  We present a new family of charged black holes with hyperscaling violating
asymptotics and non-trivial horizon topology, for arbitrary Lifshitz exponent
$z$ and hyperscaling violation parameter $\theta$. They are $(d+2)$-dimensional
analytic solutions to a generalized Einstein-Maxwell-Dilaton theory with an
additional vector field supporting spherical or hyperbolic horizons. The
hyperbolic solutions are only consistent with the null energy condition for $1
\le z < 2$ and $\theta = d(z-1)$, which explains why they are absent in the
pure Lifshitz case. We further study the (extended) thermodynamics of these
black holes, both in the fixed charge and fixed potential ensemble, and find
that phase transitions only occur for spherical black holes with $1 \le z \le
2$ and any $\theta$.
