A surge in total employment last month lifted the percentage of the population with jobs to an all-time high, but the unemployment rate remained stuck at 5.8 percent, the Labor Department reported yesterday.

More than half a million new jobs were created in November, the department said, but because of a similar increase in the number of people looking for work, the unemployment rate did not move down.

The jobs report represents one of the few bright spots for the Carter administration on an economic scene otherwise clouded by inflation and a nagging trade deficit.

On the inflation front, administration officials disclosed yesterday that they are considering still another revised profit formula intended to prevent business from realizing excessive profits in passing on higher costs to consumers.

Business would be limited to a 6.5 percent profit increase based on average profits for the best two of the previous three years. Profits earned from increased volume, however, would not be included. The 6.5 figure reflects the administration's expectations for inflation next year.

Officials cautioned that this formula is still tentative. The administration also plans to relax the 7 percent wage guideline, by excluding certain increases in workers' fringe benefits. These revisions are scheduled to be announced next Wednesday.

Employment gains in November were widespread, occurring in every major industry except the federal government, where President Carter has ordered a freeze on hiring. For the second consecutive month, there were sharp hiring increases in construction and manufacturing.

Labor Department officials said the favorable employment figures were a sign of continued vigor in the economy. But many private economists have predicted that the unemployment rate could rise next year as the government's anti-inflation drive threatens to slow overall economic growth.

Despite the expansion in employment, the unemployment rate has improved only slightly since spring. Moreover, employment gains continue to be uneven. Unemployment for blacks remained at double the national average in November. And for black teen-agers, the jobless rate rose from 34.3 percent in October to 36.2 percent last month.

Testifying before the congressional Joint Economic Committee yesterday Janet Norwood, acting commissioner of the Bureau of Labor Statistics, said that black workers nevertheless have made significant employment gains this year, outpacing the performance of whites. She attributed this, in large part, to special federal jobs programs. She declined to speculate on whether such gains might be erased should these programs fall victim to planned White House budget cuts.

Overall, Norwood said the latest jobs report shows "a very strong picture" for the economy. Though interest rates have been rising sharply in recent months and many forecasters predict a recession next year, the unemployment figures point to a still vigorous economy.

"I see nothing in our current figures to indicate that any reduction in business activity has yet taken place," she stated.

The percentage of the population at work reached 59.1 percent in November, a record level.

Total employment advanced by 540,000 in November to 95.7 million, and nonfarm payroll employment rose by 465,000 to 87.0 million. Since the first of the year, total employment has grown by 3.3 million and payroll jobs have increased by 3.5 million.

At the same time, the labor force continues to increase. Labor officials attribute this largely to the influx of women and teen-agers into the job market. In the past year, 2.6 million new workers have joined the labor force -- bringing the total to 101.6 million -- with adult women accounting for about 60 percent of this advance. Nevertheless, the largest employment gains last month occurred among men, whose employment numbers jumped from 51.4 million to 51.9 million.

The employment report also showed that it takes less time now than it did a year ago for the jobless to find work. The average unemployed person, who spent 7 weeks looking for a job a year ago, spent 5.5 weeks searching last month.

The Labor Department also reported that average weekly earnings leaped a full 1 percent last month and have risen by 8.4 percent in the past year. But in her testimony, Norwood noted that wages have barely, and perhaps not quite, kept up with inflation.

Questioned about the effect of a possible Mideast oil price increase later this month, Norwood said that with an assumed 10 percent hike, the direct effect on the consumer price index would be about 0.1 percent and wholesale prices could be expected to increase roughly 0.25 to 0.3 percent. Such increases would translate into a jump in gasoline prices at the pump of about 1.5 cents, she said.