  We construct exact solutions of magnetically charged black holes in the
vector-tensor Horndeski gravity and discuss their main features. Unlike the
analogous electric case, the field equations are linear in a simple (quite
standard) parametrization of the metric tensor and they can be solved
analytically even when a cosmological constant is added. The solutions are
presented in terms of hypergeometric functions which makes the analysis of the
black hole properties relatively straightforward. Some of the aspects of these
black holes are quite ordinary like the existence of extremal configurations
with maximal magnetic charge for a given mass, or the existence of a mass with
maximal temperature for a given charge, but others are somewhat unexpected,
like the existence of black holes with a repulsive gravitational field. We
perform our analysis for both signs of the non-minimal coupling constant and
find black hole solutions in both cases but with significant differences
between them. The most prominent difference is the fact that the black holes
for the negative coupling constant have a spherical surface of curvature
singularity rather than a single point. On the other hand, the gravitational
field produced around this kind of black holes is always attractive. Also, for
small enough magnetic charge and negative coupling constant, extremal black
holes do not exist and all magnetic black holes have a single horizon. In
addition we study the trajectories around these magnetic black holes for light
as well as massive particles either neutral or electrically charged. Finally,
we compare the main features of these black holes with their electric
counterparts, adding some aspects that have not been discussed before, like
temperature, particle trajectories and light deflection by electrically charged
Horndesky black holes.
