Subgroups — C₂×C₅⋊D₅ #1047

Order 100.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅⋊D₅	C₂	1	2	yes	maximal, direct product factor
3	C₅²	C₂²	1	1	yes	characteristic, complemented, Sylow
4	C₂×D₅	—	5	6	no	maximal
5	C₂×C₅	D₅	1	6	yes	complemented
6	D₅	—	5	12	no	—
7	C₅	C₂×D₅	1	6	yes	complemented
8	C₂²	—	25	1	no	Sylow
9	C₂	—	25	2	no	—
10	C₂	C₅⋊D₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₅²	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.