  Alternative theories of gravity and their solutions are of considerable
importance since at some fundamental level the world can reveal new features.
Indeed, it is suspected that the gravitational field might be nonminimally
coupled to the other fields at scales not yet probed, bringing into the
forefront nonminimally coupled theories. In this mode, we consider a nonminimal
Einstein-Yang-Mills theory with a cosmological constant. Imposing spherical
symmetry and staticity for the spacetime and a magnetic Wu-Yang ansatz for the
Yang-Mills field, we find expressions for the solutions of the theory. Further
imposing constraints on the nonminimal parameters, we find a family of exact
solutions of the theory depending on five parameters, namely, two nonminimal
parameters, the cosmological constant, the magnetic charge, and the mass. These
solutions represent magnetic monopoles and black holes in magnetic monopoles
with de Sitter, Minkowskian, and anti-de Sitter asymptotics, depending on the
sign and value of the cosmological constant $\Lambda$. We classify completely
the family of solutions with respect to the number and the type of horizons and
show that the spacetime solutions can have, at most, four horizons. For
particular sets of the parameters, these horizons can become double, triple,
and quadruple. For instance, for a positive cosmological constant $\Lambda$,
there is a critical $\Lambda_c$ for which the solution admits a quadruple
horizon, evocative of the $\Lambda_c$ that appears for a given energy density
in both the Einstein static and Eddington-Lema\^{\i}tre dynamical universes. As
an example of our classification, we analyze solutions in the Drummond-Hathrell
nonminimal theory that describe nonminimal black holes. Another application is
with a set of regular black holes previously treated.
