  A group $G$ is said to be factorized into subsets $A_1, A_2, \ldots,
A_s\subseteq G$ if every element $g$ in $G$ can be uniquely represented as
$g=g_1g_2\ldots g_s$, where $g_i\in A_i$, $i=1,2,\ldots,s$. We consider the
following conjecture: for every finite group $G$ and every factorization $n=ab$
of its order, there is a factorization $G=AB$ with $|A|=a$ and $|B|=b$. We show
that a minimal counterexample to this conjecture must be a nonabelian simple
group and prove the conjecture for every finite group the nonabelian
composition factors of which have orders less than $10\,000$.
