In order to investigate the periodicity and long-term trends of various classes of sunspot groups (SGs), we separated SGs into two categories: simple SGs (A/U <= 4.5, where A represents the total corrected whole spot area of the group in millionths of the solar hemisphere (msh), and U represents the total corrected umbral area of the group in msh); and complex SGs (A/U > 6.2). Based on the revised version of the Greenwich Photoheliographic Results sunspot catalogue, we investigated the periodic behaviors and long-term trends of simple and complex SGs from 1875 to 1976 using the Hilbert-Huang Transform method, and we confirm that the temporal behaviors of simple and complex SGs are quite different. Our main findings are as follows. i) For simple and complex SGs, the values of the Schwabe cycle wax and wane, following the solar activity cycle. ii) There are significant phase differences (almost antiphase) between the periodicity of 53.50 +/- 3.79 years extracted from yearly simple SG numbers and the periodicity of 56.21 +/- 2.92 years extracted from yearly complex SG numbers. iii) The adaptive trends of yearly simple and complex SG numbers are also quite different: for simple SGs, the values of the adaptive trend gradually increase during the time period of 1875 - 1949, then they decrease gradually from 1949 to 1976, similar to the rise and the maximum phase of a sine curve; for complex SGs, the values of the adaptive trend first slowly increase and then quickly increase, similar to the minimum and rise phase of a sine curve.