Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
302 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 11. #63919 | C5 | direct (N × H) |
| 19. C32×C4×C5 | Q8 | semidirect |
| 21. C5×C3⋊Dic3 | Q8 | semidirect |
| 54. C3×C4×C5 | Dic6 | semidirect |
| 66. C32×C5 | C4⋊Q8 | semidirect |
| 73. C32×C4 | C5×Q8 | semidirect |
| 75. C3⋊Dic3 | C5×Q8 | semidirect |
| 97. C4×C5 | #627 | semidirect |
| 106. C3×C5 | #888 | semidirect |
| 111. C3×C4 | C5×Dic6 | semidirect |
| 120. C32 | C5×C4⋊Q8 | semidirect |
| 132. C5 | #63919 | direct (N × H) |
| 137. C4 | C5×#627 | semidirect |
| 139. C3 | C5×#888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#627 | 2 |
| C4×C5×C3⋊Dic3 | 2 |
| C3×C5×C4⋊Dic3 | 2 |
| C5×#3724 | 2 |
| C5×#888 | 3 |
| #63919 | 5 |