Subgroups — C₅⋊D₅×C₅₆₉ #43249588

Order 28450.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₅₆₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅×C₅₆₉	—	5	6	no	maximal
3	C₅×C₅₆₉	D₅	1	6	yes	complemented
4	C₂×C₅₆₉	—	25	1	no	Hall
5	C₅₆₉	C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
6	C₅⋊D₅	C₅₆₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅²	C₂×C₅₆₉	1	1	yes	characteristic, complemented, Sylow
8	D₅	—	5	6	no	—
9	C₅	D₅×C₅₆₉	1	6	yes	complemented
10	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅₆₉	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂×C₅₆₉
Frattini	C₁	G
Fitting, socle	C₅²×C₅₆₉	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₅₆₉

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.