Variations of ionospheric ionization (represented by ionospheric electron content (IEC)) and related solar fluxes with the 10.7-cm solar flux index (F10.7) are studied for the intense solar cycle 21 when F10.7 was as high as 367. The IEC data collected at several stations during 1980-1985, the solar EUV (50-1050 Å) fluxes obtained from the EUV91 solar EUV flux model, and the measured values of Lyman α (1216 Å) flux and He I (10,830 Å) equivalent width (EW) are used for the study. It is shown that daily values of diurnal maximum IEC (IECmax) saturate (remain constant) when F10.7 (or its 81-day running average) exceeds a threshold (approximately 160-200) which depends slightly on season and latitude. Variations of the model values of the solar EUV fluxes reveal that when F10.7 exceeds the threshold: (1) the integrated solar EUV (50-1050 Å) flux increases at a very low rate, and (2) the fluxes of the important (for thermospheric heating) chromospheric lines and intervals generally saturate (remain constant), while those of the coronal lines and intervals increase at a reduced rate. Lyman α flux and He I EW, which are used as input data in the solar EUV flux model, also increase at a very low rate when F10.7 exceeds the threshold. The saturation of ionospheric ionization, observed for high values of F10.7 during the last three solar cycles 19-21, is the result of the nonlinear variation of the solar EUV and Lyman α fluxes with F10.7. IECmax increases linearly with the integrated solar EUV flux, Lyman α flux and He I EW.