Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
688 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 202 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 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C5 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C23×C4×C5 ◁ C23×C5×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×#466 | C2 | semidirect |
| 2. C5×#2233 | C2 | semidirect |
| 3. C5×#2218 | C2 | semidirect |
| 4. C5×#2184 | C2 | semidirect |
| 5. C5×#2112 | C2 | semidirect |
| 6. C22×C5×D8 | C22 | semidirect |
| 9. C2×C5×D16 | C22 | semidirect |
| 10. C2×C5×M32 | C22 | semidirect |
| 14. C5×#466 | C22 | semidirect |
| 15. C2×C5×#107 | C22 | semidirect |
| 17. C5×#367 | C22 | semidirect |
| 18. C5×#357 | C22 | semidirect |
| 19. C5×C22⋊C16 | C22 | semidirect |
| 20. #33758 | C5 | direct (N × H) |
| 45. C2×#466 | C2×C5 | semidirect |
| 46. #2233 | C2×C5 | semidirect |
| 47. #2218 | C2×C5 | semidirect |
| 48. #2184 | C2×C5 | semidirect |
| 49. #2112 | C2×C5 | semidirect |
| 80. C22×D8 | C22×C5 | semidirect |
| 83. C2×D16 | C22×C5 | semidirect |
| 84. C2×M32 | C22×C5 | semidirect |
| 88. #466 | C22×C5 | semidirect |
| 89. C2×#107 | C22×C5 | semidirect |
| 91. #367 | C22×C5 | semidirect |
| 92. #357 | C22×C5 | semidirect |
| 93. C22⋊C16 | C22×C5 | semidirect |
| 223. C5 | #33758 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#466 | 2 |
| C5×#2233 | 2 |
| C5×#2218 | 2 |
| C5×#2184 | 2 |
| C5×#2112 | 2 |
| #33758 | 5 |