William Herschel discovered NGC 5636 = H II-580 = h1816, along with II-581 = NGC 5638, on 30 Apr 1786 (sweep 558). He recorded "Two, the place is that of the most south NGC 5638]. pB, gbM, pL, R. The most north [NGC 5636] distance about 2'. eF, cL, requiring much attention to be seen." On 9 Apr 1828 (sweep 142) John Herschel noted, "eF; R; the np of 2."

On 25 Apr 1848 William Parson (or assistant Rambaut) noted "A bright, double nebula". JH assumed that one was NGC 5638 but the second object was new and assigned it a separate GC designation (3905) from II-580. Later, Dreyer realized the second object was NGC 5636 and both GC designations are combined in the NGC.

400/500mm - 17.5" (6/8/91): faint, fairly small, 1.2'x0.9', slightly elongated SW-NE, very low even surface brightness. Forms a close pair with the high surface brightness galaxy NGC 5638 1.9' SSE.

600/800mm - 24" (6/27/14): fairly faint to moderately bright, elongated 3:2 NW-SE, 0.9'x0.6', broad concentration with a slightly brighter core, but no noticeable nucleus. Forms a 2' (non-interacting) pair with the bright elliptical NGC 5638.

Notes by Steve Gottlieb