type 
P(k) = 1 
wallpaper type of kernel group, with remarks 
pmg

none 
pmg, same as the extended group 
p'_{b}mg

t_{1} 
pmg = {t_{1}^{2}, L_{v}, A}


t_{1} and L_{v} 
same as above,
i(L_{v}) = L_{v} t_{1} 
pmg'

L_{v} 
pm = {t_{1}, L_{v}^{2}, A};
R negative 
pm'g

A 
pg = {t_{1}, L_{v}};
R negative 
p'_{b}gg

t_{1} and A 
pgg = {t_{1}^{2}, L_{v}, t_{1} A};
doubled cell 

t_{1}, L_{v} and A 
same as above,
i(L_{v}) = L_{v} t_{1} 
pm'g'

L_{v} and A 
p2 = {t_{1}, L_{v}^{2}, L_{v} A};
R positive 