As the midterm primary season enters the homestretch, the candidates endorsed by former President Donald J. Trump continue to rack up primary wins.That is partly by design: Of the more than 200 Republicans Mr. Trump has endorsed this year, many ran unopposed or faced little-known, poorly funded opponents. He has also waited to make some endorsements until a clear front-runner has emerged, strategically picking the candidates most likely to win — take, for instance, his last-minute endorsement of Tudor Dixon in Michigan’s Republican primary for governor.But several of his endorsed candidates were defeated in early primaries, including notable losses in Georgia and North Carolina. For candidates like J.D. Vance in Ohio and Mehmet Oz in Pennsylvania, however, Mr. Trump’s support was crucial to securing victory — and his preferred candidates have won in large numbers in the most recent races, including in two important swing states, Arizona and Michigan.Here is a look at Mr. Trump’s endorsement record.A sweep in ArizonaThe former local television news host Kari Lake won the Republican primary for governor with Mr. Trump’s endorsement, narrowly defeating Karrin Taylor Robson, who was the choice of establishment Republicans. Ms. Lake has forcefully promoted Mr. Trump’s false claims that the 2020 election was stolen.Blake Masters, a venture capitalist who has pushed a version of the “great replacement” conspiracy theory, won his Senate primary and will challenge Senator Mark Kelly, a vulnerable Democrat, in November.State Representative Mark Finchem, who is affiliated with the far-right Oath Keepers militia group and said before the primary that he would not concede if he lost, won the Republican nomination for secretary of state, a position in which he would be responsible for overseeing Arizona elections.And David Farnsworth, another Trump endorsee, won a State Senate primary against Rusty Bowers, the Arizona House speaker who drew Trump supporters’ fury for resisting efforts to overturn the 2020 election and for testifying before the Jan. 6 congressional committee.A pro-impeachment Republican lost in MichiganRepresentative Peter Meijer, one of the 10 House Republicans who voted to impeach Mr. Trump, lost his primary to a Trump-backed challenger, John Gibbs, in Michigan’s Third Congressional District.In Georgia, several losses and one victoryGov. Brian Kemp easily defeated former Senator David Perdue, Mr. Trump’s handpicked candidate, in the Republican primary for governor. Mr. Kemp became a Trump target after he refused to overturn the president’s loss in the state in 2020. He will face the Democratic nominee, Stacey Abrams, whom he narrowly defeated four years ago.Secretary of State Brad Raffensperger, who refused Mr. Trump’s demand to “find” additional votes after his 2020 loss, also defeated a Trump-endorsed challenger, Representative Jody Hice.More Coverage of the 2022 Midterm ElectionsClimate, Health and Tax Bill: The Senate’s passage of the legislation has Democrats sprinting to sell the package by November and experiencing a flicker of an unfamiliar feeling: hope.Kansas Abortion Vote: After a decisive victory for abortion rights in deep-red Kansas, Democrats vowed to elevate the issue nationwide, while some Republicans softened their stands against abortion.Wisconsin Primary: Former President Donald J. Trump’s supporters have turned the false notion that his 2020 defeat can still be reversed into a central issue ahead of the state’s G.O.P. primary for governor.Senate Races: The key question with less than 100 days until the fall election: Can Democratic candidates in crucial Senate contests continue to outpace President Biden’s unpopularity? Attorney General Chris Carr defeated John Gordon, a Trump-supported opponent, with more than 73 percent of the vote.In a primary runoff for an open seat in Georgia’s Sixth Congressional District, Rich McCormick, a physician and retired Marine, defeated the Trump-backed candidate Jake Evans, the former chairman of the state’s ethics commission and the son of a Trump administration ambassador.The former professional football star Herschel Walker, who was endorsed by Mr. Trump, dominated a Senate primary and will face Senator Raphael Warnock, a Democrat and prolific fund-raiser, in the general election.Victories in PennsylvaniaAfter a close race that prompted a