Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
288 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 180 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. C3×C5×#208 | C2 | semidirect |
| 3. C2×C3×C5×C3⋊C8 | C2 | semidirect |
| 5. C5×#948 | C3 | direct (N × H) |
| 11. C3×#948 | C5 | direct (N × H) |
| 17. C5×#208 | C2×C3 | semidirect |
| 18. C2×C5×C3⋊C8 | C2×C3 | semidirect |
| 24. C3×#208 | C2×C5 | semidirect |
| 25. C2×C3×C3⋊C8 | C2×C5 | semidirect |
| 40. #948 | C3×C5 | direct (N × H) |
| 65. #208 | C2×C3×C5 | semidirect |
| 66. C2×C3⋊C8 | C2×C3×C5 | semidirect |
| 67. C32×C5 | #131 | semidirect |
| 105. C3×C5 | #948 | direct (N × H) |
| 106. C3×C5 | C3×#131 | semidirect |
| 118. C32 | C5×#131 | semidirect |
| 130. C5 | C3×#948 | direct (N × H) |
| 135. C3 | C5×#948 | direct (N × H) |
| 136. C3 | C3×C5×#131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C5×#41 | 2 |
| C3×C5×#208 | 2 |
| C2×C3×C5×C3⋊C8 | 2 |
| C3×C5×#131 | 3 |
| C5×#948 | 3 |
| C3×#948 | 5 |