Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
312 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 74 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. #10624283 | C2 | semidirect |
| 2. C2×C3×D60 | C2 | semidirect |
| 3. C3×C5×#208 | C2 | semidirect |
| 4. #10623803 | C2 | semidirect |
| 5. #10623799 | C2 | semidirect |
| 11. C4⋊(C3⋊D15) | C22 | semidirect |
| 13. #67180 | C22 | semidirect |
| 16. C3×C5×C3⋊C8 | C22 | semidirect |
| 21. C2×D60 | D3 | semidirect |
| 26. C5×#208 | D3 | semidirect |
| 39. C3×#208 | D5 | semidirect |
| 64. C5×C3⋊C8 | C2×D3 | semidirect |
| 84. C3×C3⋊C8 | C2×D5 | semidirect |
| 112. #208 | D15 | semidirect |
| 115. C32×C5 | AGL(1,ℤ/8) | semidirect |
| 166. C3⋊C8 | C2×D15 | semidirect |
| 184. C3×C5 | #908 | semidirect |
| 185. C3×C5 | #932 | semidirect |
| 209. C32 | #4054 | semidirect |
| 230. C5 | #63830 | semidirect |
| 239. C3 | #91312 | semidirect |
| 240. C3 | #91797 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624283 | 2 |
| C2×C3×D60 | 2 |
| C3×C5×#208 | 2 |
| #10623803 | 2 |
| #10623799 | 2 |
| #91797 | 3 |
| #91312 | 3 |
| #63830 | 5 |