Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
876 conjugacy classes of subgroups; only the 306 normal subgroups are shown.
This group has 876 conjugacy classes of subgroups — too many to draw. Only its 306 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 |
|---|---|---|
| 1. C2×C32×C5×Q8 | C2 | semidirect |
| 2. C5×#3832 | C2 | semidirect |
| 3. C5×Q8×C3⋊D3 | C2 | semidirect |
| 4. C5×#3828 | C2 | semidirect |
| 12. #64364 | C5 | direct (N × H) |
| 13. C2×C3×C5×Q8 | D3 | semidirect |
| 22. C2×C32×Q8 | C2×C5 | semidirect |
| 23. #3832 | C2×C5 | semidirect |
| 24. Q8×C3⋊D3 | C2×C5 | semidirect |
| 25. #3828 | C2×C5 | semidirect |
| 39. C2×C5×Q8 | C3⋊D3 | semidirect |
| 50. C2×C3×Q8 | C5×D3 | semidirect |
| 54. C32×C5 | 2−1+4 | semidirect |
| 85. C2×Q8 | C5×C3⋊D3 | semidirect |
| 86. C3×C5 | #1007 | semidirect |
| 94. C32 | C5×2−1+4 | semidirect |
| 104. C5 | #64364 | direct (N × H) |
| 109. C3 | C5×#1007 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C5×Q8 | 2 |
| C5×#3832 | 2 |
| C5×Q8×C3⋊D3 | 2 |
| C5×#3828 | 2 |
| C5×#1007 | 3 |
| #64364 | 5 |