Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
312 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #10624029 |
| commutator, Fitting, cosocle | C32×C4×C5 | C23 |
| Frattini, hypercenter | C4 | D32×D5 |
| socle | C2×C32×C5 | C2×D4 |
| hypocenter | C32×C5 | AGL(1,ℤ/8) |
| LCS | G ▷ C32×C4×C5 ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C2 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#3802 | C2 | semidirect |
| 2. #10624148 | C2 | semidirect |
| 3. #10623820 | C2 | semidirect |
| 4. #10623805 | C2 | semidirect |
| 5. C3×#6652 | C2 | semidirect |
| 8. #67180 | C22 | semidirect |
| 11. C32×D20 | C22 | semidirect |
| 15. C3×C3⋊#168 | C22 | semidirect |
| 23. #6652 | D3 | semidirect |
| 34. #3802 | D5 | semidirect |
| 47. C3×D20 | C2×D3 | semidirect |
| 52. C3⋊#168 | C2×D3 | semidirect |
| 94. C32×C5 | AGL(1,ℤ/8) | semidirect |
| 100. D20 | D32 | semidirect |
| 153. C3×C5 | #911 | semidirect |
| 171. C32 | #4078 | semidirect |
| 189. C5 | #63927 | semidirect |
| 198. C3 | #91494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3802 | 2 |
| #10624148 | 2 |
| #10623820 | 2 |
| #10623805 | 2 |
| C3×#6652 | 2 |
| #91494 | 3 |
| #63927 | 5 |