Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
358 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D32×D5 |
| commutator, Fitting, socle, cosocle | C22×C32×C5 | C23 |
| prime radical | C2×#67140 | C2 |
| hypocenter | C32×C5 | #124 |
| LCS | G ▷ C22×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3×#1204 | C2 | semidirect |
| 3. #10623830 | C2 | semidirect |
| 4. #10623813 | C2 | semidirect |
| 5. #10623813 | C2 | semidirect |
| 6. C5×#3722 | C2 | semidirect |
| 7. C3×Dic3×Dic5 | C2 | semidirect |
| 21. C2×#1204 | D3 | semidirect |
| 34. Dic3×Dic5 | D3 | semidirect |
| 54. #3722 | D5 | semidirect |
| 147. C32×C5 | #124 | semidirect |
| 232. C3×C5 | #875 | semidirect |
| 233. C3×C5 | #947 | semidirect |
| 271. C32 | #4031 | semidirect |
| 296. C5 | #63864 | semidirect |
| 310. C3 | #91326 | semidirect |
| 311. C3 | #91350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67140 | 2 |
| C2×C3×#1204 | 2 |
| #10623830 | 2 |
| #10623813 | 2 |
| C5×#3722 | 2 |
| C3×Dic3×Dic5 | 2 |
| #91350 | 3 |
| #91326 | 3 |
| #63864 | 5 |