While Google parent company Alphabet pours capital into self-driving vehicles with its Waymo unit, the company is making real money in transportation right now.

CapitalG, the late-stage investing arm of Alphabet, has doubled the value of its investment in Lyft, after the ride-hailing company made its stock market debut on Friday.

CapitalG invested $500 million in Lyft in October 2017 at $39.75 a share. Following Lyft's 11 percent pop to more than $80 a share, that stake is worth more than $1 billion.

Alphabet has a complicated but lucrative relationship with Lyft and its main competitor, Uber.

In 2013, the company invested more than $250 million in Uber through its early-stage venture arm, GV, formerly known as Google Ventures. Google executive David Drummond took a seat on Uber's board.

But the two companies gradually started to compete in various areas, including self-driving technology, and Drummond left the board in 2016. Then Alphabet sued Uber in 2017, claiming that Uber had stolen trade secrets when it acquired a self-driving technology start-up built by another former Google exec, Anthony Levandowski. The case was settled last February, and Uber agreed to pay Waymo a 0.34 percent equity stake, which at the time amounted to about $245 million.

Alphabet took its stake in Lyft as the lawsuit with Uber was still going on. Thanks to that stake, it's the fifth-biggest outside investor in Lyft, behind Japan's Rakuten, GM, Fidelity and venture firm Andreessen Horowitz. David Lawee, a partner at CapitalG, is on Lyft's board.

Last year, Alphabet revealed that it had gained about $3 billion from its equity investments, mostly from its 2013 Uber stake. Assuming Uber's value is the same today as it was then, Alphabet's total stake between Lyft and Uber is now worth more than $4 billion.