Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
564 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 210 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×C4×D5 | C2 | semidirect |
| 4. C32×C22⋊Dic5 | C2 | semidirect |
| 5. C32×C4⋊Dic5 | C2 | semidirect |
| 6. C3×#4084 | C3 | direct (N × H) |
| 16. C2×C3×C5×D4 | C2×C3 | semidirect |
| 17. C2×C3×C22⋊D5 | C2×C3 | semidirect |
| 18. C2×C3×C4×D5 | C2×C3 | semidirect |
| 19. C3×C22⋊Dic5 | C2×C3 | semidirect |
| 20. C3×C4⋊Dic5 | C2×C3 | semidirect |
| 27. C2×C32×D5 | D4 | semidirect |
| 28. C32×C4×C5 | D4 | semidirect |
| 31. #4084 | C32 | direct (N × H) |
| 33. C2×C32×D4 | D5 | semidirect |
| 51. C2×C5×D4 | C2×C32 | semidirect |
| 52. C2×C22⋊D5 | C2×C32 | semidirect |
| 53. C2×C4×D5 | C2×C32 | semidirect |
| 54. C22⋊Dic5 | C2×C32 | semidirect |
| 55. C4⋊Dic5 | C2×C32 | semidirect |
| 70. C2×C3×D5 | C3×D4 | semidirect |
| 71. C3×C4×C5 | C3×D4 | semidirect |
| 75. C2×C3×D4 | C3×D5 | semidirect |
| 79. C32×C5 | #121 | semidirect |
| 97. C32×C4 | C22⋊D5 | semidirect |
| 118. C2×D5 | C32×D4 | semidirect |
| 119. C4×C5 | C32×D4 | semidirect |
| 128. C2×D4 | C32×D5 | semidirect |
| 132. C3×C5 | C3×#121 | semidirect |
| 142. C3×C4 | C3×C22⋊D5 | semidirect |
| 148. C32 | #4084 | direct (N × H) |
| 162. C5 | C32×#121 | semidirect |
| 172. C4 | C32×C22⋊D5 | semidirect |
| 173. C3 | C3×#4084 | 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×C4×D5 | 2 |
| C32×C22⋊Dic5 | 2 |
| C32×C4⋊Dic5 | 2 |
| C3×#4084 | 3 |
| C32×#121 | 5 |