Finite Group Databasebeta

← C₂×C₁₃×C₁₀₁⋊C₅ #27190045

Subgroups — C₂×C₁₃×C₁₀₁⋊C₅ #27190045

Order 13130.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₀₁⋊C₅	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₃×C₁₀₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃×C₁₀₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₀₁⋊C₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₀₁⋊C₅	C₂×C₁₃	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₁₀₁	C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
7	C₂×C₅×C₁₃	—	101	1	no	maximal, Hall
8	C₁₀₁	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
9	C₅×C₁₃	—	101	1	no	Hall
10	C₂×C₁₃	C₁₀₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
11	C₁₃	C₂×C₁₀₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₅	—	101	1	no	Hall
13	C₅	—	101	1	no	Sylow
14	C₂	C₁₃×C₁₀₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₁₀₁⋊C₅	C₂	direct (N × H)
2. C₂×C₁₃×C₁₀₁	C₅	semidirect
3. C₁₃×C₁₀₁	C₂×C₅	semidirect
4. C₂×C₁₀₁⋊C₅	C₁₃	direct (N × H)
5. C₁₀₁⋊C₅	C₂×C₁₃	direct (N × H)
6. C₂×C₁₀₁	C₅×C₁₃	semidirect
8. C₁₀₁	C₂×C₅×C₁₃	semidirect
10. C₂×C₁₃	C₁₀₁⋊C₅	direct (N × H)
11. C₁₃	C₂×C₁₀₁⋊C₅	direct (N × H)
14. C₂	C₁₃×C₁₀₁⋊C₅	direct (N × H)

Maximal subgroups

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

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