  We solve for all Szekeres metrics that have a single Killing vector. For
quasi hyperboloidal ($\epsilon = -1$) metrics, we find that translational
symmetries are possible, but only in metrics that have shell crossings
somewhere, while metrics that can be made free of shell crossings only permit
rotations. The quasi planar metrics ($\epsilon = 0$) either have no Killing
vectors or they admit full planar symmetry. Single symmetries in quasi
spherical metrics ($\epsilon = +1$) are all rotations. The rotations correspond
to a known family of axially symmetric metrics, which for each $\epsilon$
value, are equivalent to each other. We consider Szekeres metrics in which the
line of dipole extrema is required to be geodesic in the 3-space, and show the
same set of families emerges. We investigate when two Szekeres metrics are
physically equivalent, and complete a previous list of transformations of the
arbitrary functions.
