Am I wrong for not inviting my friends to my birthday dinner?

Over a month ago was my 17th birthday and that night I had a birthday dinner with family and invited one friend. Now this particular friend does not get along with my other 2 friends, let's call them friend 2&3. earlier that day friend 2&3, me and some other friends had a birthday lunch with fried chicken and soda at school. So having had the opportunity to celebrate with those friends already, I decided that I would invite other friend, let call her friend 1, to my family birthday dinner

Now I didn't tell friend 2&3 about this because I knew it would cause probelms, firstly none of them seem to get along so that would make the dinner extremely awkward and uncomfortable, secondly my dad was paying and idk how he would feel about having to pay for 10 persons, thirdly I already spent literally the entirety of the day with friend 2&3, I don't see the probelm if I spent sometime with friend 1, fourthly, it's not like friend 2&3 have not done stuff without me and vice versa.

Anyways friend 2 found out, told me I was fake and I should've invited them, then went on to tell friend 1, who preceded to ignore me. Something that they are notorious for. Both friend 2&3 said that if they were invited they would've ignored friend 1, which will only lead to tension, and I was wrong for not telling them. And I would admit that I should've said something but at the same time I knew that this would be reaction. Them calling me fake and believing I value friend 1 over them. When in reality, all of them are on the same level and I try to keep it that way, in fact friend 2&3 see me and spend more time with me than me and friend 1, because we all go to the same school and plan outings outside of school quite regularly compared to friend 1, who I only see on some weekends when she comes to my house and that's basically it.

So tell me, am I the wrong for not inviting them to my birthday dinner?