Experimental studies on the role of nuclear quadrupole interaction (NQI) to the in-plane nuclear field formation are performed in single self-assembled In 0.75 Al 0.25 As= Al 0.3 Ga 0.7 As quantum dots (QDs). In Hanle-effect measurements, the electron depolarization curves deviating far from a standard Lorentzian shape are observed: the curves with anomalously large width and hysteretic behavior at the critical transverse magnetic field. These anomalies indicate the growth of an in-plane nuclear field compensating the applied transverse magnetic field up to %1 T and appear regardless of the excitation helicity. The azimuth angle dependence of the critical field of the hysteretic response reveals that the principal axis of the NQI is almost parallel to the crystal growth axis. This fact suggests that the main origin of the NQI which is related with in-plane nuclearfield formation is not random alloying among In and Al nuclei but residual strain of QDs. Furthermore, a longitudinal magnetic field by a neodymium magnet breaks the excitation-helicity independence of the Hanle curves and the shape of curves becomes very different depending on the helicity. The obtained results are explained well with a simple consideration and indicate that the NQI takes multirole in the formation of in-plane nuclear field.