Subgroups — D₅²⋊C₂ #6056

Order 200.

29 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅²	C₂	1	2	yes	maximal, complemented
2	#1044	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅⋊D₅	C₂²	1	1	yes	characteristic
4	C₅×D₅	—	2	2	no	—
5	C₅²	D₄	1	1	yes	characteristic, complemented, Sylow
6	C₂×D₅	—	10	2	no	—
7	AGL(1,𝔽₅)	—	10	1	no	—
8	C₂×C₅	—	10	2	no	—
9	D₅	—	2	2	no	—
10	D₅	—	10	1	no	—
11	D₅	—	10	2	no	—
12	D₄	—	25	1	no	maximal, Sylow
13	C₅	—	2	2	no	—
14	C₅	—	2	1	no	—
15	C₂²	—	25	2	no	—
16	C₄	—	25	1	no	—
17	C₂	—	10	2	no	—
18	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle	C₅⋊D₅	C₂²
Fitting, socle, hypocenter	C₅²	D₄
LCS	G ▷ C₅⋊D₅ ▷ C₅²
UCS	C₁

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.