Finite Group Databasebeta

← D₅×C₁₃×C₁₀₁ #27190049

Subgroups — D₅×C₁₃×C₁₀₁ #27190049

Order 13130.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₃×C₁₀₁	—	5	1	no	maximal, Hall
3	C₁₃×C₁₀₁	D₅	1	1	yes	characteristic, direct product factor, Hall
4	D₅×C₁₀₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₁₀₁	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₀₁	—	5	1	no	Hall
7	D₅×C₁₃	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₀₁	D₅×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
9	C₅×C₁₃	C₂×C₁₀₁	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₃	—	5	1	no	Hall
11	C₁₃	D₅×C₁₀₁	1	1	yes	characteristic, direct product factor, Sylow
12	D₅	C₁₃×C₁₀₁	1	1	yes	characteristic, direct product factor, Hall
13	C₅	C₂×C₁₃×C₁₀₁	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃×C₁₀₁	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₁₃×C₁₀₁
Frattini	C₁	G
Fitting, socle	C₅×C₁₃×C₁₀₁	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₁₃×C₁₀₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃×C₁₀₁	C₂	semidirect
3. C₁₃×C₁₀₁	D₅	direct (N × H)
4. D₅×C₁₀₁	C₁₃	direct (N × H)
5. C₅×C₁₀₁	C₂×C₁₃	semidirect
7. D₅×C₁₃	C₁₀₁	direct (N × H)
8. C₁₀₁	D₅×C₁₃	direct (N × H)
9. C₅×C₁₃	C₂×C₁₀₁	semidirect
11. C₁₃	D₅×C₁₀₁	direct (N × H)
12. D₅	C₁₃×C₁₀₁	direct (N × H)
13. C₅	C₂×C₁₃×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₃×C₁₀₁	2
C₂×C₁₃×C₁₀₁	5
D₅×C₁₀₁	13
D₅×C₁₃	101