> Israel is a satellite state of the US in all but name.
The US is more reflexively pro-Israel than Israel is pro-US in international policy, the opposite of what you’d expect if Israel was a US vassal.
> What ive always wondered is why the US hasn't put Israel on the security council
There are lots of reasons, but one that renders all the others secondary is that the US can’t add permanent Security Council members.
> considering it is a nuclear armed state.
India, Pakistan, North Korea, and, when it was a nuclear-armed state, South Africa also are (and were) not permanent UNSC members, a set whuch hasn't expanded, though two seats have switched hands, since the UN was founded.