Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
956 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 956 conjugacy classes of subgroups — too many to draw. Only its 130 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 | #386 |
| commutator | C24 | C22×C4×C5 |
| Frattini, cosocle | C25 | C23×C5 |
| prime radical | C23×C5×D4 | C22 |
| LCS | G ▷ C24 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C25×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C5×#1819 | C2 | semidirect |
| 5. C5×#1304 | C2 | semidirect |
| 7. C2×C5×#123 | C4 | semidirect |
| 13. C5×#386 | C4 | semidirect |
| 21. #9499 | C5 | direct (N × H) |
| 30. C23×C4×C5 | C2×C4 | semidirect |
| 31. C23×C4×C5 | C2×C4 | semidirect |
| 50. C2×C5×C22⋊C4 | C2×C4 | semidirect |
| 57. #1819 | C2×C5 | semidirect |
| 59. #1304 | C2×C5 | semidirect |
| 116. C2×#123 | C4×C5 | semidirect |
| 122. #386 | C4×C5 | semidirect |
| 195. C23×C4 | C2×C4×C5 | semidirect |
| 196. C23×C4 | C2×C4×C5 | semidirect |
| 215. C2×C22⋊C4 | C2×C4×C5 | semidirect |
| 376. C5 | #9499 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2405 | 2 |
| C5×#2308 | 2 |
| C5×#1819 | 2 |
| C5×#1781 | 2 |
| C5×#1304 | 2 |
| #9499 | 5 |