  The present paper is a continuation of Le Anh Vu's ones [13], [14], [15].
Specifically, the paper is concerned with the subclass of connected and simply
connected MD5-groups such that their MD5-algebras $\mathcal{G}$ have the
derived ideal ${\mathcal{G}}^{1} : = [ \mathcal{G},\mathcal{G} ]\equiv$
${\bf{R}}^{3}$. We shall describe the geometry of K-orbits of these MD5-groups.
The foliations formed by K-orbits of maximal dimension of these MD5-groups and
their measurability are also presented in the paper.
