Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
762 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 762 conjugacy classes of subgroups — too many to draw. Only its 90 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, Frattini, cosocle | C25 | C23×C5 |
| prime radical | C23×C5×D4 | C22 |
| LCS | G ▷ C25 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C25×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#2840 | C2 | semidirect |
| 3. C5×#1304 | C2 | semidirect |
| 9. #10390 | C5 | direct (N × H) |
| 10. C25×C5 | Q8 | semidirect |
| 16. C23×C4×C5 | Q8 | semidirect |
| 23. #2840 | C2×C5 | semidirect |
| 25. #1304 | C2×C5 | semidirect |
| 80. C25 | C5×Q8 | semidirect |
| 86. C23×C4 | C5×Q8 | semidirect |
| 165. C5 | #10390 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2840 | 2 |
| C5×#1781 | 2 |
| C5×#1304 | 2 |
| #10390 | 5 |