Pc No. 7 Cs2

 P1c1 P1n1 P1a1 UNIQUE AXIS b CELL CHOICE 1 CELL CHOICE 2 CELL CHOICE 3 Axes Coordinates Wyckoff Axes Coordinates Axes Coordinates positions 2a I Maximal translationengleiche subgroups [2] P1 (1) 2 × 1a P1 P1 II Maximal klassengleiche subgroups Enlarged unit cell, non-isomorphic [2] C1c1 2a, 2b, c (1/2)x, (1/2)y, z; +(0, (1/2), 0) 2 × 4a A1n1 a - c, x, (1/2)y, (1/2)(x + z); +(0, (1/2), 0) I1a1 a, 2b, x - (1/2)z, (1/2)y, (1/2)z; +(0, (1/2), 0) (9) 2b, 2c a + 2c [2] C1c1 2a, 2b, c (1/2)x, (1/2)y + (1/4), z; 2 × 4a A1n1 a - c, x, (1/2)y + (1/4), (1/2)(x + z); I1a1 a, 2b, x - (1/2)z, (1/2)y + (1/4), (1/2)z; (9) +(0, (1/2), 0) 2b, 2c +(0, (1/2), 0) a + 2c +(0, (1/2), 0) Enlarged unit cell, isomorphic [2] P1c1 a, 2b, c x, (1/2)y, z; +(0, (1/2), 0) 2 × 2a P1n1 a, 2b, c x, (1/2)y, z; +(0, (1/2), 0) P1a1 a, 2b, c x, (1/2)y, z; +(0, (1/2), 0) [2] P1c1 a, 2b, c x, (1/2)y + (1/4), z; +(0, (1/2), 0) 2 × 2a P1n1 a, 2b, c x, (1/2)y + (1/4), z; +(0, (1/2), 0) P1a1 a, 2b, c x, (1/2)y + (1/4), z; +(0, (1/2), 0) [3] P1c1 a, 3b, c x, (1/3)y, z; ±(0, (1/3), 0) 3 × 2a P1n1 a, 3b, c x, (1/3)y, z; ±(0, (1/3), 0) P1a1 a, 3b, c x, (1/3)y, z; ±(0, (1/3), 0) [p] P1c1 a, pb, c x, (1/p)y, z; +(0, (u/p), 0) p × 2a P1n1 a, pb, c x, (1/p)y, z; +(0, (u/p), 0) P1a1 a, pb, c x, (1/p)y, z; +(0, (u/p), 0) p = prime; u = 1, . . ., p - 1 p = prime; u = 1, . . ., p - 1 p = prime; u = 1, . . ., p - 1 [2] P1c1 2a, b, c (1/2)x, y, z; +((1/2), 0, 0) 2 × 2a P1n1 a - c, x, y, (1/2)(x + z); +(0, 0, (1/2)) P1a1 a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) b, 2c [2] P1n1 2a, b, c (1/2)x, y, z; +((1/2), 0, 0) 2 × 2a P1a1 a - c, x, y, (1/2)(x + z); +(0, 0, (1/2)) P1n1 a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) b, 2c [3] P1c1 3a, b, c (1/3)x, y, z; ±((1/3), 0, 0) 3 × 2a P1n1 a - 2c, x, y, (1/3)(2x + z); P1a1 a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) b, 3c ±(0, 0, (1/3)) [3] P1c1 a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 3 × 2a P1n1 3a, b, c (1/3)x, y, z; ±((1/3), 0, 0) P1a1 3a, b, a + c (1/3)(x - z), y, z; ±((1/3), 0, 0) [3] P1c1 a + c, x, y, (1/3)(-x + z); 3 × 2a P1n1 a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) P1a1 3a, b, c (1/3)x, y, z; ±((1/3), 0, 0) b, 3c ±(0, 0, (1/3)) [3] P1c1 a - c, x, y, (1/3)(x + z); 3 × 2a P1n1 2a + c, b, (1/3)(2x - z), y, (1/3)(-x + 2z); P1a1 3a, b, (1/3)(x + z), y, z; b, 3c ±(0, 0, (1/3)) a + 2c ±((1/3), 0, (1/3)) -a + c ±((1/3), 0, 0) [p] P1c1 pa, b, c (1/p)x, y, z; +((u/p), 0, 0) p × 2a P1n1 a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) P1a1 a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) p = prime; u = 1, . . ., p - 1; p = prime; u = 1, . . ., p - 1; p = prime; u = 1, . . ., p - 1; [p] P1c1 a + qc, x, y, (1/p)(-qx + z); p × 2a P1n1 pa, b, (1/p)(x - 2qz), y, z; P1a1 pa, b, (1/p)(x - qz), y, z; b, pc +(0, 0, (u/p)) 2qa + c +((u/p), 0, 0) qa + c +((u/p), 0, 0) p = prime > 2; u = 1, . . ., p - 1; p = prime > 2; u = 1, . . ., p - 1; p = prime > 2; u = 1, . . ., p - 1; -(1/2)(p - 1) ≤ q ≤ (1/2)(p - 1) -(1/2)(p - 1)≤ q ≤ (1/2)(p - 1) -(1/2)(p - 1)≤ q ≤ (1/2)(p - 1)

