$H ≤G$ means $H$ is a subgroup of $G$? I was reading this page:
http://www.proofwiki.org/wiki/Definition:Subgroup
I never heard that $H ≤G$ means $H$ is a subgroup of $G$. Is this standard notation ?
And if not, what is/are normal symbolic notations to say that $H$ is subgroup of $G$ ?

Yes, this is pretty much "the standard": $$H\leq G \quad\iff \quad\text{ H is a subgroup of G}$$
In a sense, it is analogous to $H \subseteq G$, which is used to denote $H$ is a subset of $G$. $H\subseteq G$ is true for of any subgroup H of group G. If $H \leq G$, then it follows that $H\subseteq G$, but the converse does not hold, since groups have added algebraic structure. And so using the symbol $\subseteq$ to denote the relationship between $H$ and $G$ doesn't convey that in addition, $H$ is a subgroup of $G$ under the operation of $G$. $\quad H \leq G$ thus conveys MORE information than does $H \subseteq G$. 
