Subgroups — C₂⁴⋊C₂₅ #87758

Order 400.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₅	C₅	1	1	yes	maximal, characteristic
2	C₂³×C₅	—	5	3	no	—
3	C₂₅	—	16	1	no	maximal, Sylow
4	C₂²×C₅	—	5	6	no	—
5	C₂²×C₅	—	5	1	no	—
6	C₂⁴	C₂₅	1	1	yes	characteristic, complemented, Sylow
7	C₂×C₅	—	5	3	no	—
8	C₂³	—	5	3	no	—
9	C₅	C₂⁴⋊C₅	1	1	yes	characteristic
10	C₂²	—	5	6	no	—
11	C₂²	—	5	1	no	—
12	C₂	—	5	3	no	—

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

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

N	H ≅ G/N	type
6. C₂⁴	C₂₅	semidirect

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

subgroup	index
C₂⁴×C₅	5
C₂₅	16