5	2	no	maximal
6	C₅²	D₄	1	1	yes	characteristic, complemented, Sylow
7	C₂²×C₅	—	5	2	no	—
8	C₂×D₅	D₅	1	2	yes	complemented
9	Dic₅	—	5	2	no	—
10	Dic₅	—	10	2	no	—
11	C₂×C₅	—	2	2	no	—
12	C₂×C₅	—	10	2	no	—
13	C₂×C₅	C₂×D₅	1	2	yes	—
14	D₅	—	2	2	no	—
15	D₄	—	25	1	no	Sylow
16	C₅	—	2	2	no	—
17	C₅	C₂²⋊D₅	1	2	yes	complemented
18	C₂²	—	5	2	no	—
19	C₄	—	25	1	no	—
20	C₂	—	10	2	no	—
21	C₂	D₅²	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅²
commutator, Fitting, socle, cosocle	C₂×C₅²	C₂²
hypocenter	C₅²	D₄
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂

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

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