Minimal normal subgroup?

Question

Let $N$ be a minimal normal subgroup of a group $G$ and suppose $T$ is a minimal normal subgroup of $N$. Since $N \triangleleft G$, we have that $g^{-1}Tg \subseteq N$, for all $g \in G$.

How does this imply that $g^{-1}Tg$ is a minimal normal subgroup of $N$, for all $g \in G$?

Answer 1

$\DeclareMathOperator{\Ad}{Ad}$ Let $\alpha$ be any automorphism of $N$. Then $\alpha(T)$ is a minimal normal subgroup of $N$. In particular this is true for $\alpha = \Ad(g)$ for $g \in G$