Cayley table
This group has two nontrivial subgroups: "J"={0,4} and "H"={0,2,4,6}, where "J" is also a subgroup of "H". The Cayley table for "H" is the top-left quadrant of the Cayley table for "G". The group "G" is cyclic, and so are its subgroups. In general, subgroups of cyclic groups are also cyclic.