Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
298 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | AΣL(1,𝔽16) |
| commutator | C2×C4⋊C4 | C2×C4×C5 |
| Frattini, cosocle | #390 | C22×C5 |
| prime radical | C5×#2006 | C2 |
| LCS | G ▷ C2×C4⋊C4 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C23×C5 ◁ C22×C4×C5 ◁ C5×#390 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#1393 | C2 | semidirect |
| 3. C5×#1270 | C2 | semidirect |
| 5. C5×#537 | C4 | semidirect |
| 9. C5×#343 | C4 | semidirect |
| 11. #7408 | C5 | direct (N × H) |
| 32. #1393 | C2×C5 | semidirect |
| 33. #1270 | C2×C5 | semidirect |
| 72. #537 | C4×C5 | semidirect |
| 76. #343 | C4×C5 | semidirect |
| 236. C5 | #7408 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2006 | 2 |
| C5×#1393 | 2 |
| C5×#1270 | 2 |
| #7408 | 5 |