  We have studied spacetime structures of static solutions in the
$n$-dimensional Einstein-Gauss-Bonnet-Maxwell-$\Lambda$ system. Especially we
focus on effects of the Maxwell charge. We assume that the Gauss-Bonnet
coefficient $\alpha$ is non-negative and $4{\tilde \alpha}/\ell^2\leq 1$ in
order to define the relevant vacuum state. Solutions have the
$(n-2)$-dimensional Euclidean sub-manifold whose curvature is $k=1,~0$, or -1.
In Gauss-Bonnet gravity, solutions are classified into plus and minus branches.
In the plus branch all solutions have the same asymptotic structure as those in
general relativity with a negative cosmological constant. The charge affects a
central region of the spacetime. A branch singularity appears at the finite
radius $r=r_b>0$ for any mass parameter. There the Kretschmann invariant
behaves as $O((r-r_b)^{-3})$, which is much milder than divergent behavior of
the central singularity in general relativity $O(r^{-4(n-2)})$. Some charged
black hole solutions have no inner horizon in Gauss-Bonnet gravity. Although
there is a maximum mass for black hole solutions in the plus branch for $k=-1$
in the neutral case, no such maximum exists in the charged case. The solutions
in the plus branch with $k=-1$ and $n\geq6$ have an "inner" black hole, and
inner and the "outer" black hole horizons. Considering the evolution of black
holes, we briefly discuss a classical discontinuous transition from one black
hole spacetime to another.
