Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
326 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C8 | D32 |
| commutator, hypocenter | C32 | C22×C5×C8 |
| Frattini | C4 | C2×C5×D32 |
| Fitting | C32×C5×C8 | C22 |
| socle | C2×C32×C5 | C22×C4 |
| prime radical | C2×C5×D32 | C4 |
| cosocle | C32×C4 | C23×C5 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C5×C8 | |
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×D3×C8 | C2 | semidirect |
| 4. C5×#3710 | C2 | semidirect |
| 5. C5×D3×C3⋊C8 | C2 | semidirect |
| 12. C32×C5×C8 | C22 | semidirect |
| 13. C5×C3⋊(C3⋊C8) | C22 | semidirect |
| 14. C3×C5×C3⋊C8 | C22 | semidirect |
| 15. D32×C8 | C5 | direct (N × H) |
| 23. C5×D3×C8 | D3 | direct (N × H) |
| 26. C5×D32 | C8 | direct (N × H) |
| 32. C8×C3⋊D3 | C2×C5 | semidirect |
| 33. C3×D3×C8 | C2×C5 | semidirect |
| 34. #3710 | C2×C5 | semidirect |
| 35. D3×C3⋊C8 | C2×C5 | semidirect |
| 46. C3×C5×C8 | C2×D3 | semidirect |
| 49. C5×C3⋊C8 | C2×D3 | semidirect |
| 52. C5×C3⋊D3 | C2×C8 | semidirect |
| 53. C3×C5×D3 | C2×C8 | semidirect |
| 64. C32×C8 | C22×C5 | semidirect |
| 65. C3⋊(C3⋊C8) | C22×C5 | semidirect |
| 66. C3×C3⋊C8 | C22×C5 | semidirect |
| 85. D3×C8 | C5×D3 | direct (N × H) |
| 86. C32×C5 | C22×C8 | semidirect |
| 94. C5×C8 | D32 | direct (N × H) |
| 97. D32 | C5×C8 | direct (N × H) |
| 107. C5×D3 | D3×C8 | direct (N × H) |
| 118. C3×C8 | C2×C5×D3 | semidirect |
| 121. C3⋊C8 | C2×C5×D3 | semidirect |
| 129. C3⋊D3 | C2×C5×C8 | semidirect |
| 130. C3×D3 | C2×C5×C8 | semidirect |
| 137. C3×C5 | C2×D3×C8 | semidirect |
| 152. C32 | C22×C5×C8 | semidirect |
| 160. C8 | C5×D32 | direct (N × H) |
| 166. D3 | C5×D3×C8 | direct (N × H) |
| 167. C5 | D32×C8 | direct (N × H) |
| 175. C3 | C2×C5×D3×C8 | 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×D3×C8 | 2 |
| C5×#3710 | 2 |
| C5×D3×C3⋊C8 | 2 |
| C2×C5×D3×C8 | 3 |
| D32×C8 | 5 |