Subgroups — C₅₉⋊Dic₅₉ #28358207

Order 13924.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉²	C₂	1	1	yes	maximal, characteristic
2	C₅₉²	C₄	1	1	yes	characteristic, complemented, Sylow
3	Dic₅₉	—	59	60	no	maximal
4	C₂×C₅₉	D₅₉	1	60	yes	—
5	C₅₉	Dic₅₉	1	60	yes	complemented
6	C₄	—	3481	1	no	Sylow
7	C₂	C₅₉⋊D₅₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₅₉⋊D₅₉
commutator, hypocenter	C₅₉²	C₄
Fitting, socle, prime radical, cosocle	C₂×C₅₉²	C₂
LCS	G ▷ C₅₉²
UCS	C₁ ◁ C₂

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

N	H ≅ G/N	type
2. C₅₉²	C₄	semidirect
5. C₅₉	Dic₅₉	semidirect

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

subgroup	index
C₂×C₅₉²	2
Dic₅₉	59