Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
998 conjugacy classes of subgroups; only the 223 normal subgroups are shown.
This group has 998 conjugacy classes of subgroups — too many to draw. Only its 223 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | (C3⋊D3)⋊D5 |
| commutator, cosocle | C2×C32×C5 | C24 |
| Frattini | C2 | C22×(C3⋊D3)⋊D5 |
| Fitting, socle | C23×C32×C5 | C22 |
| hypocenter | C32×C5 | C22×D4 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C3×D15 | C2 | semidirect |
| 2. C22×C5×C3⋊Dic3 | C2 | semidirect |
| 3. C2×#67157 | C2 | direct (N × H) |
| 7. C22×C3×D15 | C22 | semidirect |
| 8. C2×C5×C3⋊Dic3 | C22 | semidirect |
| 9. #67157 | C22 | direct (N × H) |
| 11. C23×D15 | D3 | semidirect |
| 16. C22×C32×C5 | D4 | semidirect |
| 19. C2×C3×D15 | C23 | semidirect |
| 20. C5×C3⋊Dic3 | C23 | semidirect |
| 23. C22×C3⋊Dic3 | D5 | semidirect |
| 28. C22×D15 | C2×D3 | semidirect |
| 35. C2×C32×C5 | C2×D4 | semidirect |
| 44. C2×C3⋊Dic3 | C2×D5 | semidirect |
| 48. C22×C3×C5 | #67 | semidirect |
| 51. C2×D15 | C22×D3 | semidirect |
| 61. C32×C5 | C22×D4 | semidirect |
| 67. C22×C32 | D20 | semidirect |
| 71. C3⋊Dic3 | C22×D5 | semidirect |
| 75. C2×C3×C5 | C2×#67 | semidirect |
| 88. C22×C5 | #625 | semidirect |
| 93. C2×C32 | C2×D20 | semidirect |
| 100. C3×C5 | C22×#67 | semidirect |
| 105. C22×C3 | #1202 | semidirect |
| 111. C2×C5 | C2×#625 | semidirect |
| 114. C32 | C22×D20 | semidirect |
| 123. C2×C3 | C2×#1202 | semidirect |
| 126. C5 | C22×#625 | semidirect |
| 129. C22 | #67157 | direct (N × H) |
| 133. C3 | C22×#1202 | semidirect |
| 135. C2 | C2×#67157 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×D15 | 2 |
| C22×C5×C3⋊Dic3 | 2 |
| C2×#67157 | 2 |
| C22×#1202 | 3 |
| C22×#625 | 5 |