  We discover a class of spacetime symmetries unique to time-periodic systems,
which we term "mixing symmetry" due to its combination of space and time
coordinates in the symmetry transformation. We systematically enumerate the
symmetry groups, and classify the corresponding Floquet-Bloch band theories by
utilizing the winding number of quasi-energy. Moreover, we provide a
comprehensive scheme for the experimental realization of these symmetries. The
particle propagator exhibits an intriguing pattern that remains invariant even
under transformations mixing space and time coordinates. We anticipate that
this distinct feature can be observed in current cold atom experiments.
