The PFLP are a hard Left armed Palestinian group which participated in the 10-7 invasion. They are present among the groups defending Gaza right now. They have some presence in the West Bank, but in general it is not a big group.
The biggest groups in the West Bank are the Al Aqsa Martyr’s Brigade (Fatah armed rejectionists) and Islamic Jihad. Hamas does not have a large presence there although they do have some. There is a small Mujahedin Movement presence.
The Lion’s Den, a new nonpolitical formation of young men from the West Bank with a significant presence in the West Bank, seems to be allied with Islamic Jihad and the Al Aqsa Martyr’s Brigade. Both of these latter groups often work together and combined they make up the Jenin Brigades. In addition to the Lion’s Den, there are also little grouplings just like them that have sprung up all over the West Bank. They tend to fight in their areas alone.
The groups in Gaza are Hamas (close to Iran), Islamic Jihad (close to Iran), Al-Nasser Al-Saladin Brigades (armed Fatah rejectionists), the PFLP (they have a bigger presence here than in the West Bank, significant support from Iran), the Mujahedin Brigades (mostly in Gaza, hardly in the West Bank), Popular Resistance Committees (leftwing group close to Iran, only in Gaza, made up of family clans), the DFLP (Hard Left group with about zero presence in the West Bank, but a significant presence in Gaza), and the Al Aqsa Martyr’s Brigade (a small presence in Gaza, but most of their forces are in the West Bank.
All of these groups participated in the 10-7 invasion.
The PFLP-GC, a pro-Syrian group with a big presence in Lebanon and Syria, has a very small presence in Gaza and zero in the West Bank, but they have a strong presence in Lebanon and Syria.
There are also some very small Salafist groups in Gaza, but they are not in good terms with Hamas as Hamas thinks they’re too Islamist and the Salafists feel that the Hamas have sold out Islam because they have not imposed Islamic Law.
There is a Syrian wing of Islamic Jihad made up of Palestinian refugees in Syria. They’ve participated in some of the fighting up in Lebanon.
There is also a small group of Sunni Lebanese who have taken up arms there. They fight alongside Hezbollah.
Hamas also has a significant presence in Lebanon. They mostly launch missiles.
There is an Islamic Jihad presence there too. They have staged a couple of incursions into Israel from Lebanon.
All of those groups up there operate under the control of Hezbollah. They have to get Hezbollah’s permission to engage in any attacks.