Finite Group Databasebeta

← C₅×D₉₄₃ #22628024

Subgroups — C₅×D₉₄₃ #22628024

Order 9430.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₉₄₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂₃×C₄₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×D₄₁	—	23	1	no	maximal, Hall
5	C₅×D₂₃	—	41	1	no	maximal, Hall
6	C₅×C₄₁	D₂₃	1	1	yes	characteristic, complemented, Hall
7	C₅×C₂₃	D₄₁	1	1	yes	characteristic, complemented, Hall
8	D₄₁	—	23	1	no	Hall
9	D₂₃	—	41	1	no	Hall
10	C₄₁	C₅×D₂₃	1	1	yes	characteristic, complemented, Sylow
11	C₂₃	C₅×D₄₁	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₅	—	943	1	no	Hall
13	C₅	D₉₄₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	943	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₉₄₃
commutator, hypocenter	C₂₃×C₄₁	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₂₃×C₄₁	C₂
LCS	G ▷ C₂₃×C₄₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₂₃×C₄₁	C₂	semidirect
2. D₉₄₃	C₅	direct (N × H)
3. C₂₃×C₄₁	C₂×C₅	semidirect
6. C₅×C₄₁	D₂₃	semidirect
7. C₅×C₂₃	D₄₁	semidirect
10. C₄₁	C₅×D₂₃	semidirect
11. C₂₃	C₅×D₄₁	semidirect
13. C₅	D₉₄₃	direct (N × H)