Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
780 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 191 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×C3⋊D15 |
| commutator, socle, cosocle | C22×C32×C5 | C23 |
| Fitting | C24×C32×C5 | C2 |
| hypercenter | C24 | C3⋊D15 |
| hypocenter | C32×C5 | #120 |
| LCS | G ▷ C22×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×C32×C5 | C2 | semidirect |
| 2. C2×#67184 | C2 | semidirect |
| 3. #10623913 | C2 | semidirect |
| 7. C22×C3⋊D15 | C22 | semidirect |
| 9. C2×C3⋊Dic15 | C22 | semidirect |
| 11. C24×C3×C5 | D3 | semidirect |
| 16. C22×C32×C5 | D4 | semidirect |
| 21. C24×C32 | D5 | semidirect |
| 33. C24×C5 | C3⋊D3 | semidirect |
| 43. C22×C3×C5 | #67 | semidirect |
| 47. C24×C3 | D15 | semidirect |
| 50. C32×C5 | #120 | semidirect |
| 58. C22×C32 | C22⋊D5 | semidirect |
| 73. C22×C5 | #638 | semidirect |
| 80. C24 | C3⋊D15 | semidirect |
| 83. C3×C5 | #953 | semidirect |
| 86. C22×C3 | #1220 | semidirect |
| 93. C32 | #4099 | semidirect |
| 102. C5 | #64162 | semidirect |
| 106. C22 | #67184 | semidirect |
| 109. C3 | #91842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C32×C5 | 2 |
| C2×#67184 | 2 |
| #10623913 | 2 |
| #91842 | 3 |
| #64162 | 5 |