  We study the moduli space C^2 of unitary two-dimensional conformal field
theories with central charge c=2. We construct all the 28 nonexceptional
nonisolated irreducible components of C^2 that may be obtained by an orbifold
procedure from toroidal theories. The parameter spaces and partition functions
are calculated explicitly, and all multicritical points and lines are
determined. We show that all but four of the 28 irreducible components of C^2
corresponding to nonexceptional orbifolds are directly or indirectly connected
to the moduli space of toroidal theories in C^2. We relate our results to those
by Dixon, Ginsparg, Harvey on the classification of c=3/2 superconformal field
theories and thereby give geometric interpretations to all nonisolated
orbifolds discussed there.
