Subgroups — C₄⋊(C₅⋊D₅) #6047

Order 200.

64 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	C₄×C₅²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅²	C₂²	1	1	yes	characteristic
4	C₅⋊D₅	—	2	2	no	—
5	D₂₀	—	5	6	no	maximal
6	C₅²	D₄	1	1	yes	characteristic, complemented, Sylow
7	C₂×D₅	—	5	12	no	—
8	C₄×C₅	D₅	1	6	yes	complemented
9	C₂×C₅	C₂×D₅	1	6	yes	—
10	D₅	—	10	12	no	—
11	D₄	—	25	1	no	Sylow
12	C₅	D₂₀	1	6	yes	complemented
13	C₂²	—	25	2	no	—
14	C₄	C₅⋊D₅	1	1	yes	characteristic, complemented
15	C₂	—	50	2	no	—
16	C₂	C₂×C₅⋊D₅	1	1	yes	characteristic

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.