  We classify all finite-dimensional connected Hopf algebras with large abelian
primitive spaces. We show that they are Hopf algebra extensions of restricted
enveloping algebras of certain restricted Lie algebras. For any abelian matched
pair associated with these extensions, we construct a cohomology group, which
classifies all the extensions up to equivalence. Moreover, we present a $1$-$1$
correspondence between the isomorphism classes and a group quotient of the
cohomology group deleting some exceptional points, where the group respects the
automorphisms of the abelian matched pair and the exceptional points represent
those restricted Lie algebra extensions.
