# Math Help - Finding the number of subgroups

1. ## Finding the number of subgroups

Could someone explain to me how to find the number of subgroups in Z_567,000 ?

2. Exactly the number of divisors of 567,000, which a quick internet search yields The Positive Integer 567000 as the list of such divisors. To see that this is true, let $a$ be a divisor of 567,000. Then the order of a is $r=567000/a$. Suppose g is another element of order r, so $rg = q(567000)$, thus $g=q(567000/r)=q a$, so g is in the cyclic subgroup generated by a, thus each divisor corresponds to a unique subgroup of that order.