Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
486 conjugacy classes of subgroups; only the 248 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 248 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C5 | D32 |
| commutator, hypocenter | C32 | C2×C42×C5 |
| Frattini | C22 | C2×C5×D32 |
| Fitting, socle, prime radical | C23×C32×C5 | C22 |
| cosocle | C22×C32 | C23×C5 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C23×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C5×Dic32 | C2 | direct (N × H) |
| 6. C2×C5×C3⋊Dic3 | C4 | semidirect |
| 8. C2×C3×C5×Dic3 | C4 | semidirect |
| 10. C2×Dic32 | C5 | direct (N × H) |
| 19. C5×C3⋊Dic3 | C2×C4 | semidirect |
| 20. C3×C5×Dic3 | C2×C4 | semidirect |
| 24. Dic32 | C2×C5 | direct (N × H) |
| 33. C2×C5×Dic3 | Dic3 | direct (N × H) |
| 36. C2×C32×C5 | C42 | semidirect |
| 43. C2×C3⋊Dic3 | C4×C5 | semidirect |
| 45. C2×C3×Dic3 | C4×C5 | semidirect |
| 57. C5×Dic3 | C2×Dic3 | direct (N × H) |
| 63. C32×C5 | C2×C42 | semidirect |
| 72. C3⋊Dic3 | C2×C4×C5 | semidirect |
| 73. C3×Dic3 | C2×C4×C5 | semidirect |
| 78. C2×C3×C5 | C4×Dic3 | semidirect |
| 90. C2×Dic3 | C5×Dic3 | direct (N × H) |
| 97. C2×C32 | C42×C5 | semidirect |
| 104. C3×C5 | C2×C4×Dic3 | semidirect |
| 115. Dic3 | C2×C5×Dic3 | direct (N × H) |
| 116. C2×C5 | Dic32 | direct (N × H) |
| 119. C32 | C2×C42×C5 | semidirect |
| 128. C2×C3 | C4×C5×Dic3 | semidirect |
| 132. C5 | C2×Dic32 | direct (N × H) |
| 139. C3 | C2×C4×C5×Dic3 | semidirect |
| 140. C2 | C5×Dic32 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C3⋊Dic3 | 2 |
| C22×C3×C5×Dic3 | 2 |
| C5×Dic32 | 2 |
| C2×C4×C5×Dic3 | 3 |
| C2×Dic32 | 5 |