Subgroups — C₂×C₂⁴⋊C₅ #4160

Order 160.

82 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, direct product factor
2	C₂⁵	C₅	1	1	yes	maximal, characteristic, complemented, Sylow
3	C₂⁴	—	5	3	no	—
4	C₂⁴	—	5	3	no	—
5	C₂⁴	C₂×C₅	1	1	yes	characteristic, complemented
6	C₂×C₅	—	16	1	no	maximal
7	C₂³	—	5	3	no	—
8	C₂³	—	5	6	no	—
9	C₂³	—	5	6	no	—
10	C₂³	—	5	12	no	—
11	C₂³	—	5	3	no	—
12	C₂³	—	5	1	no	—
13	C₅	—	16	1	no	Sylow
14	C₂²	—	5	6	no	—
15	C₂²	—	5	6	no	—
16	C₂²	—	5	1	no	—
17	C₂²	—	5	3	no	—
18	C₂²	—	5	12	no	—
19	C₂²	—	5	3	no	—
20	C₂	—	5	3	no	—
21	C₂	—	5	3	no	—
22	C₂	C₂⁴⋊C₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₂⁴⋊C₅
commutator, cosocle, hypocenter	C₂⁴	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₂⁵	C₅
LCS	G ▷ C₂⁴
UCS	C₁ ◁ C₂

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.