  For every natural number $n\geq 5$, we prove that the number of subuniverses
of an $n$-element lattice is $2^n$, $13\cdot 2^{n-4}$, $23\cdot 2^{n-5}$, or
less than $23\cdot 2^{n-5}$. By a subuniverse, we mean a sublattice or the
emptyset. Also, we describe the $n$-element lattices with exactly $2^n$,
$13\cdot 2^{n-4}$, or $23\cdot 2^{n-5}$ subuniverses.
