Let $(G,+)$ be a group of order $2019$. How many equivalence classes does a proper subgroup of $G$ of order at least $100$ generate? Justify your answer.
EDIT: The solution involves Lagrange's theorem:
$|G|=|H|\cdot|G:H|$
$|H|=673$
Therefore, the number of equivalence classes is $|G:H|=3$.