  We examine orbifold theories of Grand Unification with Scherk-Schwarz
twisting, performing a renormalisation group analysis and applying low energy
experimental constraints. We rule out the minimal SU(5) models, and consider
simple extensions including additional fields, such as an additional scalar
field, or additional symmetries, such as $SU(5)\times U(1)$ or $E_6$. We find
that it is very difficult to generate a large enough Higgs mass while
simultaneously passing LHC experimental search constraints.
