Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
312 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 71 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. C5×#3828 | C2 | semidirect |
| 2. C2×C3×D60 | C2 | semidirect |
| 3. C3×#6710 | C2 | semidirect |
| 4. #10623823 | C2 | semidirect |
| 5. #10623821 | C2 | semidirect |
| 11. C5×C4⋊(C3⋊D3) | C22 | semidirect |
| 13. C5×#634 | C22 | semidirect |
| 16. C3×C3⋊#168 | C22 | semidirect |
| 18. C2×D60 | D3 | semidirect |
| 23. #6710 | D3 | semidirect |
| 37. #3828 | D5 | semidirect |
| 63. C3⋊#168 | C2×D3 | semidirect |
| 79. C4⋊(C3⋊D3) | C2×D5 | semidirect |
| 81. #634 | C2×D5 | semidirect |
| 115. C32×C5 | AGL(1,ℤ/8) | semidirect |
| 184. C3×C5 | #908 | semidirect |
| 185. C3×C5 | #932 | semidirect |
| 209. C32 | #4095 | semidirect |
| 230. C5 | #63830 | semidirect |
| 239. C3 | #91298 | semidirect |
| 240. C3 | #91305 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3828 | 2 |
| C2×C3×D60 | 2 |
| C3×#6710 | 2 |
| #10623823 | 2 |
| #10623821 | 2 |
| #91305 | 3 |
| #91298 | 3 |
| #63830 | 5 |