A $1$ is the identity element. Inverse does not exist for zero. So, it is not a group.
({0,1},⊗) is not a group because : (0e)mod8=0 is haing e=0 as identity but (1e)mod8=1 should have 1 as identity so no single identity is there.
({1,7}, ⊗ ) :
1. closed
2. associative
3. Identity = 1
4. inerse: 1^{-1}=7 , 7^{-1}=1
can someone suggest 2 more subgroups.