Space groups of the series of isomorphic subgroups appear in different sequences for cell choices 1, 2 and 3

 P11a P11n P11b UNIQUE AXIS c CELL CHOICE 1 CELL CHOICE 2 CELL CHOICE 3 Axes Coordinates Wyckoff Axes Coordinates Axes Coordinates positions 2a I Maximal translationengleiche subgroups [2] P1 (1) 2 × 1a P1 P1 II Maximal klassengleiche subgroups Enlarged unit cell, non-isomorphic [2] A11a a, 2b, 2c x, (1/2)y, (1/2)z; +(0, 0, (1/2)) 2 × 4a B11n 2a, (1/2)(x + y), y, (1/2)z; +(0, 0, (1/2)) I11b 2a + b, (1/2)x, -(1/2)x + y, (1/2)z; +(0, 0, (1/2)) (9) -a + b, 2c b, 2c [2] A11a a, 2b, 2c x, (1/2)y, (1/2)z + (1/4); 2 × 4a B11n 2a, (1/2)(x + y), y, (1/2)z + (1/4); I11b 2a + b, (1/2)x, -(1/2)x + y, (1/2)z + (1/4); (9) +(0, 0, (1/2)) -a + b, 2c +(0, 0, (1/2)) b, 2c +(0, 0, (1/2)) Enlarged unit cell, isomorphic [2] P11a a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2 × 2a P11n a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) P11b a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) [2] P11a a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 2 × 2a P11n a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) P11b a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) [3] P11a a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 3 × 2a P11n a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) P11b a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) [p] P11a a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) p × 2a P11n a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) P11b a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) p = prime; u = 1, . . ., p - 1 p = prime; u = 1, . . ., p - 1 p = prime; u = 1, . . ., p - 1 [2] P11a a, 2b, c x, (1/2)y, z; +(0, (1/2), 0) 2 × 2a P11n 2a, (1/2)(x + y), y, z; +((1/2), 0, 0) P11b 2a, b, c (1/2)x, y, z; +((1/2), 0, 0) -a+b, c [2] P11n a, 2b, c x, (1/2)y, z; +(0, (1/2), 0) 2 × 2a P11b 2a, (1/2)(x + y), y, z; +((1/2), 0, 0) P11n 2a, b, c (1/2)x, y, z; +((1/2), 0, 0) -a + b, c [3] P11a a, 3b, c x, (1/3)y, z; ±(0, (1/3), 0) 3 × 2a P11n 3a, (1/3)(x + 2y), y, z; P11b 3a, b, c (1/3)x, y, z; ±((1/3), 0, 0) -2a + b, c ±((1/3), 0, 0) [3] P11a 3a, b, c (1/3)x, y, z; ±((1/3), 0, 0) 3 × 2a P11n a, 3b, c x, (1/3)y, z; ±(0, (1/3), 0) P11b a + b, 3b, c x, (1/3)(-x + y), z; ±(0, (1/3), 0) [3] P11a 3a, (1/3)(x - y), y, z; 3 × 2a P11n 3a, b, c (1/3)x, y, z; ±((1/3), 0, 0) P11b a, 3b, c x, (1/3)y, z; ±(0, (1/3), 0) a + b, c ±((1/3), 0, 0) [3] P11a 3a, (1/3)(x + y), y, z; 3 × 2a P11n 2a + b, (1/3)(2x - y), (1/3)(-x + 2y), z; P11b a - b x, (1/3)(x + y), z; -a + b, c ±((1/3), 0, 0) a + 2b, c ±((1/3), (1/3), 0) 3b, c ±(0, (1/3), 0) [p] P11a a, pb, c x, (1/p)y, z; +(0, (u/p), 0) p × 2a P11n pa, b, c (1/p)x, y, z; +((u/p), 0, 0) P11b pa, b, c (1/p)x, y, z; +((u/p), 0, 0) p = prime; u = 1, . . ., p - 1; p = prime; u = 1, . . ., p - 1; p = prime; u = 1, . . ., p - 1; [p] P11a pa, (1/p)(x - qy), y, z; p × 2a P11n a + 2qb, x, (1/p)(-2qx + y), z; P11b a + qb, x, (1/p)(-qx + y), z; qa + b, c +((u/p), 0, 0) pb, c +(0, (u/p), 0) pb, c +(0, (u/p), 0) p = prime > 2; u = 1, . . ., p - 1; p = prime > 2; u = 1, . . ., p - 1; p = prime > 2; u = 1, . . ., p - 1; -(1/2)(p - 1) ≤ q ≤ (1/2)(p - 1) -(1/2)(p - 1)≤ q ≤ (1/2)(p - 1) -(1/2)(p - 1)≤ q ≤ (1/2)(p - 1)

Space groups of the series of isomorphic subgroups appear in different sequences for cell choices 1, 2 and 3