Finite Group Databasebeta

← C₂×C₃×C₁₅₁⋊C₅ #17985397

Subgroups — C₂×C₃×C₁₅₁⋊C₅ #17985397

Order 4530.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₅₁⋊C₅	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₅₁⋊C₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃×C₁₅₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₅₁⋊C₅	C₂×C₃	1	1	yes	characteristic, direct product factor, Hall
5	C₃×C₁₅₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₅₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
7	C₁₅₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₃×C₅	—	151	1	no	maximal, Hall
9	C₃×C₅	—	151	1	no	Hall
10	C₂×C₅	—	151	1	no	Hall
11	C₂×C₃	C₁₅₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
12	C₅	—	151	1	no	Sylow
13	C₃	C₂×C₁₅₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	C₃×C₁₅₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃	C₁₅₁⋊C₅
commutator, cosocle, hypocenter	C₁₅₁	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₅₁	C₅
LCS	G ▷ C₁₅₁
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₅₁⋊C₅	C₂	direct (N × H)
2. C₂×C₁₅₁⋊C₅	C₃	direct (N × H)
3. C₂×C₃×C₁₅₁	C₅	semidirect
4. C₁₅₁⋊C₅	C₂×C₃	direct (N × H)
5. C₃×C₁₅₁	C₂×C₅	semidirect
6. C₂×C₁₅₁	C₃×C₅	semidirect
7. C₁₅₁	C₂×C₃×C₅	semidirect
11. C₂×C₃	C₁₅₁⋊C₅	direct (N × H)
13. C₃	C₂×C₁₅₁⋊C₅	direct (N × H)
14. C₂	C₃×C₁₅₁⋊C₅	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×C₁₅₁⋊C₅	2
C₂×C₁₅₁⋊C₅	3
C₂×C₃×C₁₅₁	5
C₂×C₃×C₅	151