A direct numerical simulation database is used to characterize the structure of supersonic turbulent boundary layers at Mach numbers from 3 to 5. We develop tools to calculate the average properties of the coherent structures, namely, angle, convection velocity, and length scale, and show good agreement with the available experimental data. We find that the structure angle and convection velocity increase with Mach number, while the streamwise integral length scale decreases. The structures become taller with Mach number, which is consistent with the larger structure angle. The distribution of the streaky-structure spacing at the wall is computed, and observed to be slightly narrower and more uniform with increasing Mach number. We find that the low-speed streaks carry about one-third of the total turbulent kinetic energy. Similar to the incompressible case, we observe hairpin vortices clustered into streamwise packets at all Mach numbers, and develop an algorithm to identify and characterize these hairpin packets. The average packet convection velocity, length, and number of hairpins increase with higher Mach number, while the packet height and angle decrease.