Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1062 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 1062 conjugacy classes of subgroups — too many to draw. Only its 226 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C5 |
| prime radical | C5×#2847 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ C24×C4×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#2848 | C2 | semidirect |
| 3. C5×#2077 | C2 | semidirect |
| 4. C5×#2035 | C2 | semidirect |
| 5. C5×#2034 | C2 | semidirect |
| 6. C5×#2000 | C2 | semidirect |
| 7. C5×#1779 | C2 | semidirect |
| 9. C22×C5×SD16 | C22 | semidirect |
| 13. C2×C5×#106 | C22 | semidirect |
| 14. C2×C5×#103 | C22 | semidirect |
| 15. C2×C5×#102 | C22 | semidirect |
| 23. C5×#340 | C22 | semidirect |
| 24. C5×#340 | C22 | semidirect |
| 25. #32708 | C5 | direct (N × H) |
| 56. #2848 | C2×C5 | semidirect |
| 58. #2077 | C2×C5 | semidirect |
| 59. #2035 | C2×C5 | semidirect |
| 60. #2034 | C2×C5 | semidirect |
| 61. #2000 | C2×C5 | semidirect |
| 62. #1779 | C2×C5 | semidirect |
| 66. C24×C5 | SD16 | semidirect |
| 106. C22×SD16 | C22×C5 | semidirect |
| 110. C2×#106 | C22×C5 | semidirect |
| 111. C2×#103 | C22×C5 | semidirect |
| 112. C2×#102 | C22×C5 | semidirect |
| 120. #340 | C22×C5 | semidirect |
| 121. #340 | C22×C5 | semidirect |
| 212. C24 | C5×SD16 | semidirect |
| 293. C5 | #32708 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2848 | 2 |
| C5×#2847 | 2 |
| C5×#2077 | 2 |
| C5×#2035 | 2 |
| C5×#2034 | 2 |
| C5×#2000 | 2 |
| C5×#1779 | 2 |
| #32708 | 5 |