I'd be interested in seeing where your 20% paid back claim comes from.
From the bailouts, GM received a total of $49.5 billion. After bankruptcy, that was restructured to be $9.5 billion in loans and preferred stock, with the rest of the $40 billion in the form of a government equity stake (about 61% of the company).
GM paid back what was the restructured loans and preferred stock, about $9.5 billion in total (yes, they paid back some of that with money that they had because of the equity stake the government had, but if someone loans you $50 and you turn right around and give them $20 of it back, you still just owe them $30 - they don't have a right to claim you owe them $50 because that $20 was theirs in the first place).
That left ~$40 billion outstanding.
Then the government recovered $13.5 billion in the IPO by selling some of their stock. That leaves ~$26.5 billion outstanding. But the government still owns about 500 million shares of stock. That means to recover it all, you need a share price of $26.5e9/500e6 = $53. Granted, that isn't accounting for interest on the national debt incurred because of the bailout, but that is VERY close to your $55 per share mark and in line with every other estimate I've seen. That means that:
$26.5/$49.5 = 53.5% is still outstanding, not 80%
BTW, sell all the remaining stock in GM, and the government recovers an additional $13.5 billion, putting the loss at $13 billion. That's a LOT of money, but with 79,000 people still employed at GM, if they're just paying federal taxes at the household median rate of about $8500 per year and not collecting unemployment (almost $19k per year), that's $2.2 billion in federal balance sheet improvements per year per GM employee. Throw in suppliers still at work and others whose jobs depend on economic activity from GM employees, and that $13 billion loss may have already been "recovered". That's the same sort of math Alabama, Mississippi, Georgia, etc use to justify massive incentives for foreign automakers, so if it is fair to use there, we should be using that argument at the federal level, too.