Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
710 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 232 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4×C5 | D32 |
| commutator, cosocle | C2×C32 | C24×C5 |
| Frattini | C2 | C22×C5×D32 |
| Fitting | C2×C32×C4×C5 | C22 |
| socle | C22×C32×C5 | C23 |
| hypocenter | C32 | C2×C5×#41 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2×C4×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4×C5×C3⋊D3 | C2 | semidirect |
| 2. C2×C3×C4×C5×D3 | C2 | semidirect |
| 3. C2×C5×#627 | C2 | semidirect |
| 4. C2×C5×#626 | C2 | semidirect |
| 5. C2×C5×#625 | C2 | semidirect |
| 6. C5×#3798 | C2 | direct (N × H) |
| 12. C4×C5×C3⋊D3 | C22 | semidirect |
| 14. C3×C4×C5×D3 | C22 | semidirect |
| 15. C5×#627 | C22 | semidirect |
| 16. C5×#626 | C22 | semidirect |
| 17. C5×#625 | C22 | semidirect |
| 18. C2×#3798 | C5 | direct (N × H) |
| 26. C2×C4×C5×D3 | D3 | semidirect |
| 37. C2×C4×C3⋊D3 | C2×C5 | semidirect |
| 38. C2×C3×C4×D3 | C2×C5 | semidirect |
| 39. C2×#627 | C2×C5 | semidirect |
| 40. C2×#626 | C2×C5 | semidirect |
| 41. C2×#625 | C2×C5 | semidirect |
| 42. #3798 | C2×C5 | direct (N × H) |
| 59. C4×C5×D3 | C2×D3 | semidirect |
| 62. C2×C32×C5 | #41 | semidirect |
| 76. C4×C3⋊D3 | C22×C5 | semidirect |
| 78. C3×C4×D3 | C22×C5 | semidirect |
| 79. #627 | C22×C5 | semidirect |
| 80. #626 | C22×C5 | semidirect |
| 81. #625 | C22×C5 | semidirect |
| 105. C2×C4×D3 | C5×D3 | semidirect |
| 107. C32×C5 | C2×#41 | semidirect |
| 130. C2×C3×C5 | #235 | semidirect |
| 151. C4×D3 | C2×C5×D3 | semidirect |
| 161. C2×C32 | C5×#41 | semidirect |
| 172. C3×C5 | C2×#235 | semidirect |
| 191. C2×C5 | #3798 | direct (N × H) |
| 193. C32 | C2×C5×#41 | semidirect |
| 207. C2×C3 | C5×#235 | semidirect |
| 212. C5 | C2×#3798 | direct (N × H) |
| 222. C3 | C2×C5×#235 | semidirect |
| 225. C2 | C5×#3798 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×C3⋊D3 | 2 |
| C2×C3×C4×C5×D3 | 2 |
| C2×C5×#627 | 2 |
| C2×C5×#626 | 2 |
| C2×C5×#625 | 2 |
| C5×#3798 | 2 |
| C2×C5×#235 | 3 |
| C2×#3798 | 5 |