  The present paper is a continuation of [13], [14] of the authors.
Specifically, the paper considers the MD5-foliations associated to connected
and simply connected MD5-groups such that their Lie algebras have 4-dimensional
commutative derived ideal. In the paper, we give the topological classification
of all considered MD5-foliations. A description of these foliations by certain
fibrations or suitable actions of $\mathbb{R}^{2}$ and the Connes' C*-algebras
of the foliations which come from fibrations are also given in the paper.
