  We study symmetric minimal surfaces in the three-dimensional Heisenberg group
$\mathrm{Nil}_3$ using the generalized Weierstrass type representation, the
so-called loop group method. In particular, we will discuss how to construct
minimal surfaces in $\mathrm{Nil}_3$ with non-trivial topology. Moreover, we
will classify equivariant minimal surfaces given by one-parameter subgroups of
the isometry group $\mathrm{Iso}_{\circ}(\mathrm{Nil}_3)$ of $\mathrm{Nil}_3$.
