## Small Residuated Lattices of order 6.2.58

```list:=[
[# 1
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 6, 6, 6, 6 ],
[ 4, 4, 6, 6, 6, 6 ],
[ 5, 5, 6, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 2 strictly simple
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 5, 6, 6, 6 ],
[ 4, 4, 6, 6, 6, 6 ],
[ 5, 5, 6, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 3 strictly simple
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 4, 6, 6, 6 ],
[ 4, 4, 6, 6, 6, 6 ],
[ 5, 5, 6, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 4 strictly simple
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 6, 6, 6 ],
[ 4, 4, 6, 6, 6, 6 ],
[ 5, 5, 6, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 5
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 5, 5, 6, 6 ],
[ 4, 4, 6, 6, 6, 6 ],
[ 5, 5, 6, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 6
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 4, 6, 6 ],
[ 4, 4, 6, 6, 6, 6 ],
[ 5, 5, 6, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 7 strictly simple
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 5, 5, 6 ],
[ 4, 4, 6, 6, 6, 6 ],
[ 5, 5, 6, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 8
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 4, 5, 6 ],
[ 4, 4, 6, 6, 6, 6 ],
[ 5, 5, 6, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 9 strictly simple
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 5, 6, 6, 6 ],
[ 4, 4, 5, 6, 6, 6 ],
[ 5, 5, 6, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 10
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 5, 5, 6, 6 ],
[ 4, 4, 5, 6, 6, 6 ],
[ 5, 5, 6, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 11 strictly simple
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 4, 5, 6, 6 ],
[ 4, 4, 5, 6, 6, 6 ],
[ 5, 5, 6, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 12 strictly simple
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 6, 6, 6 ],
[ 4, 4, 4, 6, 6, 6 ],
[ 5, 5, 6, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 13
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 4, 6, 6 ],
[ 4, 4, 4, 6, 6, 6 ],
[ 5, 5, 6, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 14
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 4, 5, 6 ],
[ 4, 4, 4, 6, 6, 6 ],
[ 5, 5, 6, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 15
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 5, 5, 6, 6 ],
[ 4, 4, 5, 5, 6, 6 ],
[ 5, 5, 6, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 16 strictly simple
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 4, 4, 6, 6 ],
[ 4, 4, 4, 4, 6, 6 ],
[ 5, 5, 6, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 17
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 4, 6, 6 ],
[ 4, 4, 4, 4, 6, 6 ],
[ 5, 5, 6, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 18
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 4, 5, 6 ],
[ 4, 4, 4, 4, 6, 6 ],
[ 5, 5, 6, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 19
[ 1, 1, 3, 3, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 3, 6, 6 ],
[ 3, 4, 3, 3, 6, 6 ],
[ 5, 5, 6, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 20 strictly simple
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 4, 4, 5, 6 ],
[ 4, 4, 4, 4, 5, 6 ],
[ 5, 5, 6, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 21
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 4, 5, 6 ],
[ 4, 4, 4, 4, 5, 6 ],
[ 5, 5, 6, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 22
[ 1, 1, 3, 3, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 3, 5, 6 ],
[ 3, 4, 3, 3, 5, 6 ],
[ 5, 5, 6, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 23 strictly simple
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 6, 6, 6 ],
[ 4, 4, 5, 6, 6, 6 ],
[ 5, 5, 5, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 24 strictly simple
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 5, 5, 6 ],
[ 4, 4, 5, 6, 6, 6 ],
[ 5, 5, 5, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 25 strictly simple
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 4, 5, 6 ],
[ 4, 4, 5, 6, 6, 6 ],
[ 5, 5, 5, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 26
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 6, 6, 6 ],
[ 4, 4, 4, 6, 6, 6 ],
[ 5, 5, 5, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 27
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 4, 6, 6 ],
[ 4, 4, 4, 6, 6, 6 ],
[ 5, 5, 5, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 28
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 5, 5, 6 ],
[ 4, 4, 4, 6, 6, 6 ],
[ 5, 5, 5, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 29
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 4, 5, 6 ],
[ 4, 4, 4, 6, 6, 6 ],
