Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
154 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 22 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊(#120⋊C3) |
| commutator, cosocle, hypocenter | C24×C3 | C2×C3×C5 |
| Frattini | C22 | C5×D3×A4 |
| Fitting | C24×C3×C5 | C2×C3 |
| socle | C22×C3×C5 | C2×A4 |
| LCS | G ▷ C24×C3 | |
| UCS | C1 ◁ C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×C22⋊A4 | C2 | semidirect |
| 2. C5×#953 | C3 | semidirect |
| 5. C3⋊(#120⋊C3) | C5 | direct (N × H) |
| 6. C24×C3×C5 | C2×C3 | semidirect |
| 8. C5×C22⋊A4 | D3 | semidirect |
| 14. C3×C22⋊A4 | C2×C5 | semidirect |
| 17. C22×C5×D3 | A4 | semidirect |
| 21. #953 | C3×C5 | semidirect |
| 24. C24×C5 | C3×D3 | semidirect |
| 39. C24×C3 | C2×C3×C5 | semidirect |
| 41. C22⋊A4 | C5×D3 | semidirect |
| 59. C22×D3 | C5×A4 | semidirect |
| 71. C24 | C3×C5×D3 | semidirect |
| 76. C3×C5 | #120⋊C3 | semidirect |
| 101. C5 | C3⋊(#120⋊C3) | direct (N × H) |
| 111. C3 | C5×#120⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×C22⋊A4 | 2 |
| C5×#953 | 3 |
| C5×#120⋊C3 | 3 |
| C5×D3×A4 | 4 |
| C3⋊(#120⋊C3) | 5 |