Subgroups — #6036

Order 200.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅²
commutator, hypocenter	C₅²	C₂×C₄
Fitting, socle, cosocle	C₂×C₅²	C₂²
prime radical	C₂×C₅⋊D₅	C₂
LCS	G ▷ 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.