We report the experimental results from a dark study and a photoexcited study of the high-mobility GaAs/AlGaAs system at large filling factors, $\ensuremath{\nu}$. At large $\ensuremath{\nu}$, the dark study indicates several distinct phase relations (``type 1,'' ``type 2,'' and ``type 3'') between the oscillatory diagonal and Hall resistances, as the canonical integral quantum Hall effect (IQHE) is manifested in the type 1 case of approximately orthogonal diagonal and Hall resistance oscillations. Surprisingly, the investigation indicates quantum Hall plateaus also in the type 3 case characterized by approximately ``antiphase'' Hall and diagonal resistance oscillations, suggesting an unfamiliar and distinct class of IQHE. Transport studies under microwave photoexcitation exhibit radiation-induced magnetoresistance oscillations in both the diagonal, ${R}_{xx}$, and off-diagonal, ${R}_{xy}$, resistances. Further, when the radiation-induced magnetoresistance oscillations extend into the quantum Hall regime, there occurs a radiation-induced nonmonotonic variation in the amplitude of Shubnikov--de Haas (SdH) oscillations in ${R}_{xx}$ vs $B$, and a nonmonotonic variation in the width of the quantum Hall plateaus in ${R}_{xy}$. The latter effect leads into the vanishing of IQHE at the minima of the radiation-induced ${R}_{xx}$ oscillations with increased photoexcitation. We reason that the mechanism which is responsible for producing the nonmonotonic variation in the amplitude of SdH oscillations in ${R}_{xx}$ under photoexcitation is also responsible for eliminating, under photoexcitation, the type 3 associated IQHE in the high-mobility specimen.