Subgroups — Dic₆₁₅₅ #37590083

Order 24620.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₂₃₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₂₃₁	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₂₃₁	—	5	1	no	maximal, Hall
4	C₂×C₁₂₃₁	D₅	1	1	yes	characteristic
5	C₁₂₃₁	Dic₅	1	1	yes	characteristic, complemented, Sylow
6	Dic₅	—	1231	1	no	maximal, Hall
7	C₂×C₅	D₁₂₃₁	1	1	yes	characteristic
8	C₅	Dic₁₂₃₁	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	6155	1	no	Sylow
10	C₂	D₆₁₅₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₆₁₅₅
commutator, hypocenter	C₅×C₁₂₃₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₅×C₁₂₃₁	C₂
LCS	G ▷ C₅×C₁₂₃₁
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.