Finite Group Databasebeta

← C₁₉×D₂₅₉ #23754366

Subgroups — C₁₉×D₂₅₉ #23754366

Order 9842.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₉×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×D₃₇	—	7	1	no	maximal, Hall
3	C₁₉×C₃₇	D₇	1	1	yes	characteristic, complemented, Hall
4	D₂₅₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	D₇×C₁₉	—	37	1	no	maximal, Hall
6	C₇×C₃₇	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
7	C₇×C₁₉	D₃₇	1	1	yes	characteristic, complemented, Hall
8	D₃₇	—	7	1	no	Hall
9	C₂×C₁₉	—	259	1	no	Hall
10	C₃₇	D₇×C₁₉	1	1	yes	characteristic, complemented, Sylow
11	C₁₉	D₂₅₉	1	1	yes	characteristic, direct product factor, Sylow
12	D₇	—	37	1	no	Hall
13	C₇	C₁₉×D₃₇	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	259	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉	D₂₅₉
commutator, cosocle, hypocenter	C₇×C₃₇	C₂×C₁₉
Frattini	C₁	G
Fitting, socle	C₇×C₁₉×C₃₇	C₂
LCS	G ▷ C₇×C₃₇
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₉×C₃₇	C₂	semidirect
3. C₁₉×C₃₇	D₇	semidirect
4. D₂₅₉	C₁₉	direct (N × H)
6. C₇×C₃₇	C₂×C₁₉	semidirect
7. C₇×C₁₉	D₃₇	semidirect
10. C₃₇	D₇×C₁₉	semidirect
11. C₁₉	D₂₅₉	direct (N × H)
13. C₇	C₁₉×D₃₇	semidirect