Authorities hunting three dangerous escapees from a maximum-security jail in Southern California called on the public's help to find them Sunday, offering $50,000 in rewards and saying they still don't have all the details of the elaborate escape plan.

"We're exhausting every lead that we currently have," Orange County sheriff's Lt. Jeff Hallock said at an afternoon news conference.

The three men, including an alleged killer, cut and climbed their way out of the Orange County Men's Central Jail in Santa Ana, about 40 miles southeast of Los Angeles, sometime after the 5 a.m. Friday head count, authorities said. They weren't discovered missing for some 16 hours.

The men managed to get hold of some tools and cut through a quarter-inch-thick metal screen in a wall between some bunks in a dormitory they shared with more than 60 men, then used plumbing tunnels, cutting through additional half-inch steel bars, before making it to an unguarded area of the roof of the four-story building, removing some razor wire and rappelling down using ropes braided from linens, authorities said.

Photos and surveillance video released by the Sheriff's Department showed the cut dormitory screen, one of the ropes, and vague video of a flickering light on the roof that's believed to be from at least one inmate preparing to rappel down the building, Hallock said.

A fight involving other inmates may have been staged to delay the usual 8 p.m. head count and the escape wasn't noticed until 9 p.m., authorities said.

The inmates include 20-year-old Jonathan Tieu, who had been held on a $1 million bond since October 2013 on charges of murder, attempted murder and shooting at an inhabited dwelling. His case is believed to be gang-related.

On Sunday, his mother and sister said they hadn't heard from him and tearfully pleaded for him to surrender.

"I miss you... I want my son back," his mother, Lu Ann Nguyen of Santa Ana, told KABC-TV.

"I for sure know he wasn't the one who orchestrated this. I feel he was manipulated or tricked into doing this," said his sister, Tiffany Tieu.

"Just turn in yourself in. Don't let (it) drag on," she said.

While catching the men was the priority, a separate probe was underway to determine how they got out and whether any other prisoners or jail employees were involved, Hallock said.

"What I can assure you is that the compromises in security have been shored up," he said.

Earlier in the day, Sheriff Sandra Hutchens said it wasn't possible to conduct earlier head counts during the day.

"We are handicapped in that this is a jail where a lot of movement occurs," she said. "We have people going to court, we have people going for medical treatment, and you can't leave them locked down 24 hours a day. There are requirements that they get out and exercise from time to time."

Prosecutors and others involved in their cases have been notified of the escape and measures taken to protect them, authorities said.

It was the first escape in more than 20 years from the facility, which was built in 1968 and has about 900 inmates. Two other escapes took place decades ago.

"I've been in law enforcement for 37 years, always working for sheriff's departments that manage jails. And escapes do occur from time to time," Hutchens said. "We try and limit that. We learn from the mistakes. I can tell you that this is a very sophisticated-looking operation. People in jail have a lot of time to sit around and think about ways to defeat our systems."

She said people should consider the men armed and dangerous and people shouldn't try to approach them.

The U.S. Marshals Service offered a $30,000 reward on top of $20,000 offered by the FBI for information leading to the trio's capture.

Another escaped inmate is Hossein Nayeri, 37. He had been held without bond since September 2014 on charges of kidnapping, torture, aggravated mayhem and burglary. Nayeri and three other men are accused of kidnapping a California marijuana dispensary owner in 2012. They drove the dispensary owner to a desert spot where they believed he had hidden money and then cut off his penis, authorities said.

After the crime, Nayeri fled the U.S. to his native Iran, where he remained for several months. He was arrested in Prague in November 2014 while changing flights from Iran to Spain to visit family.

The third escaped inmate, 43-year-old Bac Duong, was being held without bond since last month on charges of attempted murder, assault with a deadly weapon, shooting at an inhabited dwelling, being an ex-felon in possession of a firearm and other charges.