Iowa has been playing football since 1916, which is shorter than most Power 5 programs that started playing in the late 1800s. There are over 50 schools that Iowa has not yet played, but the number of schools Iowa has not beaten in program history.
The Hawkeyes have two schools that they have faced and not technically beat, but also not technically lost to. Iowa faced BYU and Air Force in 1958 and 1991 before college football did away with ties. The Hawkeyes tied with both BYU and Air Force, while they have not beaten them, they have just tied with them, which means they are not technically on this list.
So here are the teams that Iowa has not been able to beat in order chronologically based on their last matchup date.
Overall record: 0-1
First meeting: 10/10/1931
Second meeting: 10/10/1931
Last score: 29-0
Iowa and Texas A&M have a short history together with only one matchup and you have to go all the way back to the 1930s to find it. There wasn't much to the game as the Aggies won 29-0.
Iowa was still a fairly young program at the time when they met Texas A&M as they had just started playing football in 1916. They were younger compared to all the programs that started in the late 1800s.
Of course, this would be a matchup that would interesting to see again, and right now with the College Football Playoff expanding, it opens the door for a lot more matchups. The Aggies have a new coach this year and the Hawkeyes have been in the Big Ten title game, but going up against Goliath.
The Aggies vs. Hawkeyes matchup could happen with the bigger playoff and Iowa can avenge their one loss to Texas A&M.