The implementation of a series of optically pumped GaN photonic crystal (PhC) membrane lasers is demonstrated at room temperature. The photonic crystal is composed of a scalene-triangular arrangement of circular holes in GaN. Three defect structures are fabricated for comparing their lasing characteristics with those of perfect PhC. It is observed that all the lasing defect modes have lasing wavelengths very close to the band-edge modes in the perfect PhC structure. Although those lasing modes, including band-edge and defect modes, have different optical pump thresholds, different lasing spectral widths, different quality factors (Q factors), and different polarization ratios, all their polarization distributions show maxima in the directions around one of the hole arrangement axes. The similar lasing characteristics between the band-edge and defect modes are attributed to the existence of extremely narrow partial band gaps for forming the defect modes. Also, the oriented polarization properties are due to the scalene-triangle PhC structure. In one of the defect lasing modes, the lasing threshold is as low as 0.82 mJ cm(-2), the cavity Q factor is as large as 1743, and the polarization ratio is as large as 25.4. Such output parameters represent generally superior lasing behaviors when compared with previously reported implementations of similar laser structures.