  We explore the spectrum of lower-dimensional anti-de Sitter (AdS) solutions
in $F(4)$ gauged supergravity in six dimensions. The ansatz employed
corresponds to D4-branes partially wrapped on various supersymmetric cycles in
special holonomy manifolds. Re-visiting and extending previous results, we
study the cases of two, three, and four-dimensional supersymmetric cycles
within Calabi-Yau threefold, fourfold, $G_2$, and Spin(7) holonomy manifolds.
We also report on non-supersymmetric AdS vacua, and check their stability in
the consistently truncated lower-dimensional effective action, using the
Breitenlohner-Freedman bound. We also analyze the IR behavior and discuss the
admissibility of the singular flows.
