Background: Ara Raoul Parseghian (May 21, 1923 - August 2, 2017) was an American football player and coach who guided the University of Notre Dame to national championships in 1966 and 1973. He is noted for bringing Notre Dame's Fighting Irish football program from years of futility back into a national contender in 1964 and is widely regarded alongside Knute Rockne and Frank Leahy as a part of the "Holy Trinity" of Notre Dame head coaches. Parseghian grew up in Akron, Ohio, and played football beginning in his junior year of high school. He enrolled at the University of Akron, but soon quit to join the U.S. Navy for two years during World War II.
Context: In 1966, Parseghian guided Notre Dame to its first national championship since the Leahy era. Led by quarterback Terry Hanratty, running back Nick Eddy, star receiver Jim Seymour, and fullback Larry Conjar, the offense was best in the nation in scoring, with an average of 36.2 points per game. The defense was second in the country in points allowed, thanks to strong performances by linebacker Jim Lynch and defensive end Alan Page.  The season began with eight straight victories, propelling Notre Dame to the top of the national polls. The team then faced Michigan State (who had Bubba Smith), which ranked second in the polls and was also undefeated. The contest, one among a number referred to as the "game of the century", ended in a 10-10 tie. Parseghian was criticized for winding down the clock instead of trying to score despite having the ball in the final seconds of the game. He defended his strategy by maintaining that several key starters had been knocked out of action early in the game and that he did not want to spoil a courageous comeback from a 10-0 deficit by risking a turnover deep in his own territory late in the game. When Parseghian's team trounced USC 51-0 the following week, critics alleged that he ran up the score to impress poll voters who had split the number-one ranking between Notre Dame and Michigan State following the tie. Subsequent to the USC rout, the final wire service polls gave Parseghian's team the national championship, although Notre Dame did not participate in a post-season bowl game. Nine members of the team were selected as All-Americans, and Parseghian was named coach of the year by Sporting News.  Several winning seasons followed, but Notre Dame did not repeat as national champion in the late 1960s. In 1969, the team finished with an 8-2-1 record and accepted an invitation to play in the postseason Cotton Bowl. With this game, the school ended a long-standing policy of not playing in bowl games. The university urgently needed money to fund minority scholarships and decided to use the proceeds from bowl games for this purpose. Parseghian's team lost the game, 21-17, to the eventual national champion Texas Longhorns.
Question: What teams did they play that season?

Answer:
Parseghian's team trounced USC 51-0 the following week,