things to remember with cyclic groups:

1) every subgroup is cyclic.

2) if G is cyclic of order n, and k divides n, G has a UNIQUE subgroup of order k (so it has one, and only one, for each divisor k of n).

in particular, if G = <a>, with |a| = n, and k|n, so that n = kd, then the subgroup of order k is <a^{d}>.

for ABELIAN groups, a^{d}is usually written da. since Z/36Z is generated by 1+36Z = [1], we need only consider <d[1]> = <[d]> for each divisor d of 36.

the divisors of 36 are:

1,2,3,4,6,9,12,18, and 36.

your turn.