Given an observable system (C,A)€ K^(mxn)X K^(nxn)with K=R or C, the set of (C,A)-invariant subspaces having the restricted system fixed observability indices is a smooth manifold embedded on the corresponding Grassmannian. We obtain an explicit parametrization of it by means of an atlas of corresponding charts. As an application we obtain the set of maximal dimensional outputs making solvable a generic Disturbance Decoupling Problem.