Let $G$ be a semisimple algebraic group defined over $\mathbb{Q}$ (simply connected if it helps).
Then for almost all (maybe all) primes $p$, we can make sense of the group $G(p)$ (formed by reducing the defining equations of $G$ modulo $p$, and taking the points in $\mathbb{F}_p$).
Looking at some tables regarding Chevalley groups, I noticed the following: The order of $G(p)$ is divisible by $p$.
Is there an explanation for this fact that does not rely on classifications and tables?
Actually, I want to ask the same question more generally about $|G(p^e)|$ (Is it divisible by $p$? I guess it should be divisible by $p^e$).
If there are finitely many exceptions to this rule it's still good for me. I don't care about a finite number $N$ of exceptions, where $N$ is a function of $G$.