We analyze numerically the equation giving the number of missing label operators for reduction chains \frak{k}\rightarrow \frak{g} of Lie algebras to obtain information about the maximal possible dimension of certain types of subalgebras, mainly Abelian. Applications to the minimal dimension of faithful representations are given, and the number of invariants of codimension one and two subalgebras is analyzed.

PACS numbers: 02.20.Qs, 02.20.Sv