  We show that inductive limits of virtually nilpotent groups have strongly
quasidiagonal C*-algebras, extending results of the first author on solvable
virtually nilpotent groups. We use this result to show that the decomposition
rank of the group C*-algebra of a finitely generated virtually nilpotent group
$G$ is bounded by $2\cdot h(G)!-1$, where $h(G)$ is the Hirsch length of $G.$
This extends and sharpens results of the first and third authors on finitely
generated nilpotent groups. It then follows that if a C*-algebra generated by
an irreducible representation of a virtually nilpotent group satisfies the
universal coefficient theorem, it is classified by its Elliott invariant.
