Correct Answer - Option 2 : G may not be cyclic, but H is always cyclic.

**Concept**

According to the Lagrange theorem order of subgroups must divide the order of the group.

Property of group says if a group has prime order then it is cyclic.

**Explanation:**

Since the order of G is 6. Therefore its subgroup may have order 1,2,3,6

H is one of its subgroups with condition 1< |H| <6 so H may be of order 2 or 3 which is prime

Hence H must be cyclic

The order of G is 6 which is not prime and hence it may or may not be cyclic

Therefore option 2 is correct