The men, who were working in the construction industry here, were detained between November 16 and December 1 last year, the Ministry of Home Affairs (MHA) said.
Investigations showed that they supported the armed jihad ideology of terrorist groups such as Al-Qaeda and the Islamic State in Iraq and Syria (ISIS).
Some of them had considered waging armed jihad overseas, but they were not planning any terrorist attacks in Singapore, said the MHA.
Awlaki was killed in a drone strike in Yemen in September 2011.
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The Bangladeshi authorities were informed of the circumstances of their repatriation.
The jailed man was not a member of the study group, but was discovered to have been undergoing radicalisation. He supported extremist preachers and possessed jihadi-related material.
He was jailed for attempting to leave Singapore illegally. He will also be repatriated once he completes his sentence.
Several members also possessed a shared document with graphic images and instruction details on how to conduct "silent killings" using different methods and weapons.
An excerpt from the document, which depicts in a graphic manner how one can attack and kill with stealth.
The group members took measures to avoid detection by the authorities, sharing jihadi-related materials discreetly and holding weekly gatherings to discuss armed conflicts involving Muslims, said MHA.
A number of members admitted that they believed they should participate in and wage armed jihad on behalf of their religion.
Several contemplated travelling to the Middle East to take part in the ongoing conflict.
"Members were encouraged to return to Bangladesh and wage armed jihad against the Bangladeshi government. They had also sent monetary donations to entities believed to be linked to extremist groups in Bangladesh," said MHA.