Let k be an algebraically closed field and V a finite dimensional k-space. Let GL(V) be the general linear group of V and P a parabolic subgroup of GL(V). Now P acts on its unipotent radical Pu and on pu=LiePu, the Lie algebra of Pu, via the adjoint action. More generally, we consider the action of P on the lth member of the descending central series of pu denoted by p(l)u. All instances when P acts on p(l)u for l⩾0 with a finite number of orbits are known. In this note, we give a complete combinatorial description of the closure relation on the set of P-orbits on p(l)u, i.e., the Bruhat–Chevalley order, for every finite case. There is a canonical bijection between the set of P-orbits on p(l)u and the set of isomorphism classes of Δ-filtered modules of a particular dimension vector e of a certain quasi-hereditary algebra A(t, l). These isomorphism classes in turn are given by the orbits of a reductive group G(e) on the variety R(Δ)(e) of all A(t, l)-modules with Δ-filtration and dimension vector e. The subcategory of A(t, l)-mod of all Δ-filtered A(t, l)-modules of dimension vector e is denoted by F(Δ)(e). In our chief result, Theorem 1.1, we show that provided there is only a finite number of isomorphism classes of indecomposable modules in F(Δ) the following three posets coincide: (1)the Bruhat–Chevalley order on the set of P-orbits on p(l)u; (2)the Bruhat–Chevalley order on the set of G(e)-orbits on R(Δ)(e); (3)the poset opposite to the so called hom-order on the set of isomorphism classes of F(Δ)(e). The advantage of this hom-order is that it is given purely by discrete invariants and that it can be computed explicitly for any given finite case. Theorem 1.1 then in turn allows us to explicitly determine the closure relations for the P-orbits on p(l)u with the aid of this hom-order. We present some examples of Hasse diagrams in an Appendix.