Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
408 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 408 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 |
|---|---|---|
| 1. C5×#3828 | C2 | semidirect |
| 2. C2×C32×D20 | C2 | semidirect |
| 3. #10623904 | C2 | semidirect |
| 4. #10623760 | C2 | semidirect |
| 5. #10623757 | C2 | semidirect |
| 10. C5×C4⋊(C3⋊D3) | C22 | semidirect |
| 12. C5×#634 | C22 | semidirect |
| 15. C3⋊(C3⋊#168) | C22 | semidirect |
| 18. C2×C3×D20 | D3 | semidirect |
| 31. #3828 | D5 | semidirect |
| 50. C2×D20 | C3⋊D3 | semidirect |
| 59. C4⋊(C3⋊D3) | C2×D5 | semidirect |
| 61. #634 | C2×D5 | semidirect |
| 75. C32×C5 | AGL(1,ℤ/8) | semidirect |
| 122. C3×C5 | #932 | semidirect |
| 134. C32 | #4095 | semidirect |
| 148. C5 | #64141 | semidirect |
| 156. C3 | #91298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3828 | 2 |
| C2×C32×D20 | 2 |
| #10623904 | 2 |
| #10623760 | 2 |
| #10623757 | 2 |
| #91298 | 3 |
| #64141 | 5 |