Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1090 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 1090 conjugacy classes of subgroups — too many to draw. Only its 254 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 | #393 |
| commutator | C24 | C22×C4×C5 |
| Frattini, cosocle | C25 | C23×C5 |
| prime radical | C25×C5 | C23 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C25×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C5×#543 | C4 | semidirect |
| 12. #11394 | C5 | direct (N × H) |
| 17. C23×C4×C5 | Q8 | semidirect |
| 34. C2×C5×C22⋊C4 | Q8 | semidirect |
| 70. #543 | C4×C5 | semidirect |
| 112. C23×C4 | C5×Q8 | semidirect |
| 129. C2×C22⋊C4 | C5×Q8 | semidirect |
| 223. C5 | #11394 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#543 | 2 |
| C2×C5×#342 | 2 |
| #11394 | 5 |