Finite Group Databasebeta

← D₅×C₂₃×C₈₃ #34061823

Subgroups — D₅×C₂₃×C₈₃ #34061823

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	C₂×C₂₃×C₈₃	—	5	1	no	maximal, Hall
3	C₂₃×C₈₃	D₅	1	1	yes	characteristic, direct product factor, Hall
4	D₅×C₈₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₈₃	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
6	D₅×C₂₃	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₈₃	—	5	1	no	Hall
8	C₅×C₂₃	C₂×C₈₃	1	1	yes	characteristic, complemented, Hall
9	C₈₃	D₅×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
10	C₂×C₂₃	—	5	1	no	Hall
11	C₂₃	D₅×C₈₃	1	1	yes	characteristic, direct product factor, Sylow
12	D₅	C₂₃×C₈₃	1	1	yes	characteristic, direct product factor, Hall
13	C₅	C₂×C₂₃×C₈₃	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₃×C₈₃	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₂₃×C₈₃
Frattini	C₁	G
Fitting, socle	C₅×C₂₃×C₈₃	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂₃×C₈₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₂₃×C₈₃	C₂	semidirect
3. C₂₃×C₈₃	D₅	direct (N × H)
4. D₅×C₈₃	C₂₃	direct (N × H)
5. C₅×C₈₃	C₂×C₂₃	semidirect
6. D₅×C₂₃	C₈₃	direct (N × H)
8. C₅×C₂₃	C₂×C₈₃	semidirect
9. C₈₃	D₅×C₂₃	direct (N × H)
11. C₂₃	D₅×C₈₃	direct (N × H)
12. D₅	C₂₃×C₈₃	direct (N × H)
13. C₅	C₂×C₂₃×C₈₃	semidirect

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
C₂×C₂₃×C₈₃	5
D₅×C₈₃	23
D₅×C₂₃	83