Subgroups — 2₋¹⁺⁴⋊C₅ #4124

Order 160.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	2₋¹⁺⁴	C₅	1	1	yes	maximal, characteristic, complemented, Sylow
2	#41	—	5	2	no	—
3	C₂×Q₈	—	5	1	no	—
4	C₂×C₅	—	16	1	no	maximal
5	Q₈	—	5	2	no	—
6	D₄	—	5	2	no	—
7	C₂×C₄	—	5	1	no	—
8	C₂×C₄	—	5	2	no	—
9	C₅	—	16	1	no	Sylow
10	C₂²	—	5	1	no	—
11	C₄	—	5	2	no	—
12	C₂	—	10	1	no	—
13	C₂	C₂⁴⋊C₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, socle, hypercenter	C₂	C₂⁴⋊C₅
commutator, Fitting, cosocle, hypocenter	2₋¹⁺⁴	C₅
LCS	G ▷ 2₋¹⁺⁴
UCS	C₁ ◁ C₂

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

N	H ≅ G/N	type
1. 2₋¹⁺⁴	C₅	semidirect

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

subgroup	index
2₋¹⁺⁴	5
C₂×C₅	16