recount, Mehmet Oz, Mr. Trump’s choice, won the state’s Senate primary, narrowly defeating David McCormick.Doug Mastriano, a state senator and retired Army colonel who has promoted false claims about the 2020 election and attended the protest leading up to the Capitol riot, won the Republican nomination for governor. Mr. Trump had endorsed him just a few days before the primary.Two wins and a loss in North CarolinaRepresentative Ted Budd won the Republican nomination for Senate, and Bo Hines, a 26-year-old political novice who enthralled Mr. Trump, was catapulted to victory in his primary for a House seat outside Raleigh.But Representative Madison Cawthorn crumbled under the weight of repeated scandals and blunders. He was ousted in his primary, a stinging rejection of a Trump-endorsed candidate. Voters chose Chuck Edwards, a state senator.A split in South Carolina House racesRepresentative Tom Rice, one of 10 House Republicans who voted to impeach Mr. Trump after the Jan. 6, 2021, attack on the Capitol, was ousted by his Trump-backed challenger, State Representative Russell Fry, in the Seventh Congressional District.But Representative Nancy Mace defeated her Trump-endorsed opponent, the former state lawmaker Katie Arrington, in the First Congressional District. Ms. Mace had said that Mr. Trump bore responsibility for the Jan. 6 attack, but did not vote to impeach him. She had support from Nikki Haley and Mick Mulvaney, who both held office in the state before working in the Trump administration.Election deniers win in NevadaAdam Laxalt won a Senate primary and will face the incumbent, Senator Catherine Cortez Masto, who is seen as one of the most vulnerable Democrats this fall. Mr. Laxalt, a former attorney general, was endorsed by Mr. Trump and had helped lead his efforts to overturn the 2020 presidential election results in Nevada.Joseph Lombardo, the Las Vegas sheriff, won the Republican nomination for governor and will face the incumbent, Gov. Steve Sisolak, a Democrat.Victories in Illinois, with outside helpState Senator Darren Bailey, who got a last-minute endorsement from Mr. Trump, won the Republican primary for governor. Democratic spending, including by Gov. J.B. Pritzker, may have helped Mr. Bailey, whom Democrats saw as easier to beat in the general election.Representative Mary Miller, endorsed by Mr. Trump months ago, won her House primary against fellow Representative Rodney Davis after redistricting put them in the same district.Victories in OhioThe Senate candidate J.D. Vance defeated a field of well-funded rivals, nearly all of whom pitched themselves as Trump-like Republicans. Mr. Vance, an author and venture capitalist, had transformed himself from a self-described “never Trump guy” in 2016 to a Trump-supported “America First” candidate in 2022.Max Miller, a former Trump aide who denied assault allegations from an ex-girlfriend and was later endorsed by Mr. Trump, won his House primary.Mr. Trump also endorsed Madison Gesiotto Gilbert, a lawyer who had been a surrogate for his presidential campaign. She won a seven-way primary for a congressional seat.In Maryland, a win aided by DemocratsDan Cox, a first-term state legislator who embraced Mr. Trump’s lies about the 2020 election, handily defeated Kelly Schulz in the Republican primary for governor. Ms. Schulz was seen as a protégé of Gov. Larry Hogan, a leader of the party’s anti-Trump wing.Mr. Cox raised little money. But he benefited from more than $1.16 million in television advertising from the Democratic Governors Association, which helped his primary campaign in hopes that he would be easier to defeat in the general election.A loss in NebraskaCharles W. Herbster, a wealthy agribusiness executive, lost his three-way primary for governor to Jim Pillen, a University of Nebraska regent supported by Gov. Pete Ricketts, who has long clashed with Mr. Trump. Late in the campaign, Mr. Herbster was accused of groping several women. He denied the accusations.And another loss in IdahoGov. Brad Little overcame Mr. Trump’s endorsement of the state’s lieutenant governor, Janice McGeachin, who was challenging him in the Republican primary.A victory in West VirginiaRepresentative Alex Mooney prevailed over Representative David McKinley in a newly drawn congressional district. Mr. Trump’s backing was seen as the decisive factor.Alyce McFadden More