# Character table and symmetry operations

It's been a while since I've dealt with these, but do character tables include all possible symmetry operations?

I am looking at the $$D_{\infty h}$$ point group table and it lists $$C_\infty$$, $$\sigma_v$$, $$S_\infty$$, $$i$$, and $$C_2$$. But doesn't it also have a $$\sigma_h$$? Why is this not included?

Am I missing something here?