I am working with this Cayley diagram. I have labeled it as shown. Dotted line is $a$ and solid is $b$. I am listing all the subgroups. I currently have: $\{e,a\},\{e, ab\},\{e,ab^2\},\{e,ab^3\},\{e, ab^4\},\{e,b,b^2,b^3,b^4\}$ where $e$ is the identity element. Am I missing any subgroups?
