Subgroups — C₅⋊S₄ #1228

Order 120.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×A₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²⋊D₅	—	3	1	no	maximal, Hall
3	D₁₅	—	4	1	no	maximal
4	S₄	—	5	1	no	maximal, Hall
5	C₂²×C₅	D₃	1	1	yes	characteristic, complemented
6	C₂×D₅	—	3	1	no	—
7	Dic₅	—	3	1	no	—
8	C₃×C₅	—	4	1	no	Hall
9	A₄	D₅	1	1	yes	characteristic, complemented
10	C₂×C₅	—	3	1	no	—
11	D₅	—	6	1	no	—
12	D₄	—	15	1	no	Sylow
13	D₃	—	20	1	no	—
14	C₅	S₄	1	1	yes	characteristic, complemented, Sylow
15	C₂²	—	15	1	no	—
16	C₂²	D₁₅	1	1	yes	characteristic, complemented
17	C₄	—	15	1	no	—
18	C₃	—	4	1	no	Sylow
19	C₂	—	3	1	no	—
20	C₂	—	30	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₅×A₄	C₂
Fitting, socle	C₂²×C₅	D₃
LCS	G ▷ C₅×A₄
UCS	C₁

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.