  We give an efficient algorithm for the enumeration up to isomorphism of the
inverse semigroups of order n, and we count the number S(n) of inverse
semigroups of order n<=15. This improves considerably on the previous
highest-known value S(9). We also give a related algorithm for the enumeration
up to isomorphism of the finite inverse semigroups S with a given underlying
semilattice of idempotents E, a given restriction of Green's D-relation on S to
E, and a given list of maximal subgroups of S associated to the elements of E.
