Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
312 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 76 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×#3830 | C2 | semidirect |
| 2. C5×#3802 | C2 | semidirect |
| 3. C3×C5×#213 | C2 | semidirect |
| 4. C5×#3716 | C2 | semidirect |
| 5. C5×#3712 | C2 | semidirect |
| 8. C32×C5×D4 | C22 | semidirect |
| 12. C5×#634 | C22 | semidirect |
| 15. C3×C5×C3⋊C8 | C22 | semidirect |
| 16. #63927 | C5 | direct (N × H) |
| 22. C5×#213 | D3 | semidirect |
| 33. #3830 | C2×C5 | semidirect |
| 34. #3802 | C2×C5 | semidirect |
| 35. C3×#213 | C2×C5 | semidirect |
| 36. #3716 | C2×C5 | semidirect |
| 37. #3712 | C2×C5 | semidirect |
| 41. C3×C5×D4 | C2×D3 | semidirect |
| 53. C5×C3⋊C8 | C2×D3 | semidirect |
| 65. C32×D4 | C22×C5 | semidirect |
| 69. #634 | C22×C5 | semidirect |
| 72. C3×C3⋊C8 | C22×C5 | semidirect |
| 91. #213 | C5×D3 | semidirect |
| 94. C32×C5 | AGL(1,ℤ/8) | semidirect |
| 100. C5×D4 | D32 | semidirect |
| 123. C3×D4 | C2×C5×D3 | semidirect |
| 135. C3⋊C8 | C2×C5×D3 | semidirect |
| 153. C3×C5 | #911 | semidirect |
| 171. C32 | C5×AGL(1,ℤ/8) | semidirect |
| 177. D4 | C5×D32 | semidirect |
| 189. C5 | #63927 | direct (N × H) |
| 198. C3 | C5×#911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3830 | 2 |
| C5×#3802 | 2 |
| C3×C5×#213 | 2 |
| C5×#3716 | 2 |
| C5×#3712 | 2 |
| C5×#911 | 3 |
| #63927 | 5 |