Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
300 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 108 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×C4⋊AGL(1,𝔽5) | C2 | semidirect |
| 3. C32×D5⋊C8 | C2 | semidirect |
| 4. C3×#4007 | C3 | direct (N × H) |
| 7. C32×C5×D4 | C4 | semidirect |
| 9. C32×D20 | C4 | semidirect |
| 14. C3×C4⋊AGL(1,𝔽5) | C2×C3 | semidirect |
| 15. C3×D5⋊C8 | C2×C3 | semidirect |
| 24. #4007 | C32 | direct (N × H) |
| 30. C3×C5×D4 | C3×C4 | semidirect |
| 32. C3×D20 | C3×C4 | semidirect |
| 42. C4⋊AGL(1,𝔽5) | C2×C32 | semidirect |
| 43. D5⋊C8 | C2×C32 | semidirect |
| 47. C32×D4 | AGL(1,𝔽5) | semidirect |
| 62. C32×C5 | #102 | semidirect |
| 65. C5×D4 | C32×C4 | semidirect |
| 67. D20 | C32×C4 | semidirect |
| 87. C3×D4 | C3×AGL(1,𝔽5) | semidirect |
| 107. C3×C5 | C3×#102 | semidirect |
| 121. C32 | #4007 | direct (N × H) |
| 125. D4 | C32×AGL(1,𝔽5) | semidirect |
| 134. C5 | C32×#102 | semidirect |
| 143. C3 | C3×#4007 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×D4×D5 | 2 |
| C32×C4⋊AGL(1,𝔽5) | 2 |
| C32×D5⋊C8 | 2 |
| C3×#4007 | 3 |
| C32×#102 | 5 |