## Small Residuated Lattices of order 5.2.23

```list:=[
[# 1
[ 1, 1, 3, 4, 5 ],
[ 1, 2, 3, 4, 5 ],
[ 3, 3, 5, 5, 5 ],
[ 4, 4, 5, 5, 5 ],
[ 5, 5, 5, 5, 5 ]
],
[# 2
[ 1, 1, 3, 3, 5 ],
[ 1, 2, 3, 4, 5 ],
[ 3, 3, 5, 5, 5 ],
[ 4, 4, 5, 5, 5 ],
[ 5, 5, 5, 5, 5 ]
],
[# 3 strictly simple
[ 1, 1, 3, 4, 5 ],
[ 1, 2, 3, 4, 5 ],
[ 3, 3, 4, 5, 5 ],
[ 4, 4, 5, 5, 5 ],
[ 5, 5, 5, 5, 5 ]
],
[# 4
[ 1, 1, 3, 4, 5 ],
[ 1, 2, 3, 4, 5 ],
[ 3, 3, 3, 5, 5 ],
[ 4, 4, 5, 5, 5 ],
[ 5, 5, 5, 5, 5 ]
],
[# 5
[ 1, 1, 3, 4, 5 ],
[ 1, 2, 3, 4, 5 ],
[ 3, 3, 3, 4, 5 ],
[ 4, 4, 5, 5, 5 ],
[ 5, 5, 5, 5, 5 ]
],
[# 6
[ 1, 1, 3, 4, 5 ],
[ 1, 2, 3, 4, 5 ],
[ 3, 3, 5, 5, 5 ],
[ 3, 4, 5, 5, 5 ],
[ 5, 5, 5, 5, 5 ]
],
[# 7
[ 1, 1, 3, 3, 5 ],
[ 1, 2, 3, 4, 5 ],
[ 3, 3, 5, 5, 5 ],
[ 3, 4, 5, 5, 5 ],
[ 5, 5, 5, 5, 5 ]
],
[# 8
[ 1, 1, 3, 4, 5 ],
[ 1, 2, 3, 4, 5 ],
[ 3, 3, 3, 5, 5 ],
[ 4, 4, 4, 5, 5 ],
[ 5, 5, 5, 5, 5 ]
],
[# 9
[ 1, 1, 3, 4, 5 ],
[ 1, 2, 3, 4, 5 ],
[ 3, 3, 3, 4, 5 ],
[ 4, 4, 4, 5, 5 ],
[ 5, 5, 5, 5, 5 ]
],
[# 10
[ 1, 1, 1, 4, 5 ],
[ 1, 2, 3, 4, 5 ],
[ 3, 3, 3, 4, 5 ],
[ 4, 4, 4, 5, 5 ],
[ 5, 5, 5, 5, 5 ]
],
[# 11
[ 1, 1, 3, 4, 5 ],
[ 1, 2, 3, 4, 5 ],
[ 1, 3, 3, 4, 5 ],
[ 4, 4, 4, 5, 5 ],
[ 5, 5, 5, 5, 5 ]
],
[# 12
[ 1, 1, 1, 4, 5 ],
[ 1, 2, 3, 4, 5 ],
[ 1, 3, 3, 4, 5 ],
[ 4, 4, 4, 5, 5 ],
[ 5, 5, 5, 5, 5 ]
],
[# 13
[ 1, 1, 3, 4, 5 ],
[ 1, 2, 3, 4, 5 ],
[ 3, 3, 4, 4, 5 ],
[ 4, 4, 4, 4, 5 ],
[ 5, 5, 5, 5, 5 ]
],
[# 14
[ 1, 1, 3, 4, 5 ],
[ 1, 2, 3, 4, 5 ],
[ 3, 3, 3, 4, 5 ],
[ 4, 4, 4, 4, 5 ],
[ 5, 5, 5, 5, 5 ]
],
[# 15
[ 1, 1, 1, 4, 5 ],
[ 1, 2, 3, 4, 5 ],
[ 3, 3, 3, 4, 5 ],
[ 4, 4, 4, 4, 5 ],
[ 5, 5, 5, 5, 5 ]
],
[# 16
[ 1, 1, 3, 4, 5 ],
[ 1, 2, 3, 4, 5 ],
[ 1, 3, 3, 4, 5 ],
[ 4, 4, 4, 4, 5 ],
[ 5, 5, 5, 5, 5 ]
],
[# 17
[ 1, 1, 1, 4, 5 ],
[ 1, 2, 3, 4, 5 ],
[ 1, 3, 3, 4, 5 ],
[ 4, 4, 4, 4, 5 ],
[ 5, 5, 5, 5, 5 ]
],
[# 18
[ 1, 1, 1, 1, 5 ],
[ 1, 2, 3, 4, 5 ],
[ 1, 3, 3, 4, 5 ],
[ 4, 4, 4, 4, 5 ],
[ 5, 5, 5, 5, 5 ]
],
[# 19
[ 1, 1, 1, 1, 5 ],
[ 1, 2, 3, 4, 5 ],
[ 1, 3, 4, 4, 5 ],
[ 1, 4, 4, 4, 5 ],
[ 5, 5, 5, 5, 5 ]
],
[# 20
[ 1, 1, 1, 4, 5 ],
[ 1, 2, 3, 4, 5 ],
[ 1, 3, 3, 4, 5 ],
[ 1, 4, 4, 4, 5 ],
[ 5, 5, 5, 5, 5 ]
],
[# 21
[ 1, 1, 1, 1, 5 ],
[ 1, 2, 3, 4, 5 ],
[ 1, 3, 3, 4, 5 ],
[ 1, 4, 4, 4, 5 ],
[ 5, 5, 5, 5, 5 ]
]
];
```

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