Finite Group Databasebeta

← C₁₅₁⋊#1039 #28419081

Subgroups — C₁₅₁⋊#1039 #28419081

Order 15100.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×C₁₅₁	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₅₁	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₇₅₅	—	5	6	no	maximal
4	C₂×C₅×C₁₅₁	D₅	1	6	yes	—
5	C₅×C₁₅₁	Dic₅	1	6	yes	complemented
6	Dic₁₅₁	—	25	1	no	Hall
7	C₂×C₁₅₁	C₅⋊D₅	1	1	yes	characteristic
8	C₁₅₁	#1039	1	1	yes	characteristic, complemented, Sylow
9	#1039	—	151	1	no	maximal, Hall
10	C₂×C₅²	D₁₅₁	1	1	yes	characteristic
11	C₅²	Dic₁₅₁	1	1	yes	characteristic, complemented, Sylow
12	Dic₅	—	755	6	no	—
13	C₂×C₅	D₇₅₅	1	6	yes	—
14	C₅	Dic₇₅₅	1	6	yes	complemented
15	C₄	—	3775	1	no	Sylow
16	C₂	C₅⋊D₇₅₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₅⋊D₇₅₅
commutator, hypocenter	C₅²×C₁₅₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₅²×C₁₅₁	C₂
LCS	G ▷ C₅²×C₁₅₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₅²×C₁₅₁	C₄	semidirect
5. C₅×C₁₅₁	Dic₅	semidirect
8. C₁₅₁	#1039	semidirect
11. C₅²	Dic₁₅₁	semidirect
14. C₅	Dic₇₅₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅²×C₁₅₁	2
Dic₇₅₅	5
#1039	151