  We have investigated the effect of unidirectional periodic potential
modulation on the fractional quantum Hall (FQH) states located within the
filling factor range $1<\nu<2$. We find that odd-numerator FQH states are
strongly suppressed, while the even-numerator ones are less affected or even
enhanced, by the introduction of the modulation. In the picture of the
composite fermions (CFs), the behaviors are equivalent to the suppression of
the spin splitting of the CFs by the modulation. We discuss the origin of the
suppression and the possible modulation-induced phase transition from the FQH
state to the stripe state.
