C${\mathrm{O}}_{2}$-laser---induced phonon-assisted cyclotron-resonance harmonics (PACRH) in $n$-type InSb are investigated at low magnetic fields with photoconductivity techniques. The high resolution allowed transitions up to the 23rd harmonic to be seen. Polarization studies of PACRH show that strong resonances are present for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{e}}\ensuremath{\perp}\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}}$ (but not for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{e}}\ensuremath{\parallel}\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}}$) in the Voigt geometry. In the Faraday geometry, the resonances were found to be of approximately equal amplitude for both ${\ensuremath{\sigma}}_{R}$ and ${\ensuremath{\sigma}}_{L}$ circularly polarized light. A large variety of intra-conduction-band magneto-optical experimental work has been unified and explained using a modified Pidgeon-Brown energy-band model and only one set of band parameters. These include cyclotron resonance, combined resonance, cyclotron-resonance harmonics, combined resonance harmonics, electron-spin resonance, and PACRH data from a wide variety of authors. The resulting set of energy-band parameters are ${E}_{g}=235.2$ meV, ${E}_{p}=23.2$ eV, $\ensuremath{\Delta}=0.803$ eV, ${\ensuremath{\gamma}}_{1}=3.25$, ${\ensuremath{\gamma}}_{2}=\ensuremath{-}0.2$, ${\ensuremath{\gamma}}_{3}=0.9$, $\ensuremath{\kappa}=\ensuremath{-}1.3$, $F=\ensuremath{-}0.2$, $q=0.0$, ${N}_{1}=\ensuremath{-}0.55$. These parameters are also shown to explain the variation of the effective $g$ factor with magnetic field. In addition, these parameters also quantitatively explain recent two-photon magnetoabsorption data and recent intra-valence-band data.