Subgroups — Dic₁₁⋊C₅ #6346

Order 220.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₁₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₁₁	C₂×C₅	1	1	yes	characteristic
5	C₄×C₅	—	11	1	no	maximal, Hall
6	C₁₁	C₄×C₅	1	1	yes	characteristic, complemented, Sylow
7	C₂×C₅	—	11	1	no	—
8	C₅	—	11	1	no	Sylow
9	C₄	—	11	1	no	Sylow
10	C₂	AGL(1,𝔽₁₁)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	AGL(1,𝔽₁₁)
commutator, hypocenter	C₁₁	C₄×C₅
Fitting, socle, cosocle	C₂×C₁₁	C₂×C₅
prime radical	C₂×C₁₁⋊C₅	C₂
LCS	G ▷ C₁₁
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.