She has never invited me to go out with her and her friends. she claims I wouldn't like them.
Forgive me, bro, but this needs to be said:
You've been with this girl for 10 months, you guys don't hang out on the weekends. Hell, you've never been invited to hang out with your GIRLFRIEND'S friends!!
You guys hardly fight, and your 'very serious about each other', but every weekend, she's out with her friends (the ones that you wouldn't like

) instead of hanging out with her BOYFRIEND!
I'm not meaning to sound like a ****, and I really don't know the situation like you do.....but personally, I'd drop her in favor of a girl who has some actuall interest in me. The fact that you don't know her friends or get invited to chill with them is absolutely inexcuseable. Bottom line. This is not a healthy relationship.
Girls with real interest want to spend time with you. If you think about this, you'll know that it is the truth.
I'd go find another girl if I were in that situation. There's only 100 million to choose from.
EDIT: I guess you probably want an answer to your actuall question
If you want her to take more interest in you, back off alot. Don't call. Wait for her. Don't make plans with her. Let her initiate that. Next time she wants to go do something, you can't because your busy with something else. Something fun.
You'll know if she's a keeper pretty quick. Either she'll express interest, or she won't.
Good luck with this.