G=D_4 and K={R_0, R_180}

Cayley Table for G showing G/K

R_0

R_180

R_90

R_270

H

V

D

D'

R_0

R_0

R_180

R_90

R_270

H

V

D

D'

R_180

R_180

R_0

R_270

R_90

V

H

D'

D

R_90

R_90

R_270

R_180

R_0

D'

D

H

V

K=

{R_0,R_180}

R_270

R_270

R_90

R_0

R_180

D

D'

V

H

R_90K=

{R_90, R_270}

H

H

V

D

D'

R_0

R_180

R_90

R_270

HK=

{H,V}

V

V

H

D'

D

R_180

R_0

R_270

R_90

DK=

{D,D'}

D

D

D'

V

H

R_270

R_90

R_0

R_180

D'

D'

D

H

V

R_90

R_270

R_180

R_0

Cayley Table for G/K

K

R_90K

HK

DK

K

K

R_90K

HK

DK

R_90K

R_90K

K

DK

HK

HK

HK

DK

K

R_90K

DK

DK

HK

R_90K

K