Canon 80D has a Canon EF/EF-S lens mount and currently there are 319 native lenses available for this mount.
Canon 80D doesn't have a sensor based image stabilization system but 107 of these lenses already comes with optical image stabilization.
Since Canon 80D has a APS-C sensor, it has a focal length multiplier of 1.6x so you have to multiply lenses original focal length with this multiplier to find the Full Frame equivalent focal length of the lens when mounted on 80D.
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Canon 80D Lenses with Image Stabilization
Canon 80D Lenses with Weather Sealings