Finite Group Databasebeta

← C₅²×C₃⋊D₃ #90666

Subgroups — C₅²×C₃⋊D₃ #90666

Order 450.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅²×D₃	—	3	4	no	maximal
3	C₅×C₃⋊D₃	C₅	1	6	yes	maximal, direct product factor
4	C₃×C₅²	D₃	1	4	yes	complemented
5	C₂×C₅²	—	9	1	no	Hall
6	C₃²×C₅	C₂×C₅	1	6	yes	complemented
7	C₅×D₃	—	3	24	no	—
8	C₅²	C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
9	C₃⋊D₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₅	C₅×D₃	1	24	yes	complemented
11	C₂×C₅	—	9	6	no	—
12	C₃²	C₂×C₅²	1	1	yes	characteristic, complemented, Sylow
13	D₃	—	3	4	no	—
14	C₅	C₅×C₃⋊D₃	1	6	yes	direct product factor
15	C₃	C₅²×D₃	1	4	yes	complemented
16	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₅²
Frattini	C₁	G
Fitting, socle	C₃²×C₅²	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₅²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅²	C₂	semidirect
3. C₅×C₃⋊D₃	C₅	direct (N × H)
4. C₃×C₅²	D₃	semidirect
6. C₃²×C₅	C₂×C₅	semidirect
8. C₅²	C₃⋊D₃	direct (N × H)
9. C₃⋊D₃	C₅²	direct (N × H)
10. C₃×C₅	C₅×D₃	semidirect
12. C₃²	C₂×C₅²	semidirect
14. C₅	C₅×C₃⋊D₃	direct (N × H)
15. C₃	C₅²×D₃	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅²	2
C₅²×D₃	3
C₅×C₃⋊D₃	5