Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2590 conjugacy classes of subgroups; only the 1054 normal subgroups are shown.
This group has 2590 conjugacy classes of subgroups — too many to draw. Only its 1054 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 | D8 |
| commutator, Frattini, cosocle | C8 | C25×C5 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C5 ◁ C23×C4×C5 ◁ C23×C5×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C5×D8 | C2 | semidirect |
| 2. C22×C5×D16 | C2 | direct (N × H) |
| 3. C23×C5×C16 | C2 | semidirect |
| 6. C22×C5×D8 | C22 | semidirect |
| 8. C2×C5×D16 | C22 | direct (N × H) |
| 9. C22×C5×C16 | C22 | semidirect |
| 10. C23×D16 | C5 | direct (N × H) |
| 16. C2×C5×D8 | C23 | semidirect |
| 19. C5×D16 | C23 | direct (N × H) |
| 20. C2×C5×C16 | C23 | semidirect |
| 21. C23×D8 | C2×C5 | semidirect |
| 22. C22×D16 | C2×C5 | direct (N × H) |
| 23. C23×C16 | C2×C5 | semidirect |
| 32. C5×D8 | C24 | semidirect |
| 35. C5×C16 | C24 | semidirect |
| 38. C22×D8 | C22×C5 | semidirect |
| 40. C2×D16 | C22×C5 | direct (N × H) |
| 41. C22×C16 | C22×C5 | semidirect |
| 44. C23×C5 | D16 | direct (N × H) |
| 57. C2×D8 | C23×C5 | semidirect |
| 60. D16 | C23×C5 | direct (N × H) |
| 61. C2×C16 | C23×C5 | semidirect |
| 64. C22×C5 | C2×D16 | direct (N × H) |
| 76. D8 | C24×C5 | semidirect |
| 79. C16 | C24×C5 | semidirect |
| 81. C2×C5 | C22×D16 | direct (N × H) |
| 85. C23 | C5×D16 | direct (N × H) |
| 93. C5 | C23×D16 | direct (N × H) |
| 96. C22 | C2×C5×D16 | direct (N × H) |
| 101. C2 | C22×C5×D16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×D8 | 2 |
| C22×C5×D16 | 2 |
| C23×C5×C16 | 2 |
| C23×D16 | 5 |