  Starting from type IIB string theory on an $ADE$ singularity, the $(2,0)$
little string arises when one takes the string coupling $g_s$ to 0. In this
setup, we give a unified description of the codimension-two defects of the
little string, labeled by a simple Lie algebra ${\mathfrak{g}}$. Geometrically,
these are D5 branes wrapping 2-cycles of the singularity, subject to a certain
folding operation when the algebra is non simply-laced. Equivalently, the
defects are specified by a certain set of weights of $^L {\mathfrak{g}}$, the
Langlands dual of ${\mathfrak{g}}$. As a first application, we show that the
instanton partition function of the ${\mathfrak{g}}$-type quiver gauge theory
on the defect is equal to a 3-point conformal block of the
${\mathfrak{g}}$-type deformed Toda theory in the Coulomb gas formalism. As a
second application, we argue that in the $(2,0)$ CFT limit, the Coulomb branch
of the defects flows to a nilpotent orbit of ${\mathfrak{g}}$.
