Subgroups — H(3,𝔽₉)⋊C₅ #16814454

Order 3645.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	H(3,𝔽₉)	C₅	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃²⋊H(3,𝔽₃)	—	5	8	no	—
3	C₃⁴	—	5	2	no	—
4	C₃×H(3,𝔽₃)	—	5	16	no	—
5	C₃×H(3,𝔽₃)	—	5	8	no	—
6	C₃²×C₅	—	81	1	no	maximal
7	C₃³	—	5	8	no	—
8	C₃³	—	45	8	no	—
9	H(3,𝔽₃)	—	45	16	no	—
10	H(3,𝔽₃)	—	45	8	no	—
11	C₃×C₅	—	81	4	no	—
12	C₃²	—	15	16	no	—
13	C₃²	—	15	16	no	—
14	C₃²	—	45	18	no	—
15	C₃²	C₃⁴⋊C₅	1	1	yes	characteristic
16	C₅	—	81	1	no	Sylow
17	C₃	—	45	8	no	—
18	C₃	H(5,𝔽₃)⋊C₅	1	4	yes	—

	subgroup	G/H
center, Frattini, socle, hypercenter	C₃²	C₃⁴⋊C₅
commutator, Fitting, cosocle, hypocenter	H(3,𝔽₉)	C₅
LCS	G ▷ H(3,𝔽₉)
UCS	C₁ ◁ C₃²

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

N	H ≅ G/N	type
1. H(3,𝔽₉)	C₅	semidirect

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

subgroup	index
H(3,𝔽₉)	5
C₃²×C₅	81