Finite Group Databasebeta

← C₂²×C₃×C₅² #64506

Subgroups — C₂²×C₃×C₅² #64506

Order 300.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅²	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₅²	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅²	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂²×C₃×C₅	C₅	1	6	yes	maximal, direct product factor
5	C₂×C₅²	C₂×C₃	1	3	yes	direct product factor
6	C₂×C₃×C₅	C₂×C₅	1	18	yes	direct product factor
7	C₅²	C₂²×C₃	1	1	yes	characteristic, direct product factor, Sylow
8	C₂²×C₅	C₃×C₅	1	6	yes	direct product factor
9	C₃×C₅	C₂²×C₅	1	6	yes	direct product factor
10	C₂²×C₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₅	C₂×C₃×C₅	1	18	yes	direct product factor
12	C₂×C₃	C₂×C₅²	1	3	yes	direct product factor
13	C₅	C₂²×C₃×C₅	1	6	yes	direct product factor
14	C₂²	C₃×C₅²	1	1	yes	characteristic, direct product factor, Sylow
15	C₃	C₂²×C₅²	1	1	yes	characteristic, direct product factor, Sylow
16	C₂	C₂×C₃×C₅²	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅²	C₂	direct (N × H)
2. C₂²×C₅²	C₃	direct (N × H)
3. C₃×C₅²	C₂²	direct (N × H)
4. C₂²×C₃×C₅	C₅	direct (N × H)
5. C₂×C₅²	C₂×C₃	direct (N × H)
6. C₂×C₃×C₅	C₂×C₅	direct (N × H)
7. C₅²	C₂²×C₃	direct (N × H)
8. C₂²×C₅	C₃×C₅	direct (N × H)
9. C₃×C₅	C₂²×C₅	direct (N × H)
10. C₂²×C₃	C₅²	direct (N × H)
11. C₂×C₅	C₂×C₃×C₅	direct (N × H)
12. C₂×C₃	C₂×C₅²	direct (N × H)
13. C₅	C₂²×C₃×C₅	direct (N × H)
14. C₂²	C₃×C₅²	direct (N × H)
15. C₃	C₂²×C₅²	direct (N × H)
16. C₂	C₂×C₃×C₅²	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅²	2
C₂²×C₅²	3
C₂²×C₃×C₅	5