Finite Group Databasebeta

← C₅×C₁₃⋊C₃×C₁₀₇ #35229352

Subgroups — C₅×C₁₃⋊C₃×C₁₀₇ #35229352

Order 20865.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃×C₁₀₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃⋊C₃×C₁₀₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₀₇	—	13	1	no	maximal, Hall
4	C₁₃×C₁₀₇	C₃×C₅	1	1	yes	characteristic, complemented, Hall
5	C₅×C₁₀₇	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₁₀₇	—	13	1	no	Hall
7	C₅×C₁₃⋊C₃	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₀₇	C₅×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
9	C₅×C₁₃	C₃×C₁₀₇	1	1	yes	characteristic, complemented, Hall
10	C₁₃⋊C₃	C₅×C₁₀₇	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₅	—	13	1	no	Hall
12	C₁₃	C₃×C₅×C₁₀₇	1	1	yes	characteristic, complemented, Sylow
13	C₅	C₁₃⋊C₃×C₁₀₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₃	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₀₇	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₃×C₅×C₁₀₇
Frattini	C₁	G
Fitting, socle	C₅×C₁₃×C₁₀₇	C₃
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	C₃	semidirect
2. C₁₃⋊C₃×C₁₀₇	C₅	direct (N × H)
4. C₁₃×C₁₀₇	C₃×C₅	semidirect
5. C₅×C₁₀₇	C₁₃⋊C₃	direct (N × H)
7. C₅×C₁₃⋊C₃	C₁₀₇	direct (N × H)
8. C₁₀₇	C₅×C₁₃⋊C₃	direct (N × H)
9. C₅×C₁₃	C₃×C₁₀₇	semidirect
10. C₁₃⋊C₃	C₅×C₁₀₇	direct (N × H)
12. C₁₃	C₃×C₅×C₁₀₇	semidirect
13. C₅	C₁₃⋊C₃×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	3
C₁₃⋊C₃×C₁₀₇	5
C₃×C₅×C₁₀₇	13
C₅×C₁₃⋊C₃	107