Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
278 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
| 3. C3×C5×#216 | C2 | semidirect |
| 4. C3×C5×#215 | C2 | semidirect |
| 5. C3×C5×#208 | C2 | semidirect |
| 7. C5×#942 | C3 | direct (N × H) |
| 17. C3×#942 | C5 | direct (N × H) |
| 20. C2×C3×C5×Q8 | D3 | semidirect |
| 21. C2×C3×C5×Q8 | C2×C3 | semidirect |
| 26. C5×#216 | C2×C3 | semidirect |
| 27. C5×#215 | C2×C3 | semidirect |
| 28. C5×#208 | C2×C3 | semidirect |
| 36. C2×C32×Q8 | C2×C5 | semidirect |
| 38. C3×#216 | C2×C5 | semidirect |
| 39. C3×#215 | C2×C5 | semidirect |
| 40. C3×#208 | C2×C5 | semidirect |
| 64. #942 | C3×C5 | direct (N × H) |
| 69. C2×C5×Q8 | C3×D3 | semidirect |
| 100. C2×C3×Q8 | C5×D3 | semidirect |
| 101. C2×C3×Q8 | C2×C3×C5 | semidirect |
| 106. #216 | C2×C3×C5 | semidirect |
| 107. #215 | C2×C3×C5 | semidirect |
| 108. #208 | C2×C3×C5 | semidirect |
| 109. C32×C5 | #137 | semidirect |
| 166. C2×Q8 | C3×C5×D3 | semidirect |
| 171. C3×C5 | #942 | direct (N × H) |
| 172. C3×C5 | C3×#137 | semidirect |
| 192. C32 | C5×#137 | semidirect |
| 210. C5 | C3×#942 | direct (N × H) |
| 218. C3 | C5×#942 | direct (N × H) |
| 219. C3 | C3×C5×#137 | 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 |
| C3×C5×#235 | 2 |
| C3×C5×#216 | 2 |
| C3×C5×#215 | 2 |
| C3×C5×#208 | 2 |
| C3×C5×#137 | 3 |
| C5×#942 | 3 |
| C3×#942 | 5 |