  The traditional symmetries that protect superconductivity are time-reversal
and inversion. Here, we examine the minimal symmetries protecting
superconductivity in two dimensions and find that time-reversal symmetry and
inversion symmetry are not required, and having a combination of either
symmetry with a mirror operation on the basal plane is sufficient. We classify
superconducting states stabilized by these two symmetries, when time-reversal
and inversion symmetries are not present, and provide realistic minimal models
as examples. Interestingly, several experimentally realized systems, such as
transition metal dichalcogenides and the two-dimensional Rashba system belong
to this category, when subject to an applied magnetic field.
