Subgroups — Dic₅₉₅₉ #37558604

Order 23836.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₅₉×C₁₀₁	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₀₁	—	59	1	no	maximal, Hall
4	Dic₅₉	—	101	1	no	maximal, Hall
5	C₂×C₁₀₁	D₅₉	1	1	yes	characteristic
6	C₂×C₅₉	D₁₀₁	1	1	yes	characteristic
7	C₁₀₁	Dic₅₉	1	1	yes	characteristic, complemented, Sylow
8	C₅₉	Dic₁₀₁	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	5959	1	no	Sylow
10	C₂	D₅₉₅₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅₉₅₉
commutator, hypocenter	C₅₉×C₁₀₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₅₉×C₁₀₁	C₂
LCS	G ▷ C₅₉×C₁₀₁
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.