Finite Group Databasebeta

← C₅×C₂₃×C₁₀₃⋊C₃ #48001067

Subgroups — C₅×C₂₃×C₁₀₃⋊C₃ #48001067

Order 35535.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₃×C₁₀₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₃×C₁₀₃⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂₃×C₁₀₃	C₃×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×C₁₀₃⋊C₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₁₀₃	C₃×C₂₃	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅×C₂₃	—	103	1	no	maximal, Hall
7	C₁₀₃⋊C₃	C₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₂₃	C₁₀₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
9	C₁₀₃	C₃×C₅×C₂₃	1	1	yes	characteristic, complemented, Sylow
10	C₃×C₂₃	—	103	1	no	Hall
11	C₂₃	C₅×C₁₀₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₃×C₅	—	103	1	no	Hall
13	C₅	C₂₃×C₁₀₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₃	—	103	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₂₃	C₁₀₃⋊C₃
commutator, cosocle, hypocenter	C₁₀₃	C₃×C₅×C₂₃
Frattini	C₁	G
Fitting, socle	C₅×C₂₃×C₁₀₃	C₃
LCS	G ▷ C₁₀₃
UCS	C₁ ◁ C₅×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₂₃×C₁₀₃	C₃	semidirect
2. C₂₃×C₁₀₃⋊C₃	C₅	direct (N × H)
3. C₂₃×C₁₀₃	C₃×C₅	semidirect
4. C₅×C₁₀₃⋊C₃	C₂₃	direct (N × H)
5. C₅×C₁₀₃	C₃×C₂₃	semidirect
7. C₁₀₃⋊C₃	C₅×C₂₃	direct (N × H)
8. C₅×C₂₃	C₁₀₃⋊C₃	direct (N × H)
9. C₁₀₃	C₃×C₅×C₂₃	semidirect
11. C₂₃	C₅×C₁₀₃⋊C₃	direct (N × H)
13. C₅	C₂₃×C₁₀₃⋊C₃	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×C₂₃×C₁₀₃	3
C₂₃×C₁₀₃⋊C₃	5
C₅×C₁₀₃⋊C₃	23
C₃×C₅×C₂₃	103