When playing in the signature key of C which chord F or G is dominate and subdominate chord?

In the key of C major, the dominant chord is G major and the subdominant chord is F major.

The dominant chord is the chord built on the fifth degree of the scale. In C major, the fifth degree is G, so the dominant chord is G major.

The subdominant chord is the chord built on the fourth degree of the scale. In C major, the fourth degree is F, so the subdominant chord is F major.