Wedderburn decomposition of a semisimple group algebra $\mathbb{F}_qG$ from a subalgebra of factor group of $G$

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In this paper, we derive a condition under which the Wedderburn decomposition of a semisimple group algebra $\mathbb{F}_qG$ can be deduced from the Wedderburn decomposition of $\mathbb{F}_q(G/H)$, where $H$ is a normal subgroup of $G$ having two elements and $q=p^k$ for some prime $p$ and $k\in \mathbb{Z}^+$. In order to complement the abstract theory of the paper, we deduce the Wedderburn decomposition and hence the unit group of semisimple group algebra $\mathbb{F}_q(A_5\rtimes C_4)$, where $A_5\rtimes C_4$ is a non-metabelian group and $C_4$ is a cyclic group of order $4$.