Let G=D4 and K={R0, R180}
Cayley Table for G, Cayley Table for G/K
with the 4 cosets of K shaded
  R0 R180 R90 R270 H V D D'   K R90K HK DK
R0 R0 R180 R90 R270 H V D D' K K R90K HK DK
R180 R180 R0 R270 R90 V H D' D
R90 R90 R270 R180 R0 D' D H V R90K R90K K DK HK
R270 R270 R90 R0 R180 D D' V H
H H V D D' R0 R180 R90 R270 HK HK DK K R90K
V V H D' D R180 R0 R270 R90
D D D' V H R270 R90 R0 R180 DK DK HK R90K K
D' D' D H V R90 R270 R180 R0
K={R0,R180}
R90K={R90, R270}
HK={H,V}
DK={D,D'}