Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
294 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 104 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×C8×C3⋊D3 | C2 | semidirect |
| 3. C3×C5×ΓL(1,𝔽25) | C2 | semidirect |
| 4. C5×#3711 | C2 | semidirect |
| 5. C5×#3710 | C2 | semidirect |
| 12. C32×C5×C8 | C22 | semidirect |
| 13. C5×C3⋊(C3⋊C8) | C22 | semidirect |
| 14. C3×C5×C3⋊C8 | C22 | semidirect |
| 15. #63791 | C5 | direct (N × H) |
| 20. C5×ΓL(1,𝔽25) | D3 | semidirect |
| 32. C8×C3⋊D3 | C2×C5 | semidirect |
| 33. C3×ΓL(1,𝔽25) | C2×C5 | semidirect |
| 34. #3711 | C2×C5 | semidirect |
| 35. #3710 | C2×C5 | semidirect |
| 46. C3×C5×C8 | C2×D3 | semidirect |
| 49. C5×C3⋊C8 | C2×D3 | semidirect |
| 52. C5×C3⋊D3 | M16 | semidirect |
| 64. C32×C8 | C22×C5 | semidirect |
| 65. C3⋊(C3⋊C8) | C22×C5 | semidirect |
| 66. C3×C3⋊C8 | C22×C5 | semidirect |
| 82. ΓL(1,𝔽25) | C5×D3 | semidirect |
| 86. C32×C5 | C2×M16 | semidirect |
| 94. C5×C8 | D32 | semidirect |
| 118. C3×C8 | C2×C5×D3 | semidirect |
| 121. C3⋊C8 | C2×C5×D3 | semidirect |
| 129. C3⋊D3 | C5×M16 | semidirect |
| 137. C3×C5 | D3×M16 | semidirect |
| 152. C32 | C2×C5×M16 | semidirect |
| 160. C8 | C5×D32 | semidirect |
| 167. C5 | #63791 | direct (N × H) |
| 175. C3 | C5×D3×M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×D32 | 2 |
| C5×C8×C3⋊D3 | 2 |
| C3×C5×ΓL(1,𝔽25) | 2 |
| C5×#3711 | 2 |
| C5×#3710 | 2 |
| C5×D3×M16 | 3 |
| #63791 | 5 |