Show that an elliptic curve is isomorphic to $\mathbb{Z}_{n_1} \times \mathbb{Z}_{n_2}$

Question

[Theorem] Let $E$ be an elliptic curve defined over $\mathbb{F}_q$, $q=p^n$ for some prime $p$. Then there exists positive integers $n_1$ and $n_2$ such that $E \simeq \mathbb{Z}_{n_1} \times \mathbb{Z}_{n_2}$ where $n_2 \mid n_1$.

I'm given an elliptic curve $E$ defined over $\mathbb{F}_p$ for some prime $p$, and using maple I was able to find the orders of elements in $E$:

1. Of course, Point at infinity has order $1$.
2. There are $24$ elements of order $5$.
3. There are $400$ elements of order $401$.
4. There are $9600$ elements of order $2005$.
5. Total number of elements of $E$ is $10025$.

Now, I want to find positive integers $n_1, n_2$ in the Theorem. I know that there is one sub-cyclic group of order $401$, so I suppose $n_1=10025$ and $n_2=401$? But I don't know if this is really true.