Finite Group Databasebeta

← C₅×D₁₉₀₉ #34061822

Subgroups — C₅×D₁₉₀₉ #34061822

Order 19090.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₃×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₉₀₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂₃×C₈₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×D₈₃	—	23	1	no	maximal, Hall
5	C₅×C₈₃	D₂₃	1	1	yes	characteristic, complemented, Hall
6	C₅×D₂₃	—	83	1	no	maximal, Hall
7	D₈₃	—	23	1	no	Hall
8	C₅×C₂₃	D₈₃	1	1	yes	characteristic, complemented, Hall
9	C₈₃	C₅×D₂₃	1	1	yes	characteristic, complemented, Sylow
10	D₂₃	—	83	1	no	Hall
11	C₂₃	C₅×D₈₃	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₅	—	1909	1	no	Hall
13	C₅	D₁₉₀₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	1909	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₁₉₀₉
commutator, cosocle, hypocenter	C₂₃×C₈₃	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₂₃×C₈₃	C₂
LCS	G ▷ C₂₃×C₈₃
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₂₃×C₈₃	C₂	semidirect
2. D₁₉₀₉	C₅	direct (N × H)
3. C₂₃×C₈₃	C₂×C₅	semidirect
5. C₅×C₈₃	D₂₃	semidirect
8. C₅×C₂₃	D₈₃	semidirect
9. C₈₃	C₅×D₂₃	semidirect
11. C₂₃	C₅×D₈₃	semidirect
13. C₅	D₁₉₀₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₂₃×C₈₃	2
D₁₉₀₉	5
C₅×D₈₃	23
C₅×D₂₃	83