Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
150 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 42 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. C4⋊(C9⋊AGL(1,𝔽5)) | C2 | semidirect |
| 3. C9×D5⋊C8 | C2 | semidirect |
| 7. D180 | C4 | semidirect |
| 8. C5×D36 | C4 | semidirect |
| 43. D5⋊C8 | D9 | semidirect |
| 49. D36 | AGL(1,𝔽5) | semidirect |
| 62. C5×C9 | #102 | semidirect |
| 121. C9 | #4007 | semidirect |
| 134. C5 | #63380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×D36 | 2 |
| C4⋊(C9⋊AGL(1,𝔽5)) | 2 |
| C9×D5⋊C8 | 2 |
| #91152 | 3 |
| #63380 | 5 |