Finite Group Databasebeta

← C₂×C₃²×C₂₅ #90645

Subgroups — C₂×C₃²×C₂₅ #90645

Order 450.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₅	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₂₅	C₃	1	4	yes	maximal, direct product factor
3	C₂×C₃²×C₅	C₅	1	1	yes	maximal, characteristic
4	C₃×C₂₅	C₂×C₃	1	4	yes	direct product factor
5	C₂×C₂₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₅	C₂×C₅	1	1	yes	characteristic
7	C₂×C₃×C₅	C₃×C₅	1	4	yes	—
8	C₂₅	C₂×C₃²	1	1	yes	characteristic, direct product factor, Sylow
9	C₂×C₃²	C₂₅	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₅	C₂×C₃×C₅	1	4	yes	—
11	C₂×C₅	C₃²×C₅	1	1	yes	characteristic
12	C₃²	C₂×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₃	C₃×C₂₅	1	4	yes	direct product factor
14	C₅	C₂×C₃²×C₅	1	1	yes	characteristic
15	C₃	C₂×C₃×C₂₅	1	4	yes	direct product factor
16	C₂	C₃²×C₂₅	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₂×C₃²×C₅
socle, prime radical	C₂×C₃²×C₅	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃²×C₂₅	C₂	direct (N × H)
2. C₂×C₃×C₂₅	C₃	direct (N × H)
4. C₃×C₂₅	C₂×C₃	direct (N × H)
5. C₂×C₂₅	C₃²	direct (N × H)
8. C₂₅	C₂×C₃²	direct (N × H)
9. C₂×C₃²	C₂₅	direct (N × H)
12. C₃²	C₂×C₂₅	direct (N × H)
13. C₂×C₃	C₃×C₂₅	direct (N × H)
15. C₃	C₂×C₃×C₂₅	direct (N × H)
16. C₂	C₃²×C₂₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₂₅	2
C₂×C₃×C₂₅	3
C₂×C₃²×C₅	5