[ 5, 5, 5, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 30
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 4, 5, 6 ],
[ 4, 4, 4, 5, 6, 6 ],
[ 5, 5, 5, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 31
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 4, 6, 6 ],
[ 4, 4, 4, 4, 6, 6 ],
[ 5, 5, 5, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 32
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 4, 5, 6 ],
[ 4, 4, 4, 4, 6, 6 ],
[ 5, 5, 5, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 33
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 4, 5, 6 ],
[ 4, 4, 4, 4, 5, 6 ],
[ 5, 5, 5, 6, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 34
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 4, 4, 6, 6 ],
[ 4, 4, 4, 4, 6, 6 ],
[ 5, 5, 5, 5, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 35
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 4, 6, 6 ],
[ 4, 4, 4, 4, 6, 6 ],
[ 5, 5, 5, 5, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 36
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 4, 5, 6 ],
[ 4, 4, 4, 4, 6, 6 ],
[ 5, 5, 5, 5, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 37
[ 1, 1, 3, 3, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 3, 6, 6 ],
[ 3, 4, 3, 3, 6, 6 ],
[ 5, 5, 5, 5, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 38
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 4, 4, 5, 6 ],
[ 4, 4, 4, 4, 5, 6 ],
[ 5, 5, 5, 5, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 39
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 4, 5, 6 ],
[ 4, 4, 4, 4, 5, 6 ],
[ 5, 5, 5, 5, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 40
[ 1, 1, 3, 3, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 3, 5, 6 ],
[ 3, 4, 3, 3, 5, 6 ],
[ 5, 5, 5, 5, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 41
[ 1, 1, 1, 1, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 1, 3, 1, 1, 5, 6 ],
[ 1, 4, 1, 1, 5, 6 ],
[ 5, 5, 5, 5, 6, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 42
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 5, 5, 5, 6 ],
[ 4, 4, 5, 5, 5, 6 ],
[ 5, 5, 5, 5, 5, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 43
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 4, 5, 5, 6 ],
[ 4, 4, 5, 5, 5, 6 ],
[ 5, 5, 5, 5, 5, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 44
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 5, 5, 6 ],
[ 4, 4, 5, 5, 5, 6 ],
[ 5, 5, 5, 5, 5, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 45
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 4, 5, 6 ],
[ 4, 4, 5, 5, 5, 6 ],
[ 5, 5, 5, 5, 5, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 46
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 5, 5, 6 ],
[ 4, 4, 4, 5, 5, 6 ],
[ 5, 5, 5, 5, 5, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 47
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 4, 5, 6 ],
[ 4, 4, 4, 5, 5, 6 ],
[ 5, 5, 5, 5, 5, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 48
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 4, 4, 5, 6 ],
[ 4, 4, 4, 4, 5, 6 ],
[ 5, 5, 5, 5, 5, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 49
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 4, 5, 6 ],
[ 4, 4, 4, 4, 5, 6 ],
[ 5, 5, 5, 5, 5, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 50
[ 1, 1, 3, 3, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 3, 5, 6 ],
[ 3, 4, 3, 3, 5, 6 ],
[ 5, 5, 5, 5, 5, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 51
[ 1, 1, 1, 1, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 1, 3, 1, 1, 5, 6 ],
[ 1, 4, 1, 1, 5, 6 ],
[ 5, 5, 5, 5, 5, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 52
[ 1, 1, 3, 4, 4, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 4, 4, 4, 6 ],
[ 4, 4, 4, 4, 4, 6 ],
[ 5, 5, 5, 5, 5, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 53
[ 1, 1, 3, 4, 4, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 4, 4, 6 ],
[ 4, 4, 4, 4, 4, 6 ],
[ 5, 5, 5, 5, 5, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 54
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 4, 4, 5, 6 ],
[ 4, 4, 4, 4, 5, 6 ],
[ 4, 5, 4, 4, 5, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 55
[ 1, 1, 3, 4, 5, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 4, 5, 6 ],
[ 4, 4, 4, 4, 5, 6 ],
[ 4, 5, 4, 4, 5, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 56
[ 1, 1, 3, 4, 4, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 4, 4, 4, 6 ],
[ 4, 4, 4, 4, 4, 6 ],
[ 4, 5, 4, 4, 5, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
],
[# 57
[ 1, 1, 3, 4, 4, 6 ],
[ 1, 2, 3, 4, 5, 6 ],
[ 3, 3, 3, 4, 4, 6 ],
[ 4, 4, 4, 4, 4, 6 ],
[ 4, 5, 4, 4, 5, 6 ],
[ 6, 6, 6, 6, 6, 6 ]
]
];
```

Computed by Peter Jipsen using GAP 4.1 (this list can be copied and read into GAP)