Finite Group Databasebeta

← C₂×C₅²×C₉ #90654

Subgroups — C₂×C₅²×C₉ #90654

Order 450.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₅²	C₃	1	1	yes	maximal, characteristic
3	C₂×C₅×C₉	C₅	1	6	yes	maximal, direct product factor
4	C₃×C₅²	C₂×C₃	1	1	yes	characteristic
5	C₂×C₅²	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₅×C₉	C₂×C₅	1	6	yes	direct product factor
7	C₂×C₃×C₅	C₃×C₅	1	6	yes	—
8	C₅²	C₂×C₉	1	1	yes	characteristic, direct product factor, Sylow
9	C₂×C₉	C₅²	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₅	C₂×C₃×C₅	1	6	yes	—
11	C₂×C₅	C₅×C₉	1	6	yes	direct product factor
12	C₉	C₂×C₅²	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₃	C₃×C₅²	1	1	yes	characteristic
14	C₅	C₂×C₅×C₉	1	6	yes	direct product factor
15	C₃	C₂×C₃×C₅²	1	1	yes	characteristic
16	C₂	C₅²×C₉	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂×C₃×C₅²
socle, prime radical	C₂×C₃×C₅²	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅²×C₉	C₂	direct (N × H)
3. C₂×C₅×C₉	C₅	direct (N × H)
5. C₂×C₅²	C₉	direct (N × H)
6. C₅×C₉	C₂×C₅	direct (N × H)
8. C₅²	C₂×C₉	direct (N × H)
9. C₂×C₉	C₅²	direct (N × H)
11. C₂×C₅	C₅×C₉	direct (N × H)
12. C₉	C₂×C₅²	direct (N × H)
14. C₅	C₂×C₅×C₉	direct (N × H)
16. C₂	C₅²×C₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×C₉	2
C₂×C₃×C₅²	3
C₂×C₅×C₉	5