Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
312 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 96 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. C32×C22⋊AGL(1,𝔽5) | C2 | semidirect |
| 3. C3×#3999 | C3 | direct (N × H) |
| 4. C22×C32×D5 | C4 | semidirect |
| 7. C2×C32×C4×C5 | C4 | semidirect |
| 11. C3×C22⋊AGL(1,𝔽5) | C2×C3 | semidirect |
| 19. #3999 | C32 | direct (N × H) |
| 22. C22×C3×D5 | C3×C4 | semidirect |
| 25. C2×C3×C4×C5 | C3×C4 | semidirect |
| 33. C22⋊AGL(1,𝔽5) | C2×C32 | semidirect |
| 38. C2×C32×C4 | AGL(1,𝔽5) | semidirect |
| 48. C32×C5 | #99 | semidirect |
| 49. C22×D5 | C32×C4 | semidirect |
| 52. C2×C4×C5 | C32×C4 | semidirect |
| 70. C2×C3×C4 | C3×AGL(1,𝔽5) | semidirect |
| 84. C3×C5 | C3×#99 | semidirect |
| 96. C32 | #3999 | direct (N × H) |
| 101. C2×C4 | C32×AGL(1,𝔽5) | semidirect |
| 106. C5 | C32×#99 | semidirect |
| 114. C3 | C3×#3999 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D20 | 2 |
| C32×C22⋊AGL(1,𝔽5) | 2 |
| C3×#3999 | 3 |
| C32×#99 | 5 |