Here are the 10 known Illuminati groups and their abilities. Or, perhaps, what THEY want you to think their abilities are. Or maybe just what WE want you to think they want you to think their abilities are.
The Original Eight:
Power 10 / 10, Income 9. May make one privileged attack per turn at a cost of 5 MB. Special Goal: Control Groups with a total power of 35 or more (including their own Power of 10).
Power 8 / 8, Income 9. May reorganize groups freely at end of turn. Special Goal: Control at least one Group of each alignment. A Group with more than one alignment counts for each of its alignments.
Power 8 / 8, Income 8. +4 on any attempt to control Weird groups. Immune to attacks from Government or Straight groups. Special Goal: Control five Weird groups.
Gnomes of Zurich
Power 7 / 7, Income 12. May move money freely at end of turn. Special Goal: Collect 150 megabucks (in the whole Power Structures treasuries).
Power 7 / 7, Income 9. Turns over two cards at beginning of turn. Special Goal: Control Groups with a total Transferable Power of 25 (including their own 7).
Servants of Cthulhu
Power 9 / 9, Income 7. +2 on any attempt to destroy any group. Special Goal: Destroy eight groups.
Society of Assassins
Power 8 / 8, Income 8. +4 on any attempt to neutralize any group. Special Goal: Control six Violent Groups.
Power 6 / 6, Income 8. Illuminati group may participate in two attacks per turn. Special Goal: At the beginning of the game, after players choose their Illuminati, the UFO player picks one of the seven Special Goals listed above. He writes it down, keeping it secret from the other players.
Added in Y2K:
Church of the SubGenius
Power 6 / 6, Income 9. Gets 10 MB from the bank for each of its groups which is captured, neutralized, or destroyed. Special Goal: Its regular goal is 1 less than for all other Illuminati so, for instance, if the regular goal for other players is 10 groups, the Church of the SubGenius wins if it gets nine.
Power 7 / 7, Income 8. +6 on any attempt to control Peaceful groups. +4 defense against any attack to destroy. Special Goal: Control five Peaceful Groups.