h*g is in right coset Hg if h is in subgroup H of G and g is in group G.
Let g be a fixed element of Group G.
Let H be a subgroup of G.
Left Coset of H by g is gH.
![{\displaystyle \forall \;g\in G:{\color {OliveGreen}g}H=\lbrace {\color {OliveGreen}g}\ast h\;|\;h\in H\rbrace }](https://wikimedia.org/api/rest_v1/media/math/render/svg/2adc5c976c33862ec7f923f4172975ecdb3499d1)
Right Coset of H by g is Hg.
![{\displaystyle \forall \;g\in G:H{\color {OliveGreen}g}=\lbrace {h\ast \color {OliveGreen}g}\;|\;h\in H\rbrace }](https://wikimedia.org/api/rest_v1/media/math/render/svg/ebf9c54cf87bc54c2920df450afba687ebdd7cf2)
Notice that such cosets are not necessarily subgroups of G.