Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2502 conjugacy classes of subgroups; only the 462 normal subgroups are shown.
This group has 2502 conjugacy classes of subgroups — too many to draw. Only its 462 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C5 | C24 |
| commutator | C23 | C23×C4×C5 |
| Frattini, cosocle | C24 | C24×C5 |
| prime radical | C22×C5×#127 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C5×#383 | C2 | semidirect |
| 3. C5×#1438 | C2 | semidirect |
| 6. C2×C5×#127 | C4 | semidirect |
| 11. #14661 | C5 | direct (N × H) |
| 24. C2×#383 | C2×C5 | semidirect |
| 25. #1438 | C2×C5 | semidirect |
| 39. C42×C5 | C22⋊C4 | semidirect |
| 42. C2×#127 | C4×C5 | semidirect |
| 94. C42 | C5×C22⋊C4 | semidirect |
| 113. C5 | #14661 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#127 | 2 |
| C2×C5×#383 | 2 |
| C5×#1438 | 2 |
| #14661 | 5 |