Swan bands - characteristic molecular absorption features of the C2 molecule - are a spectroscopic signature of carbon-enhanced stars. They can also be used to identify carbon-enhanced metal-poor (CEMP) stars. The GALAH (GALactic Archaeology with Hermes) is a magnitude-limited survey of stars producing high-resolution, high-signal-to-noise spectra. We used 627708 GALAH spectra to search for carbon-enhanced stars with a supervised and unsupervised classification algorithm, relying on the imprint of the Swan bands. We identified 918 carbon-enhanced stars, including 12 already described in the literature. An unbiased selection function of the GALAH survey allows us to perform a population study of carbon-enhanced stars. Most of them are giants, out of which we find 28 CEMP candidates. A large fraction of our carbon-enhanced stars with repeated observations show variation in radial velocity, hinting that there is a large fraction of variables among them. 32 of the detected stars also show strong Lithium enhancement in their spectra.