Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
408 conjugacy classes of subgroups; only the 250 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 250 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. C5×#3748 | C2 | direct (N × H) |
| 3. C2×C5×C3⋊(C3⋊C8) | C2 | semidirect |
| 10. C5×C3⋊(C3⋊C8) | C22 | semidirect |
| 11. C2×#3748 | C5 | direct (N × H) |
| 23. #3748 | C2×C5 | direct (N × H) |
| 24. C2×C3⋊(C3⋊C8) | C2×C5 | semidirect |
| 33. C2×C32×C5 | M16 | semidirect |
| 43. C3⋊(C3⋊C8) | C22×C5 | semidirect |
| 53. C32×C5 | C2×M16 | semidirect |
| 68. C2×C3×C5 | #208 | semidirect |
| 83. C2×C32 | C5×M16 | semidirect |
| 88. C3×C5 | C2×#208 | semidirect |
| 96. C2×C5 | #3748 | direct (N × H) |
| 98. C32 | C2×C5×M16 | semidirect |
| 106. C2×C3 | C5×#208 | semidirect |
| 108. C5 | C2×#3748 | direct (N × H) |
| 115. C3 | C2×C5×#208 | semidirect |
| 117. C2 | C5×#3748 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C4×C5 | 2 |
| C5×#3748 | 2 |
| C2×C5×C3⋊(C3⋊C8) | 2 |
| C2×C5×#208 | 3 |
| C2×#3748 | 5 |