Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
132 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 32 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. C2×C5×AGL(1,𝔽9) | C2 | semidirect |
| 3. C5×#3777 | C2 | semidirect |
| 8. C5×GO+(4,𝔽2) | C4 | semidirect |
| 10. GO+(4,𝔽2)⋊C4 | C5 | direct (N × H) |
| 20. C2×AGL(1,𝔽9) | C2×C5 | semidirect |
| 21. #3777 | C2×C5 | semidirect |
| 34. GO+(4,𝔽2) | C4×C5 | semidirect |
| 41. C32×C5 | #102 | semidirect |
| 86. C32 | C5×#102 | semidirect |
| 98. C5 | GO+(4,𝔽2)⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×GO+(4,𝔽2) | 2 |
| C2×C5×AGL(1,𝔽9) | 2 |
| C5×#3777 | 2 |
| GO+(4,𝔽2)⋊C4 | 5 |
| C5×#102 | 9 |