Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
456 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 154 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. C2×C5×#634 | C2 | semidirect |
| 3. C32×C42×C5 | C2 | semidirect |
| 4. C5×#3752 | C2 | semidirect |
| 12. #64084 | C5 | direct (N × H) |
| 15. C3×C42×C5 | D3 | semidirect |
| 25. C2×#634 | C2×C5 | semidirect |
| 26. C32×C42 | C2×C5 | semidirect |
| 27. #3752 | C2×C5 | semidirect |
| 41. C42×C5 | C3⋊D3 | semidirect |
| 56. C3×C42 | C5×D3 | semidirect |
| 58. C32×C5 | #124 | semidirect |
| 93. C42 | C5×C3⋊D3 | semidirect |
| 94. C3×C5 | #875 | semidirect |
| 104. C32 | C5×#124 | semidirect |
| 114. C5 | #64084 | direct (N × H) |
| 121. C3 | C5×#875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C4⋊(C3⋊D3) | 2 |
| C2×C5×#634 | 2 |
| C32×C42×C5 | 2 |
| C5×#3752 | 2 |
| C5×#875 | 3 |
| #64084 | 5 |