Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
662 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 136 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×#624 | C2 | semidirect |
| 3. C3×C5×#217 | C2 | semidirect |
| 4. C5×#3722 | C2 | semidirect |
| 8. C22×C5×C3⋊D3 | C4 | semidirect |
| 11. C2×C3×C5×Dic3 | C22 | semidirect |
| 13. #63974 | C5 | direct (N × H) |
| 18. C5×#217 | D3 | semidirect |
| 21. C22×C32×C5 | C2×C4 | semidirect |
| 26. C2×C5×C3⋊D3 | C2×C4 | semidirect |
| 31. C2×#624 | C2×C5 | semidirect |
| 32. C3×#217 | C2×C5 | semidirect |
| 33. #3722 | C2×C5 | semidirect |
| 45. C2×C5×Dic3 | C2×D3 | semidirect |
| 52. C5×C3⋊D3 | C22⋊C4 | semidirect |
| 59. C22×C3⋊D3 | C4×C5 | semidirect |
| 62. C2×C3×Dic3 | C22×C5 | semidirect |
| 68. C22×C3×C5 | C4×D3 | semidirect |
| 86. #217 | C5×D3 | semidirect |
| 88. C32×C5 | C2×C22⋊C4 | semidirect |
| 97. C22×C32 | C2×C4×C5 | semidirect |
| 102. C2×C3⋊D3 | C2×C4×C5 | semidirect |
| 127. C2×Dic3 | C2×C5×D3 | semidirect |
| 135. C22×C5 | #624 | semidirect |
| 142. C3⋊D3 | C5×C22⋊C4 | semidirect |
| 148. C3×C5 | D3×C22⋊C4 | semidirect |
| 153. C22×C3 | C4×C5×D3 | semidirect |
| 172. C32 | C2×C5×C22⋊C4 | semidirect |
| 190. C5 | #63974 | direct (N × H) |
| 197. C22 | C5×#624 | semidirect |
| 201. C3 | C5×D3×C22⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×C3⋊D3 | 2 |
| C2×C5×#624 | 2 |
| C3×C5×#217 | 2 |
| C5×#3722 | 2 |
| C5×D3×C22⋊C4 | 3 |
| #63974 | 5 |