  It is widely considered that the classical Higgs branch of 4d $\mathcal{N}=2$
SQCD is a well understood object. However there is no satisfactory
understanding of its structure. There are two complications: (1) the Higgs
branch chiral ring contains nilpotent elements, as can easily be checked in the
case of $\mathrm{SU}(N)$ with 1 flavour. (2) the Higgs branch as a geometric
space can in general be decomposed into two cones with nontrivial intersection,
the baryonic and mesonic branches. To study the second point in detail we use
the recently developed tool of magnetic quivers for five-brane webs, using the
fact that the classical Higgs branch for theories with 8 supercharges does not
change through dimensional reduction. We compare this approach with the
computation of the hyper-K\"ahler quotient using Hilbert series techniques,
finding perfect agreement if nilpotent operators are eliminated by the
computation of a so called radical. We study the nature of the nilpotent
operators and give conjectures for the Hilbert series of the full Higgs branch,
giving new insights into the vacuum structure of 4d $\mathcal{N}=2$ SQCD. In
addition we demonstrate the power of the magnetic quiver technique, as it
allows us to identify the decomposition into cones, and provides us with the
global symmetries of the theory, as a simple alternative to the techniques that
were used to date.
