  An intriguing class of 6d supersymmetric theories are known as little strings
theories, which exhibit a rich network of T-dualities. A robust feature of
these theories are their Higgs branches. Focusing on the little string theories
that are realised on a single curve of zero self-intersection, we utilise brane
systems to derive the magnetic quivers. Using a variety of techniques
(including branching rules, brane dynamics, F-theory geometry, quiver
subtraction, and the decay and fission algorithm), we detail the Higgs branch
Hasse diagram and determine the transverse slices for every elementary Higgs
branch RG-flow. Building on these insights, we pursue two directions: firstly,
we used the established connection between the change of the 2-Group structure
constants along Higgs branch RG-flows and the transition-type in the Hasse
diagram to infer putative T-dual models. Secondly, we conjecture an algorithm
that predicts the non-Abelian flavour symmetry of the compactified little
string theory by inspecting the magnetic quivers of all T-dual frames.
