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Let $\mathcal{C}(\mathfrak{g},k)$ be the unitary modular tensor categoriesarising from the representation theory of quantum groups at roots of unity forarbitrary simple finite-dimensional complex Lie algebra $\mathfrak{g}$ andpositive integer levels $k$. Here we classify nondegenerate fusionsubcategories 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 anapplication we classify relations in the Witt group of nondegenerately braidedfusion categories generated by the equivalency classes of$\mathcal{C}(\mathfrak{so}_5,k)$ and $\mathcal{C}(\mathfrak{g}_2,k)$ for$k\in\mathbb{Z}_{\geq1}$.

Prime decomposition of modular tensor categories of local modules of Type D