Subgroups — (C₂⁴⋊C₅)⋊C₂ #4159

Order 160.

43 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	#120	—	5	1	no	maximal, Sylow
3	C₂⁴	D₅	1	1	yes	characteristic, complemented
4	C₂×D₄	—	5	3	no	—
5	C₂²⋊C₄	—	5	3	no	—
6	D₅	—	16	1	no	maximal
7	C₂³	—	5	3	no	—
8	C₂³	—	5	1	no	—
9	D₄	—	10	6	no	—
10	C₂×C₄	—	5	3	no	—
11	C₅	—	16	1	no	Sylow
12	C₂²	—	5	6	no	—
13	C₂²	—	5	1	no	—
14	C₂²	—	10	3	no	—
15	C₄	—	10	3	no	—
16	C₂	—	5	3	no	—
17	C₂	—	20	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₂⁴⋊C₅	C₂
Fitting, socle	C₂⁴	D₅
LCS	G ▷ C₂⁴⋊C₅
UCS	C₁

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

N	H ≅ G/N	type
1. C₂⁴⋊C₅	C₂	semidirect
3. C₂⁴	D₅	semidirect

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