Subgroups — C₅×C₁₁⋊C₅ #63277

Order 275.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁	C₅	1	1	yes	maximal, characteristic, complemented
2	C₁₁⋊C₅	C₅	1	5	yes	maximal, direct product factor
3	C₅²	—	11	1	no	maximal, Sylow
4	C₁₁	C₅²	1	1	yes	characteristic, complemented, Sylow
5	C₅	—	11	5	no	—
6	C₅	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₅	C₁₁⋊C₅
commutator, cosocle, hypocenter	C₁₁	C₅²
Frattini	C₁	G
Fitting, socle	C₅×C₁₁	C₅
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₅

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.