Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
312 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 59 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×#3832 | C2 | semidirect |
| 2. #10624227 | C2 | semidirect |
| 3. C3×#6717 | C2 | semidirect |
| 4. #10623821 | C2 | semidirect |
| 5. #10623820 | C2 | semidirect |
| 8. C32×C5×Q8 | C22 | semidirect |
| 10. C5×C4⋊(C3⋊D3) | C22 | semidirect |
| 15. C3×C3⋊#168 | C22 | semidirect |
| 20. #6717 | D3 | semidirect |
| 33. #3832 | D5 | semidirect |
| 40. C3×C5×Q8 | C2×D3 | semidirect |
| 52. C3⋊#168 | C2×D3 | semidirect |
| 65. C32×Q8 | C2×D5 | semidirect |
| 67. C4⋊(C3⋊D3) | C2×D5 | semidirect |
| 94. C32×C5 | AGL(1,ℤ/8) | semidirect |
| 96. C5×Q8 | D32 | semidirect |
| 122. C3×Q8 | D3×D5 | semidirect |
| 153. C3×C5 | #914 | semidirect |
| 171. C32 | #4095 | semidirect |
| 173. Q8 | (C3⋊D3)⋊D5 | semidirect |
| 189. C5 | #63941 | semidirect |
| 198. C3 | #91504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3832 | 2 |
| #10624227 | 2 |
| C3×#6717 | 2 |
| #10623821 | 2 |
| #10623820 | 2 |
| #91504 | 3 |
| #63941 | 5 |