500 troops is enough for a Battalion.
I agree.
That's enough organic ground support to knock over most non-industrial (Population: 6-) worlds, even before factoring in the tech level differential (TL=15 vs TL=14-). When you get to "bows and arrows against the lightning" levels of tech differential, it gets even more lopsided in favor of the Tigress battalion. And then there's the ortillery factor of a Meson-T being used against ground targets while fighters provide interface superiority as previously mentioned and things can get REALLY UNFAIR™ in an absolute hurry.
Policing rates are typically 1‰ to 7‰. (yes, per mille, ie, 1-7 per 1000.) In the US, the typical rates are 1‰-2‰ for local police, 1‰-2‰ for the sheriff's department, and 0.5‰ to 1.5‰ for state police, 0.1‰ FBI, 0.02‰ USSS, 0.005 DEA, 0.05‰ DIA... and several other feds, basically hitting about 0.3‰... so 2.0‰ to 5.9% (since DEA and several others are localized oddly). This is solely for illustrative purpose; many European nations run slightly under 1‰ but also have Interpol and auxiliary &/or military forces to bring it up to 1.5‰ or even 2‰ in crisis situations. Most nations with under 1‰ also qualify as "lawless" or "thoroughly corrupt" to western eyes. Monaco's 515 officers hit a whopping 13‰ of it's 39k population... but given 15K tourists per year, and an assumption of 3 days each, that's 1300 persons more on a daily basis, and tourists probably should count double...
Occupation rates run 5‰(=0.5%) to 5%, historically, after the initial battles... with some outliers at up to 15%.
500 troops are sufficient for 10,000 extremely hostile to 100,000 basically cooperative occupied peoples. And could wartime garrison 100k to 500k friendlies as the police force. If there's an extremely motivated "5th column" resistance, maybe as few as 3000 people kept in check by the 500 men.
Of course, if the local police are militarized, they can basically be counted as negating an equal number of incoming occupiers... If merely paramilitary, 1/4 to 3/4 of them per
So 500 men in a transport are probably not a good size for most invasions over pop rating 4... but they are enough to beachhead a city of thousands, which is often more important than the world as a whole.