Subloop of index two is normal

Statement
Suppose $$L$$ is an finite algebra loop and $$S$$ is a subloop of $$L$$ with size half that of $$L$$, then $$S$$ is a normal subloop.

Related facts

 * Subgroup of index two is normal
 * Subquasigroup of size more than half is whole quasigroup
 * Subgroup of size more than half is whole group