Finite Group Databasebeta

← C₃⋊(D₁₁₅₁⋊C₅) #46828708

Subgroups — C₃⋊(D₁₁₅₁⋊C₅) #46828708

Order 34530.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁₅₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₁₅₁⋊C₅	—	3	1	no	maximal, Hall
3	D₃₄₅₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₁₅₁⋊C₅	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁₅₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	D₁₁₅₁	—	3	1	no	Hall
7	C₁₁₅₁	C₅×D₃	1	1	yes	characteristic, complemented, Sylow
8	C₅×D₃	—	1151	1	no	maximal, Hall
9	C₃×C₅	—	1151	1	no	Hall
10	C₂×C₅	—	3453	1	no	Hall
11	D₃	—	1151	1	no	Hall
12	C₅	—	1151	1	no	Sylow
13	C₃	D₁₁₅₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	3453	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₁₅₁	C₂×C₅
LCS	G ▷ C₃×C₁₁₅₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁₅₁⋊C₅	C₂	semidirect
3. D₃₄₅₃	C₅	semidirect
4. C₁₁₅₁⋊C₅	D₃	semidirect
5. C₃×C₁₁₅₁	C₂×C₅	semidirect
7. C₁₁₅₁	C₅×D₃	semidirect
13. C₃	D₁₁₅₁⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₁₅₁⋊C₅	2
D₁₁₅₁⋊C₅	3
D₃₄₅₃	5
C₅×D₃	1151