Finite Group Databasebeta

← D₃×C₅₉×C₈₉ #44538481

Subgroups — D₃×C₅₉×C₈₉ #44538481

Order 31506.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅₉×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₅₉×C₈₉	—	3	1	no	maximal, Hall
3	C₅₉×C₈₉	D₃	1	1	yes	characteristic, direct product factor, Hall
4	D₃×C₈₉	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	D₃×C₅₉	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₈₉	C₂×C₅₉	1	1	yes	characteristic, complemented, Hall
7	C₂×C₈₉	—	3	1	no	Hall
8	C₃×C₅₉	C₂×C₈₉	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅₉	—	3	1	no	Hall
10	C₈₉	D₃×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
11	C₅₉	D₃×C₈₉	1	1	yes	characteristic, direct product factor, Sylow
12	D₃	C₅₉×C₈₉	1	1	yes	characteristic, direct product factor, Hall
13	C₃	C₂×C₅₉×C₈₉	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅₉×C₈₉	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₅₉×C₈₉
Frattini	C₁	G
Fitting, socle	C₃×C₅₉×C₈₉	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₅₉×C₈₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₅₉×C₈₉	C₂	semidirect
3. C₅₉×C₈₉	D₃	direct (N × H)
4. D₃×C₈₉	C₅₉	direct (N × H)
5. D₃×C₅₉	C₈₉	direct (N × H)
6. C₃×C₈₉	C₂×C₅₉	semidirect
8. C₃×C₅₉	C₂×C₈₉	semidirect
10. C₈₉	D₃×C₅₉	direct (N × H)
11. C₅₉	D₃×C₈₉	direct (N × H)
12. D₃	C₅₉×C₈₉	direct (N × H)
13. C₃	C₂×C₅₉×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅₉×C₈₉	2
C₂×C₅₉×C₈₉	3
D₃×C₈₉	59
D₃×C₅₉	89