  Symmetries of the Two-Higgs-Doublet Model (2HDM) potential that can be
extended to the whole Lagrangian, i.e. the CP-symmetries CP1, CP2, CP3 and the
Higgs-family symmetries Z2, U(1) and SO(3) are discussed. Sufficient and
necessary conditions in terms of constraints on masses and physical couplings
for the potential to respect each of these symmetries are found. Each symmetry
can be realized through several alternative cases, each case being a set of
relations among physical parameters. We will show that some of those relations
are invariant under the renormalization group, but others are not. The cases
corresponding to each symmetry group are illustrated by analyzing the interplay
between the potential and the vacuum expectation values.
