We present a multi-wavelength study of the nature of the SDSS galaxies divided into fine classes based on their morphology, colour and spectral features. The SDSS galaxies are classified into early-type and late-type; red and blue; passive, HII, Seyfert and LINER, which returns a total of 16 fine classes of galaxies. The properties of galaxies in each fine class are investigated from radio to X-ray, using 2MASS, IRAS, FIRST, NVSS, GALEX and ROSAT data. The UV - optical - NIR colours of blue early-type galaxies (BEGs) seem to result from the combination of old stellar population and recent star formation (SF). Non-passive red early-type galaxies (REGs) have larger metallicity and younger age than passive REGs, which implies that non-passive REGs have suffered recent SF adding young and metal-rich stars to them. The radio detection fraction of REGs strongly depends on their optical absolute magnitudes, while that of most late-type galaxies does not, implying the difference in their radio sources: AGN and SF. The UV - optical colours and the radio detection fraction of passive RLGs show that they have properties similar to REGs rather than non-passive RLGs. Dust extinction may not be a dominant factor making RLGs red, because RLGs are detected in the mid- and far-infrared bands less efficiently than blue late-type galaxies (BLGs). The passive BLGs have very blue UV - optical - NIR colours, implying either recent SF quenching or current SF in their outskirts. Including star formation rate, other multi-wavelength properties in each fine class are investigated, and their implication on the identity of each fine class is discussed (abridged).
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