We study hadronic transitions between bottomonium states using 496 fb(-1) data collected at the gamma(4S) resonance with the Belle detector at the KEKB asymmetric energy e(+)e(-) collider. We measure: B(gamma(4S) -> pi(+)pi(-)gamma(1S)) = (8.2 +/- 0.5(stat.)+/- 0.4(syst.)) x 10(-5), B(gamma(4S) -> pi(+)pi(-)gamma(2S)) = (7.9 +/- 1.0(stat.)+/- 0.4(syst.)) x 10(-5), and B(gamma(4S) -> eta gamma(1S)) = (1.70 +/- 0.23(stat.) +/- 0.08(syst.)) x 10(-4). We measure the ratio of branching fractions R=B(gamma(4S) -> eta gamma(1S))/B(gamma(4S) -> pi(+)pi(-)gamma(1S)) = 2.07 +/- 0.30(stat.)+/- 0.11(syst.). We search for the decay gamma(1(3)D(1,2)) -> eta gamma(1S), but do not find significant evidence for such a transition. We also measure the initial state radiation production cross sections of the gamma(2S,3S) resonances and we find values compatible with the expected ones. Finally, the analysis of the gamma(4S) -> pi(+)pi(-)gamma(1S) events shows indications for a resonant contribution due to the f(0)(980) meson.