A court heard that the men met victims in a park and then targeted them in the Levenshulme area and using social media between 2016 and 2018.
A judge said other perpetrators linked to the group, who are Romanian, have fled abroad and were being sought by police.
Brothers Sebastian and Ilie Baltatu targeted the youngest victim alongside friend Parizian Calin.
Parizian’s cousin, Adrian Calin, was also part of the group and was jailed for inciting a 15-year-old girl into sexual activity.
The abuse was exposed when the first victim, who was in care, alerted police and child services in 2018.
Greater Manchester Police started an operation that identified at least two further victims, who were between the ages of 12 and 15 at the time of the abuse.
Sentencing the men on Monday, Judge Suzanne Goddard QC, called their actions “heartless, immoral and illegal”.
“Each of these girls was particularly vulnerable because of their personal circumstances as children in care who had all had difficult childhoods,” she told Manchester Crown Court.
“Each had to move away from Manchester, away from their family and friends, because of the behaviour of you and others like you. That has added to the distress they suffered.”
The court heard that the first victim, who was 12 at the time, met the group at Crowcroft Park in Longsight.
Parizian, a 20-year-old father, raped the girl in some bushes and then “made her available to others”.
He also took her to what she described as a “brothel house” in Levenshulme, where he then sent another Romanian man into the room.
Prosecutors said the girl was moved away from Manchester by authorities after they recognised she was at risk from sexual exploitation, but when she returned to the city aged 14 Parizian saw her, ordered her into his car and raped her again.
He was convicted of four counts of raping a child under 13, raping a second victim aged 14, arranging the commission of a child sex offence, inciting a child under 13 to engage in sexual activity and assault of a child.
Parizian, of Slade Lane in Levenshulme, was jailed for 13 years, made to sign the sex offenders register for life and subjected to a 13-year sexual harm prevention order.
His friend Sebastian Baltatu, 18, was found guilty of raping a girl on a bench in Crowcroft Park when she was 12 and he was 14.
A defence lawyer told the court that Sebastian had himself been “exploited” by other members of the group, and had been influenced by his older brother’s attitude towards women.
Sebastian has a child and partner, who he persuaded to smuggle cannabis into prison after being jailed for an unrelated dangerous driving offence.
He was sentenced to three years in a young offenders institution and made to sign the sex offenders register for life.
His brother Ilie “Danny” Baltatu, 22, pleaded guilty to grooming, three counts of sexual activity with a child and abduction of a 13-year-old girl, and incitement and sexual assault of another victim aged 12.
The court heard he sent “numerous” text messages asking the first victim for oral sex over a period of months, while posing as the “nice guy” of the group.
His second victim was another girl in care who had been introduced to the gang through friends, and believed she was Ilie’s girlfriend after being groomed.
He was served a child abduction notice to prevent the abuse in October 2017 but continued to see the teenager.
Ilie was jailed for eight years, put on the sex offenders register indefinitely and subjected to a 10-year sexual harm prevention order.
Parizian’s cousin, 20-year-old Adrian Calin, was convicted of inciting a third victim who was 15 at the time to have oral sex in the park.
Jailing him for a year, Judge Goddard said the girl was also in care following a troubled childhood, and suffered from communication problems.
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The judge told Adrian, of Reynell Road in Levenshulme: “I find that you all knew of the sexual exploitation that was occurring with girls at Crowcroft Park among your group of friends. You would have known these were underage girls.”
A probation officer told the court that Adrian, who has three children, had a “sense of sexual entitlement and a lack of respect in your relationships with women”.
Prosecutors said the men had deliberately targeted and groomed the victims because they were underage and vulnerable.
“The victims were just children when they were subjected to appalling sexual exploitation but they have shown great courage in coming forward and giving evidence against their abusers,” said senior crown prosecutor Lisa O’Neill.
Greater Manchester Police vowed to tackle child sexual exploitation and appealed for any other victims to come forward.
Superintendent Rebecca Boyce said: “The young girls who suffered the most unimaginable and traumatic abuse have remained at the forefront of this entire investigation, as we have worked tirelessly to bring the perpetrators to justice.
“These victims have shown the utmost bravery by giving evidence and we cannot underestimate the courage and strength it takes for victims of these abhorrent crimes to come forward.”
The men were jailed days after a report warned that councils were unwittingly acting as “recruiting sergeants” for grooming and drugs gangs by sending children in care away from their home areas into unsafe accommodation.
Manchester City Council said it was working closely with police to identify and tackle child sex abuse.