Finite Group Databasebeta

← D₅×C₅₃×C₅₉ #44530784

Subgroups — D₅×C₅₃×C₅₉ #44530784

Order 31270.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₅₃×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₅₃×C₅₉	—	5	1	no	maximal, Hall
3	C₅₃×C₅₉	D₅	1	1	yes	characteristic, direct product factor, Hall
4	D₅×C₅₉	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	D₅×C₅₃	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₅₉	C₂×C₅₃	1	1	yes	characteristic, complemented, Hall
7	C₅×C₅₃	C₂×C₅₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₅₉	—	5	1	no	Hall
9	C₂×C₅₃	—	5	1	no	Hall
10	C₅₉	D₅×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
11	C₅₃	D₅×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
12	D₅	C₅₃×C₅₉	1	1	yes	characteristic, direct product factor, Hall
13	C₅	C₂×C₅₃×C₅₉	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅₃×C₅₉	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₅₃×C₅₉
Frattini	C₁	G
Fitting, socle	C₅×C₅₃×C₅₉	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₅₃×C₅₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₅₃×C₅₉	C₂	semidirect
3. C₅₃×C₅₉	D₅	direct (N × H)
4. D₅×C₅₉	C₅₃	direct (N × H)
5. D₅×C₅₃	C₅₉	direct (N × H)
6. C₅×C₅₉	C₂×C₅₃	semidirect
7. C₅×C₅₃	C₂×C₅₉	semidirect
10. C₅₉	D₅×C₅₃	direct (N × H)
11. C₅₃	D₅×C₅₉	direct (N × H)
12. D₅	C₅₃×C₅₉	direct (N × H)
13. C₅	C₂×C₅₃×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₅₃×C₅₉	2
C₂×C₅₃×C₅₉	5
D₅×C₅₉	53
D₅×C₅₃	59