The four suspects - three men and a 23-year-old woman identified as Denise Vanessa G. - were arrested last May, two days before they allegedly planned to strike at a migrant shelter in the eastern state of Saxony.
Their choice of weapon was modified "pyrotechnic explosives, particularly in the form of fire and nail bombs", which they were planning to hurl into a refugee home, said the prosecutor.
The group had therefore "accepted that people could be killed," chief prosecutor Joern Hauschild told the court.
In the dock on Wednesday, co-accused Andreas Thomas H., 57, looked on with a smile, while the heavily tattooed Markus W., 30, glanced around the room mockingly.
The four suspects, who also included 38-year-old Olaf O., met through the Internet in 2014.
In preparation for the attacks, they bought large quantities of banned fireworks from the Czech Republic and subsequently decided to cover the explosives with a layer of nails to make them more lethal.
Hauschild described their plan for the Saxony attack as very concrete, adding that the authorities had learned the details from chat logs and phone intercepts.
The prosecutor added that the neo-Nazi group had between 10 and 15 members, with investigations still ongoing against other suspects.
Group emblems published on media websites feature Germanic runes popular in the neo-Nazi scene, bloody hatchets and skulls with the slogan: "One bullet is not enough."
Amateur videos posted on YouTube and attributed to the group also use racist and xenophobic slurs in appeals for new recruits.
Rise in far-right attacks
A record influx of asylum seekers to Germany has fuelled a sharp rise in the number of far-right attacks, with Saxony state gaining special notoriety for such violence.
The number of extreme-right crimes, including assaults against asylum seekers and arson at refugee homes, tripled to 784 cases last year in Saxony compared to 235 in 2014, official data showed.
Germany's domestic security agency also noted that the number of violent far-right activists in the former communist state has soared to 1,300 in 2015 from 300 the previous year.
Last week, an elite anti-terror unit also arrested five suspects accused of belonging to an extremist organisation called the Freital Group, named after a town in Saxony where the female defendant in the Old School Society case was born.
Prosecutors say the Freital Group aimed to "carry out explosives attacks on homes for asylum seekers as well as the homes of political enemies".
Like the Old School Society, the suspects stockpiled fireworks from the Czech Republic to use in attacks.
The group allegedly carried out at least three attacks.
In the first, fireworks were used to blow out the windows of the kitchen of a refugee shelter in Freital in September 2015, while the other involved hurling fireworks and stones at a building housing leftist activists.
Prosecutors said that the cell also attacked another refugee shelter in Freital in November last year, where a resident suffered cuts to his face from flying glass.