I am confused by the notation in this problem, i have an idea about showing a group to be a subgroup, but i am not sure what the notation means and i am not seeing it anywhere in my books or online, i am hoping someone can help.

In $\displaystyle G = {Z_{21}}^{x}$, show that $\displaystyle H = {[x]_{21}| x\equiv 1 (mod 3)} $ and $\displaystyle K = {[x]_{21}| x\equiv 1 (mod 7)}$

are subgroups of G.