  $N$ M5-branes probing the intersection between the orbifold
$\mathbb{C}^2/\Gamma_\text{ADE}$ and an $E_8$ wall give rise to 6d $(1,0)$
SCFTs known as ADE-type orbi-instantons. At fixed $N$ and order of the
orbifold, each element of $\text{Hom}(\Gamma_\text{ADE},E_8)$ defines a
different SCFT. The SCFTs are connected by Higgs branch RG flows, which
generically reduce the flavor symmetry of the UV fixed point. We determine the
full hierarchy of these RG flows for type A, i.e. $\mathbb{C}^2/\mathbb{Z}_k$,
for any value of $N$ and $k$. The hierarchy takes the form of an intricate
Hasse diagram: each node represents an IR orbi-instanton (homomorphism), and
each edge an allowed flow, compatibly with the 6d $a$-theorem. The partial
order is defined via quiver subtraction of the 3d magnetic quivers associated
with the 6d SCFTs, which is equivalent to performing a so-called Kraft-Procesi
transition between homomorphisms.
