A subset K of a group G is a  twisted subgroup of G if it
Satisfies

1) $1\in K$

2) for all $x,y\in K, xyx\in K$
      I am looking to find some twisted subgroups that are not subgroups
which 
contain a transversal of a subgroup. I will appreciate any help.
Thank you,

Tuval Foguel
foguel@prairie.nodak.edu