Iowa State has been playing football since 1916, which is a shorter period of time than most Power 5 programs that began play in the late 1800s. He has more than 50 schools that Iowa State hasn't played yet, but that's the number of schools Iowa State hasn't beaten in the program's history.
The Hawkeyes have two schools that they played against and technically didn't beat, but they technically didn't lose. Iowa State faced BYU and Air Force in 1958 and 1991, before there were no ties in college football. The Hawkeyes tied both BYU and Air Force, but they didn't beat them, but they just tied them. So technically it's not on this list.
Here are the teams Iowa State failed to beat, ordered chronologically based on the date of their last matchup.
Overall record: 0-1
First meeting: 1931/10/10
Second meeting: 1931/10/10
final score:29-0
Iowa and Texas A&M have a short history, having only played against each other once, and you have to go all the way back to the 1930s to find it. There were no major changes in the game as the Aggies won 29-0.
At the time they met Texas A&M, Iowa was still a fairly young program, having only started playing football in 1916. They were young compared to all his programs that started in the late 1800s.
Of course, this would be an interesting matchup to watch again, and with the College Football Playoff currently expanding, the door is open for more matchups. The Aggies have a new coach this year and the Hawkeyes are in the Big Ten title game against Goliath.
A matchup between the Aggies and Hawkeyes could happen in a bigger playoff game, where Iowa could avenge its one loss to Texas A&M.