Let $G=\Bbb Z_{1980}$ and 2 sub-groups $H_1=\langle85\rangle, H_2=\langle117\rangle$
I found that 45 generates $H_1 \cap H_2$ and that number of element in the latter is 45 too.
Plus I know that there are 24 generators is $H_1 \cap H_2$.
How can I find number of all sub groups of $H_1 \cap H_2$?
I found 2, $H_1 \cap H_2$ itself and ${e}$.
Note: I don't need to find them just know their number.