Cc No. 9 Cs4

 C1c1 A1n1 I1a1 UNIQUE AXIS b CELL CHOICE 1 CELL CHOICE 2 CELL CHOICE 3 Axes Coordinates Wyckoff Axes Coordinates Axes Coordinates positions 4a I Maximal translationengleiche subgroups [2] P1 (1) (1/2)(a - b), 2x, x + y, z 2 × 2a P1 a, b, x, x + y, 2z P1 a, x + y, 2y, y + z b, c (1/2)(-b + c) (1/2)(-a + b - c), c II Maximal klassengleiche subgroups Loss of centring translations [2] P1c1 (7) 2 × 2a P1n1 P1a1 [2] P1n1 (7) x, y + (1/4), z 2 × 2a P1a1 x, y + (1/4), z P1c1 x, y + (1/4), z Enlarged unit cell, isomorphic [3] C1c1 a, 3b, c x, (1/3)y, z; ±(0, (1/3), 0) 3 × 4a A1n1 a, 3b, c x, (1/3)y, z; ±(0, (1/3), 0) I1a1 a, 3b, c x, (1/3)y, z; ±(0, (1/3), 0) [p] C1c1 a, pb, c x, (1/p)y, z; +(0, (u/p), 0) p × 4a A1n1 a, pb, c x, (1/p)y, z; +(0, (u/p), 0) I1a1 a, pb, c x, (1/p)y, z; +(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 [3] C1c1 3a, b, c (1/3)x, y, z; ±((1/3), 0, 0) 3 × 4a A1n1 a - 2c, b, 3c x, y, (1/3)(2x + z); I1a1 a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) ±(0, 0, (1/3)) [3] C1c1 3a, b, 2a + c (1/3)(x - 2z), y, z; 3 × 4a A1n1 a + 2c, b, 3c x, y, (1/3)(-2x + z); I1a1 3a, b, 2a + c (1/3)(x - 2z), y, z; ±((1/3), 0, 0) ±(0, 0, (1/3)) ±((1/3), 0, 0) or: 3a, b, -a + c (1/3)(x + z), y + (1/4), z; ±((1/3), 0, 0) [3] C1c1 3a, b, (1/3)(x + 2z), y, z; 3 × 4a A1n1 a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) I1a1 3a, b, c (1/3)x, y, z; ±((1/3), 0, 0) -2a + c ±((1/3), 0, 0) or: 3a, b, a + c (1/3)(x - z), y + (1/4), z; ±((1/3), 0, 0) [3] C1c1 a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 3 × 4a A1n1 3a, b, c (1/3)x, y, z; ±((1/3), 0, 0) I1a1 3a, b, -2a + c (1/3)(x + 2z), y, z; ±((1/3), 0, 0) [p] C1c1 a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) p × 4a A1n1 pa, b, c (1/p)x, y, z; +((u/p), 0, 0) I1a1 pa, b, c (1/p)x, y, z; +((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 [p] C1c1 pa, b, (1/p)(x - 2qz), y, z; p × 4a A1n1 a + 2qc, b, pc x, y, (1/p)(-2qx + z); I1a1 a + 2qc, b, pc x, y, (1/p)(-2qx + z); 2qa + c +((u/p), 0, 0) +(0, 0, (u/p)) +(0, 0, (u/p)) 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

 A11a B11n I11b 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 a, x, 2y, y + z 2 × 2a P1 (1/2)(a - c), 2x, y, y + z P1 a, b, x + y, y + z, 2z (1/2)(b - c), c b, c (1/2)(-a - b + c) II Maximal klassengleiche subgroups Loss of centring translations [2] P11a 2 × 2a P11n P11b [2] P11n x, y, z + (1/4) 2 × 2a P11b x, y, z + (1/4) P11a x, y, z + (1/4) Enlarged unit cell, isomorphic [3] A11a a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 3 × 4a B11n a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) I11b a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) [p] A11a a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) p × 4a B11n a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) I11b a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) p = prime > 2; u = 1, . . ., p - 1 p = prime > 2; u = 1, . . ., p - 1 p = prime > 2; u = 1, . . ., p - 1 [3] A11a a, 3b, c x, (1/3)y, z; ±(0, (1/3), 0) 3 × 4a B11n 3a, -2a + b, c (1/3)(x + 2y), y, z; I11b 3a, b, c (1/3)x, y, z; ±((1/3), 0, 0) ±((1/3), 0, 0) [3] A11a a + 2b, 3b, c x, (1/3)(-2x + y), z; 3 × 4a B11n 3a, 2a + b, c (1/3)(x - 2y), y, z; I11b a + 2b, 3b, c x, (1/3)(-2x + y), z; ±(0, (1/3), 0) ±((1/3), 0, 0) ±(0, (1/3), 0) or: a - b, 3b, c x, (1/3)(x + y), z + (1/4); ±(0, (1/3), 0) [3] A11a a - 2b, x, (1/3)(2x + y), z; 3 × 4a B11n 3a, b, c (1/3)x, y, z; ±((1/3), 0, 0) I11b a, 3b, c x, (1/3)y, z; ±(0, (1/3), 0) 3b, c ±(0, (1/3), 0) or: a + b, 3b, c x, (1/3)(-z + y), z + (1/4); ±(0, (1/3), 0) [3] A11a 3a, b, c (1/3)x, y, z; ±((1/3), 0, 0) 3 × 4a B11n a, 3b, c x, (1/3)y, z; ±(0, (1/3), 0) I11b a - 2b, 3b, c x, (1/3)(2x + y), z; ±(0, (1/3), 0) [p] A11a pa, b, c (1/p)x, y, z; +((u/p), 0, 0) p × 4a B11n a, pb, c x, (1/p)y, z; +(0, (u/p), 0) I11b a, pb, c x, (1/p)y, z; +(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 [p] A11a a + 2qb, x, (1/p)(-2qx + y), z; p × 4a B11n pa, 2qa + b, c (1/p)(x - 2qy), y, z; I11b pa, 2qa + b, c (1/p)(x - 2qy), y, z; pb, c +(0, (u/p), 0) +((u/p), 0, 0) +((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