  In this paper we construct and study two new families of finite dimensional
pointed Hopf algebras which generalize Radford's families. We show that over
any infinite field which contains a primitive nth root of unity, one of the
families contains infinitely many non-isomorphic Hopf algebras of any dimension
of the form Nn^2, where 2<n<N are integers so that n divides N. We thus answer
in the negative Kaplansky's 10th conjecture from 1975 on the finite number of
types of Hopf algebras of a given dimension.
