The compound shown is 1,3-dimethylcyclohexane drawn without stereochemistry. Treat the ring as planar and consider configuration only. Which of the following statements are correct?

C1 and C3 are stereocentres (the two ring paths from each are of different length). The molecule has a symmetry element exchanging C1 and C3: the plane through C2 and C5. In the cis isomer both methyls lie on the same face and this plane is a mirror plane, so cis is meso. In the trans isomer the methyls are on opposite faces, the plane is not a mirror plane, and trans is chiral: $(1R,3R)$ and $(1S,3S)$. Total $1+2=3$, not 4.