Lord Hordak

Adora
Lord Hordak saw great potential in Adora as she was growing up in The Fright Zone; enough potential to make her a Force Captain and lead a crew to end The Rebellion for good. When she defected, he wanted everyone -especially Shadow Weaver- to forget about her and assign a new Force Captain. When he found out that Shadow Weaver had been attempting to bring Adora back, he fires her as second-in-command hires Catra. He wants to forget about bringing her back and just move on with his military.

Catra
Since Adora defected, Lord Hordak has promoted Catra twice and seen great results since. Getting the Sword of Protection, capturing a princess and converting a princess into The Horde; Lord Hordak wants to use her to his advantage in order to take over Etheria.

Entrapta
Lord Hordak wasn't aware that Catra and Scorpia had found a princess left behind in The Fright Zone. Once his Imp found out about it and recorded audio of their conversation, he gave them all his blessing to continue their research on the runestones.

The Horde
It's unclear what his motives are behind taking over Etheria are, but The Horde is at his will. Whatever he says is the final ruling and nothing will stop him from achieving his goals. If someone defects -à la Adora- or disobeys a direct order -à la Shadow Weaver- he will find a replacement.

Imp
The Imp as far as we know is Lord Hordak's pet. He is used as a mobile recording device whose purpose is to get information to him about what his crew is talking about.

The Princess Alliance/The Rebellion
His only other goal besides taking over Etheria is to take out The Rebellion and the Princesses. He doesn't seem to mind that both Entrapta and Scorpia are themselves princesses; using them to get more of an advantage on the rebellions.

Shadow Weaver
Shadow Weaver continuously went against Lord Hordak's orders and ended up getting her position taken away from her. It's unclear if she is still in command of anyone or if she's been kicked from The Horde entirely, but Lord Hordak did not want her bringing Adora back.