Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
648 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 222 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C32×C5×D4 | C2 | semidirect |
| 2. C2×C32×C22⋊D5 | C2 | semidirect |
| 3. C2×C32×D20 | C2 | semidirect |
| 4. C32×C4×Dic5 | C2 | semidirect |
| 5. C3×#4086 | C3 | direct (N × H) |
| 14. C2×C3×C5×D4 | C2×C3 | semidirect |
| 15. C2×C3×C22⋊D5 | C2×C3 | semidirect |
| 16. C2×C3×D20 | C2×C3 | semidirect |
| 17. C3×C4×Dic5 | C2×C3 | semidirect |
| 23. C32×C4×C5 | D4 | semidirect |
| 24. C32×Dic5 | D4 | semidirect |
| 25. #4086 | C32 | direct (N × H) |
| 28. C2×C32×D4 | D5 | semidirect |
| 42. C2×C5×D4 | C2×C32 | semidirect |
| 43. C2×C22⋊D5 | C2×C32 | semidirect |
| 44. C2×D20 | C2×C32 | semidirect |
| 45. C4×Dic5 | C2×C32 | semidirect |
| 58. C3×C4×C5 | C3×D4 | semidirect |
| 59. C3×Dic5 | C3×D4 | semidirect |
| 62. C2×C3×D4 | C3×D5 | semidirect |
| 64. C32×C5 | #127 | semidirect |
| 78. C32×C4 | C22⋊D5 | semidirect |
| 96. C4×C5 | C32×D4 | semidirect |
| 97. Dic5 | C32×D4 | semidirect |
| 104. C2×D4 | C32×D5 | semidirect |
| 106. C3×C5 | C3×#127 | semidirect |
| 113. C3×C4 | C3×C22⋊D5 | semidirect |
| 118. C32 | #4086 | direct (N × H) |
| 130. C5 | C32×#127 | semidirect |
| 137. C4 | C32×C22⋊D5 | semidirect |
| 138. C3 | C3×#4086 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C5×D4 | 2 |
| C2×C32×C22⋊D5 | 2 |
| C2×C32×D20 | 2 |
| C32×C4×Dic5 | 2 |
| C3×#4086 | 3 |
| C32×#127 | 5 |