Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
270 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 270 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 |
|---|---|---|
| 2. C8×C3⋊D15 | C2 | semidirect |
| 3. C3×#6705 | C2 | semidirect |
| 4. C3×C5×ΓL(1,𝔽25) | C2 | semidirect |
| 5. #10623797 | C2 | semidirect |
| 6. D3×C3⋊#168 | C2 | semidirect |
| 7. C3⋊C8×D15 | C2 | semidirect |
| 27. #6705 | D3 | semidirect |
| 32. C5×ΓL(1,𝔽25) | D3 | semidirect |
| 48. C3×ΓL(1,𝔽25) | D5 | semidirect |
| 127. ΓL(1,𝔽25) | D15 | semidirect |
| 133. C32×C5 | #131 | semidirect |
| 207. C3×C5 | #907 | semidirect |
| 208. C3×C5 | #907 | semidirect |
| 230. C32 | #4053 | semidirect |
| 252. C5 | #63805 | semidirect |
| 261. C3 | #91268 | semidirect |
| 262. C3 | #91796 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624199 | 2 |
| C8×C3⋊D15 | 2 |
| C3×#6705 | 2 |
| C3×C5×ΓL(1,𝔽25) | 2 |
| #10623797 | 2 |
| D3×C3⋊#168 | 2 |
| C3⋊C8×D15 | 2 |
| #91796 | 3 |
| #91268 | 3 |
| #63805 | 5 |