Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
262 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 3. C3×C5×Dic12 | C2 | semidirect |
| 4. C5×#3718 | C2 | semidirect |
| 12. #63802 | C5 | direct (N × H) |
| 16. C5×Dic12 | D3 | semidirect |
| 26. C3×Dic12 | C2×C5 | semidirect |
| 27. #3718 | C2×C5 | semidirect |
| 40. C5×C3⋊D3 | Q16 | semidirect |
| 62. Dic12 | C5×D3 | semidirect |
| 65. C32×C5 | C2×Q16 | semidirect |
| 96. C3⋊D3 | C5×Q16 | semidirect |
| 102. C3×C5 | D3×Q16 | semidirect |
| 113. C32 | C2×C5×Q16 | semidirect |
| 124. C5 | #63802 | direct (N × H) |
| 130. C3 | C5×D3×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3797 | 2 |
| C5×C8×C3⋊D3 | 2 |
| C3×C5×Dic12 | 2 |
| C5×#3718 | 2 |
| C5×D3×Q16 | 3 |
| #63802 | 5 |