Orbit-stabiliser theorem

Let $G$ a group acting on a set $X$ and $x$ in $X$. The map
$$\begin{aligned} \varphi: G / G_x & \longrightarrow \operatorname{Orb} (x) \\ g G_x & \longmapsto g \cdot x \end{aligned}$$is a well-defined bijection from the set of left cosets of $G_{x}$ onto the orbit of $x$.