Subgroups — Dic₅₂₉ #14523739

Order 2116.

9 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₂₉	C₂	1	1	yes	maximal, characteristic
2	C₅₂₉	C₄	1	1	yes	characteristic, complemented, Sylow
3	Dic₂₃	—	23	1	no	maximal
4	C₂×C₂₃	D₂₃	1	1	yes	characteristic
5	C₂₃	Dic₂₃	1	1	yes	characteristic
6	C₄	—	529	1	no	Sylow
7	C₂	D₅₂₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	D₅₂₉
commutator, hypocenter	C₅₂₉	C₄
Frattini, socle, prime radical	C₂×C₂₃	D₂₃
Fitting, cosocle	C₂×C₅₂₉	C₂
LCS	G ▷ C₅₂₉
UCS	C₁ ◁ C₂

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₅₂₉	C₄	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅₂₉	2
Dic₂₃	23