2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110045The paper presents a subclass of the class of MD5-algebras and MD5-groups, i.e., five dimensional solvable Lie algebras and Lie groups such that their orbits in the co-adjoint representation (K-orbit) are orbit of zero or maximal dimension. The main results of the paper is the classification up to an isomorphism of all MD5-algebras $\mathcal{G}$ with the derived ideal ${\mathcal{G}}^{1} := [\mathcal{G}, \mathcal{G}]$ is a 3-dimensional commutative Lie algebra.14 pages, no figureRepresentation TheoryPrimary 22E45, Secondary 46E25, 20C20text