Finite Group Databasebeta

← C₃×D₅×C₁₄₉ #17985014

Subgroups — C₃×D₅×C₁₄₉ #17985014

Order 4470.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅×C₁₄₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃×C₁₄₉	—	5	1	no	maximal, Hall
4	C₅×C₁₄₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₄₉	D₅	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₁₄₉	—	5	1	no	Hall
7	C₁₄₉	C₃×D₅	1	1	yes	characteristic, direct product factor, Sylow
8	C₃×D₅	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₅	C₂×C₁₄₉	1	1	yes	characteristic, complemented, Hall
10	D₅	C₃×C₁₄₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃	—	5	1	no	Hall
12	C₅	C₂×C₃×C₁₄₉	1	1	yes	characteristic, complemented, Sylow
13	C₃	D₅×C₁₄₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₄₉	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₃×C₁₄₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₄₉	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₃×C₁₄₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₄₉	C₂	semidirect
2. D₅×C₁₄₉	C₃	direct (N × H)
4. C₅×C₁₄₉	C₂×C₃	semidirect
5. C₃×C₁₄₉	D₅	direct (N × H)
7. C₁₄₉	C₃×D₅	direct (N × H)
8. C₃×D₅	C₁₄₉	direct (N × H)
9. C₃×C₅	C₂×C₁₄₉	semidirect
10. D₅	C₃×C₁₄₉	direct (N × H)
12. C₅	C₂×C₃×C₁₄₉	semidirect
13. C₃	D₅×C₁₄₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₁₄₉	2
D₅×C₁₄₉	3
C₂×C₃×C₁₄₉	5
C₃×D₅	149