Drop-down menu on the top navigation bar

I would like to display a drop-down menu in place of the top navigation bar. For this, I first created the sub-categories on the category page. Then I added them under the relevant parent categories, on the Menu page of Appearance. The problem with this method is that, on the home page, both the category and the sub-category of the posts are getting displayed. I would like to have only the primary category visible on the homepage (under the title of each post), along with a drop-down menu on the navigation bar. How do I do that?

Thanks.