Let's take a look at European airlines. According to https://www.airportsineurope.com/flight-info/largest-airlines-europe/ the top airlines are:

 

Position Airlines Passengers x 1,000,000

1 Lufthansa Group (incl. Lufthansa, Austrian, Swiss, Eurowings) 107,7

2 Ryanair 101,4

3 IAG (British Airways, Iberia, Vueling, Aer Lingus) 94,9

4 Air France-KLM (incl. Air France, KLM, HOP!, Transavia) 89,8

5 easyJet 69,9

6 Turkish Airlines 61,2

7 Aeroflot Group (incl. Aeroflot, Rossiya, Pobeda) 39,4

8 Air Berlin Group (incl. Air Berlin, NIKI) 30,2

9 SAS Group (Scandinavian Airlines) 27,1

10 Norwegian 25,8

11 Alitalia 23,0

12 Pegasus Airlines 22,3

13 Wizz Air 19,2

14 TAP Portugal /

15 Aegean Airlines (and Olympic Air) 11,6

16 S7 Airlines 10,6

17 Finnair 10,2

18 Air Europa 9,0

19 UTair 8,8

20 SunExpress 8,7

 

Let's keep it simple and use companies that only run one brand, and only three to start with: Ryanair, easyJet, Turkish Airlines.