Suppose that R is a commutative ring and |R|=30. IfIis an ideal of R and |I|=10, prove thatIis a maximal ideal.

Im pretty sure I understand why its maximal, its because if there was an ideal that properly containedIthen the order would be greater than 10 but the order of all proper sub-rings of R would be positive divisors which stop at 10. ok my problem is proving this elegantly on paper... any thoughts. thanks