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In this paper results are proved with applications to the orbits of$(n-1)$-dimensional subspaces disjoint from a regulus $\cR$ of$(n-1)$-subspaces in $\PG(2n-1,q)$, with respect to the subgroup of$\PGL(2n,q)$ fixing $\cR$. Such results have consequences on several aspects offinite geometry. First of all, a necessary condition for an $(n-1)$-subspace$U$ and a regulus $\cR$ of $(n-1)$-subspaces to be extendable to a Desarguesianspread is given. The description also allows to improve results in\cite{BaJa12} on the Andr\'e-Bruck-Bose representation of a $q$-subline in$\PG(2,q^n)$. Furthermore, the results in this paper are applied to theclassification of linear sets, in particular clubs.

Subspaces intersecting each element of a regulus in one point, Andr\'e-Bruck-Bose representation and clubs