  Let $\mathcal{C}(\mathfrak{g},k)$ be the unitary modular tensor categories
arising from the representation theory of quantum groups at roots of unity for
arbitrary simple finite-dimensional complex Lie algebra $\mathfrak{g}$ and
positive integer levels $k$. Here we classify nondegenerate fusion
subcategories of the modular tensor categories of local modules
$\mathcal{C}(\mathfrak{g},k)_R^0$ where $R$ is the regular algebra of Tannakian
$\text{Rep}(H)\subset\mathcal{C}(\mathfrak{g},k)_\text{pt}$. For
$\mathfrak{g}=\mathfrak{so}_5$ we describe the decomposition of
$\mathcal{C}(\mathfrak{g},k)_R^0$ into prime factors explicitly and as an
application we classify relations in the Witt group of nondegenerately braided
fusion categories generated by the equivalency classes of
$\mathcal{C}(\mathfrak{so}_5,k)$ and $\mathcal{C}(\mathfrak{g}_2,k)$ for
$k\in\mathbb{Z}_{\geq1}$.
