If a group has order 30 there are 4 unique groups (up to isomorphism) to which it could be isomorphic.

Abelian

1) this is the one you are looking for

Nonabelian

2) (Dihedral group)

3)

4)

If its abelian its easy to see why it must be cyclic by the fundamental theorem of finitely generated abelian groups, and noting

hope this helps