Finite Group Databasebeta

← C₅×D₁₃×C₁₀₇ #28358113

Subgroups — C₅×D₁₃×C₁₀₇ #28358113

Order 13910.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₃×C₁₀₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₃×C₁₀₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅×C₁₀₇	—	13	1	no	maximal, Hall
5	C₅×C₁₀₇	D₁₃	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₁₀₇	—	13	1	no	Hall
7	C₅×D₁₃	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₀₇	C₅×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
9	C₅×C₁₃	C₂×C₁₀₇	1	1	yes	characteristic, complemented, Hall
10	D₁₃	C₅×C₁₀₇	1	1	yes	characteristic, direct product factor, Hall
11	C₁₃	C₂×C₅×C₁₀₇	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₅	—	13	1	no	Hall
13	C₅	D₁₃×C₁₀₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₀₇	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₅×C₁₀₇
Frattini	C₁	G
Fitting, socle	C₅×C₁₃×C₁₀₇	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₅×C₁₀₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃×C₁₀₇	C₂	semidirect
2. D₁₃×C₁₀₇	C₅	direct (N × H)
3. C₁₃×C₁₀₇	C₂×C₅	semidirect
5. C₅×C₁₀₇	D₁₃	direct (N × H)
7. C₅×D₁₃	C₁₀₇	direct (N × H)
8. C₁₀₇	C₅×D₁₃	direct (N × H)
9. C₅×C₁₃	C₂×C₁₀₇	semidirect
10. D₁₃	C₅×C₁₀₇	direct (N × H)
11. C₁₃	C₂×C₅×C₁₀₇	semidirect
13. C₅	D₁₃×C₁₀₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₁₃×C₁₀₇	2
D₁₃×C₁₀₇	5
C₂×C₅×C₁₀₇	13
C₅×D₁₃	107