  The discrete cocompact subgroups of the five-dimensional connected, simply
connected nilpotent Lie groups are determined up to isomorphism. Moreover, we
prove if $G=N\times A$ is a connected, simply connected, nilpotent Lie group
with an Abelian factor $A$, then every uniform subgroup of $G$ is the direct
product of a uniform subgroup of $N$ and ${\mathbb Z}^r$ where $r=\dim A$.
