Subfield

If a subset $S$ of the elements of a Field $F$ satisfies the Field Axioms with the same operations of $F$, then $S$ is called a subfield of $F$. Let $F$ be a Finite Field of order $p^n$, then there exists a subfield of Order $p^m$ for Prime $p$ Iff $m$ Divides $n$.

See also Field, Submanifold, Subspace