Aims:Magnetic elements are thought to be described by flux tube models, and are well reproduced by MHD simulations. However, these simulations are only partially constrained by observations. We observationally investigate the relationship between G-band bright points and magnetic structures to clarify conditions, which make magnetic structures bright in G-band. Methods: The G-band filtergrams together with magnetograms and dopplergrams were taken for a plage region covered by abnormal granules as well as ubiquitous G-band bright points, using the Swedish 1-m Solar Telescope (SST) under very good seeing conditions. Results: High magnetic flux density regions are not necessarily associated with G-band bright points. We refer to the observed extended areas with high magnetic flux density as magnetic islands to separate them from magnetic elements. We discover that G-band bright points tend to be located near the boundary of such magnetic islands. The concentration of G-band bright points decreases with inward distance from the boundary of the magnetic islands. Moreover, G-band bright points are preferentially located where magnetic flux density is higher, given the same distance from the boundary. There are some bright points located far inside the magnetic islands. Such bright points have higher minimum magnetic flux density at the larger inward distance from the boundary. Convective velocity is apparently reduced for such high magnetic flux density regions regardless of whether they are populated by G-band bright points or not. The magnetic islands are surrounded by downflows. Conclusions: These results suggest that high magnetic flux density, as well as efficient heat transport from the sides or beneath, are required to make magnetic elements bright in G-band.