How to find the order of these groups? I don't know why but I just cannot see how to find the orders of these groups:
$YXY^{-1}=X^2$
$YXY^{-1}=X^4$
$YXY^{-1}=X^3$
With the property that $X^5 = 1$ and $Y^4 =1$
How would I go about finding the order? The questions asks me to find which of these groups are isomorphic. 
Thanks. 

Hint: You should treat those relations as a rule on how to commute $Y$ past $X$, for example the first can be written:
$$YX = X^2Y$$
Then you know that every element can be written in the form $X^nY^m$ for some $n$ and $m$.  Use the orders of $X$ and $Y$ to figure out how many elements there are of this form.
