For questions related to Orbit-Stabilizer Theorem.
The Orbit-Stabilizer Theorem says that, given a group $G$ which acts on a set $X$, then there exists a bijection between the orbit of an element $x\in X$ and the set of left cosets of the stabilizer group of $x$ in $G$. In other words, that the cardinality of the orbit of an element $x\in X$ is equal to the index of its stabilizer subgroup in $G$.