Subgroups — C₃⁴⋊C₅ #87955

Order 405.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁴	C₅	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃³	—	5	8	no	—
3	C₃²	—	5	16	no	—
4	C₃²	—	5	10	no	—
5	C₅	—	81	1	no	maximal, Sylow
6	C₃	—	5	8	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃⁴	C₅
LCS	G ▷ C₃⁴
UCS	C₁

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

N	H ≅ G/N	type
1. C₃⁴	C₅	semidirect

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

subgroup	index
C₃⁴	5
C₅	81