Deformations of the five dimensional Heisenberg Lie algebra

In this note we explicitly give all the equivalent classes of deformations of the 5-dimensional Heisenberg Lie algebra ${\mathfrak{h}}_2$ over complex or real number fields. We show that there are altogether 20 infinitesimal deformations (families), 18 of them being extendable to real deformations and 2 of them are only infinitesimal.