Hundreds of people — from White House officials and titans of the mainstream media to senators, Supreme Court justices and many of her top colleagues at the State Department — could have known about Hillary Clinton’s secret email account, if only they’d cared to look closely enough.

Listed on some of the more than 28,000 messages Mrs. Clinton released so far are several White House chiefs of staff and a former director of the Office of Management and Budget, much of the rest of official Washington, and a number of people who had oversight of the State Department’s key operations and open-records obligations. President Obama was also on a series of messages, though the government is withholding those.

But just how widely disseminated Mrs. Clinton’s address was became clear in a single 2011 message from Anne-Marie Slaughter, who appeared to include Mrs. Clinton on a message alongside Supreme Court Justices Stephen G. Breyer and Elena Kagan, reporters Jeffrey Toobin, David Brooks, Fred Hiatt and Evan Thomas, CIA Director David H. Petraeus, top Obama aide Benjamin Rhodes and former White House counsel Gregory Craig.

Computer specialists said they would have had to know what they were looking for to spot Mrs. Clinton’s address, but it was there for anyone who did look — raising questions about how her unique arrangement remained secret for so long. It came to the public’s attention when news broke in March 2015 in The New York Times — after it was uncovered by a congressional investigation into the 2012 Benghazi terrorist attack.

The State Department has since acknowledged that it did not search Mrs. Clinton’s messages in response to open-records requests filed under federal law, and federal District Judge Emmet G. Sullivan is prodding the department about how the situation got so out of hand.

“We’re talking about a Cabinet-level official who was accommodated by the government for reasons unknown to the public. And I think that’s a fair statement — for reasons unknown to the public,” the judge said at a hearing last week, where he decided to approve conservative legal group Judicial Watch’s request for discovery to pry loose more details about who approved the odd email setup and how it ducked the rules.

“All the public can do is speculate,” Judge Sullivan told the government lawyers who have been fighting to drag out the release of the messages Mrs. Clinton has turned over, and to prevent her from having to relinquish thousands of others. “You want me to say it’s done, but I can’t do that right now.”

The final batch of messages the State Department has in its custody — 2,000 of them — is due to be released Monday.

The facts have changed dramatically since the emails were first revealed and Mrs. Clinton insisted that she set up her unique arrangement out of “convenience” for herself and insisted no classified material was sent on the account.

Already, 1,782 messages have been deemed to contain classified material, and 22 of those messages contain “secret” information. Another 22 messages contain “top secret” material so sensitive that the government won’t even release any part of them, meaning they will remain completely hidden from the public.

Mrs. Clinton’s arrangement set off public policy and security debates. Analysts said her server was likely unprotected against any moderately sophisticated attack.

Although details remain sketchy as to what protection Mrs. Clinton used, analysts said having one person maintaining her server is no way to protect sensitive information from a hack. Christopher Soghoian, principal technologist at the American Civil Liberties Union, said there is no evidence that Mrs. Clinton was having her server tested by independent specialists — a major oversight.

“You cannot secure your server with one guy working part time,” Mr. Soghoian said.

That one person, Bryan Pagliano, who reportedly worked for Mrs. Clinton at the State Department and on the side as her server technician, asserted his Fifth Amendment right against incriminating himself in testimony to Congress last year.

Even if the server itself wasn’t compromised, Mr. Soghoian said, Mrs. Clinton was sending email over the broader Internet, where an enterprising opponent could have intercepted messages. If she had been using a State.gov account to email others within the government, that wouldn’t have been possible, he said.

There is no evidence that Mrs. Clinton was hacked, but analysts said that’s of little comfort. Even if the FBI doesn’t find evidence, it is not conclusive.

“Clinton’s use of unencrypted email left her vulnerable to nation states. There’s no amount of investigation the FBI can do to prove that didn’t happen,” Mr. Soghoian said.

Bob Gourley, co-founder of cybersecurity consultancy Cognitio, said the government has to assume Mrs. Clinton’s server was compromised, and he said it begs the question of why she declined to use a State.gov account and instead set up her own off-site server.

“All indications are this was not just a matter of convenience,” he said. “There’s no reason why she should have used her own server and go to all the trouble to do that unless she wanted to hide something.”

That something, Mr. Gourley believes, is the negotiating she did on behalf of the Clinton Foundation, founded by her husband, former President Bill Clinton. She helped lead the foundation as soon as she stepped down from the secretary’s job.

The security analyst said he suspects details of those negotiations are part of the 30,000 messages Mrs. Clinton indicated she sent during her time in office but that she declined to turn back to the State Department. The former secretary said those messages were personal business, such as scheduling yoga classes or arranging her daughter Chelsea’s wedding.

Judicial Watch is trying to get Mrs. Clinton to turn over those messages to the State Department, and that’s the case pending before Judge Sullivan.

“The big story on Monday is, wow, now we have reviewed about half of Mrs. Clinton’s reported records. Where’s the other half?” said Judicial Watch President Tom Fitton. “That’s what our discovery is about. Where’s the other half, and how can we find out so they can be retrieved and reviewed and released to the public?”

Mrs. Clinton says the Obama administration is overclassifying her messages. She says she would like all of the messages she returned to the government released, including presumably the 22 the government deems so “top secret” that they can’t be shared even in part.

She and her campaign have questioned the political motivations or conclusions of the inspectors general who have pushed for classification, to Judge Sullivan, whose order of discovery could force her aides to answer tough questions and could eventually lead to her having to return the rest of her emails.

Mr. Fitton said the questions Judicial Watch will ask during discovery include how the government supported her email server, why the folks who handled Freedom of Information Act open-records requests weren’t made aware of it, who else used it, what security precautions were taken and who approved it.

A Washington Times analysis of the more than 28,000 messages that have been released show dozens of State Department employees, from the lowest to the highest levels, were aware that Mrs. Clinton was using her unique arrangement to conduct government business.

The extensive awareness within the department struck Judge Sullivan.

“How on earth can the court conclude that there’s not, at a minimum, a reasonable suspicion of bad faith regarding the State Department’s response to this FOIA request?” he said at a hearing last week.

Mrs. Clinton’s successor, current Secretary of State John F. Kerry, was one of those who emailed with Mrs. Clinton on her secret account during his time in the Senate. He was one of a handful of senators The Times found who were pen pals with Mrs. Clinton.

Last week, Mr. Kerry tried to explain how he missed Mrs. Clinton’s behavior and told Congress he simply mailed the address he was given.

“I didn’t think about it. I didn’t know if she had an account, or what the department gave her at that point in time, or what she was operating with. I had no knowledge,” he told Rep. Darrell E. Issa, a California Republican who prodded him on the matter.

Stories about odd email practices have continued to dog Mr. Obama’s tenure. His former administrator at the Environmental Protection Agency, Lisa P. Jackson, used a secret agency email address to conduct government business, but the EPA says those messages were searched in open-records requests.

Defense Secretary Ashton Carter used a private address to conduct some government business in the first months after taking office. He said the practice was wrong and apologized for it.

Mr. Gourley, the cybersecurity specialist, said Mrs. Clinton’s practice went beyond that. He compared it to a phone, saying everyone has a home phone or personal cellphone, and even top government officials occasionally use it for official business. But in Mrs. Clinton’s case, she rejected an official government email account and used only her secret account.

“Those kinds of rules were just totally flouted by Clinton,” he said.

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