Midrange periodicities in solar flare occurrence have been analyzed with new methods for cycles 19-23. During cycle 23, periodicities of 129 and 33.5 days were in operation. Five episodes of high activity occurred periodically with the 129 day period. The 33.5 day periodicity mainly operated for energetic flares. Results for cycles 19-21 are generally in agreement with previous analyses. For cycle 19, the 51 day periodicity is confirmed to be statistically significant. In the spectrum for cycle 20, two peaks are found at 84 and 129 days. The 129 day periodicity was in operation for eight cycles of 129 days. The 153 day periodicity, which operated during cycle 21, was more effective for modulating occurrence rates of energetic flares than for those of less energetic flares. No statistically significant periodicities are found from occurrence rates of energetic flares (!M1.0) of cycle 22. In the power spectra of major flare occurrence times for the time intervals analyzed by Ozguc and Atac and by Bai, the strongest peaks are found at 73, 76, and 51 days, in agreement with their results, but these periodicities are not statistically significant. It is interesting that the periods of 51, 129, and 153 days are very close to integral multiples of 25.5 days.