Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
294 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 2. C5×#3797 | C2 | semidirect |
| 3. C5×C8×C3⋊D3 | C2 | semidirect |
| 4. C3×C5×#204 | C2 | semidirect |
| 5. C5×#3715 | C2 | semidirect |
| 10. C3×C5×Dic6 | C22 | semidirect |
| 14. C32×C5×C8 | C22 | semidirect |
| 15. C5×C3⋊(C3⋊C8) | C22 | semidirect |
| 16. #63796 | C5 | direct (N × H) |
| 22. C5×#204 | D3 | semidirect |
| 33. #3797 | C2×C5 | semidirect |
| 34. C8×C3⋊D3 | C2×C5 | semidirect |
| 35. C3×#204 | C2×C5 | semidirect |
| 36. #3715 | C2×C5 | semidirect |
| 46. C5×Dic6 | C2×D3 | semidirect |
| 48. C3×C5×C8 | C2×D3 | semidirect |
| 53. C5×C3⋊D3 | SD16 | semidirect |
| 63. C3×Dic6 | C22×C5 | semidirect |
| 67. C32×C8 | C22×C5 | semidirect |
| 68. C3⋊(C3⋊C8) | C22×C5 | semidirect |
| 85. #204 | C5×D3 | semidirect |
| 88. C32×C5 | C2×SD16 | semidirect |
| 97. C5×C8 | D32 | semidirect |
| 120. Dic6 | C2×C5×D3 | semidirect |
| 122. C3×C8 | C2×C5×D3 | semidirect |
| 132. C3⋊D3 | C5×SD16 | semidirect |
| 140. C3×C5 | D3×SD16 | semidirect |
| 155. C32 | C2×C5×SD16 | semidirect |
| 164. C8 | C5×D32 | semidirect |
| 171. C5 | #63796 | direct (N × H) |
| 179. C3 | C5×D3×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3802 | 2 |
| C5×#3797 | 2 |
| C5×C8×C3⋊D3 | 2 |
| C3×C5×#204 | 2 |
| C5×#3715 | 2 |
| C5×D3×SD16 | 3 |
| #63796 | 5 |