Is There a Difference in Genetics Between Men and Women?

The population of Britain at this point is estimated by some to have been scarcely over 2 million people. Current studies suggest that the migration was significantly smaller than that. How did you get the men of England looking rather Germanic on a genetic level? I mean, if the Anglo-Saxons came over and just mixed in with the substantially larger local population, there wouldn't have been that extreme of a change.