Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
5942 conjugacy classes of subgroups; only the 438 normal subgroups are shown.
This group has 5942 conjugacy classes of subgroups — too many to draw. Only its 438 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 | C24×C5×D4 | 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 |
|---|---|---|
| 2. C2×C5×#450 | C2 | semidirect |
| 3. C5×#2848 | C2 | semidirect |
| 4. C5×#1786 | C2 | semidirect |
| 5. C5×#1779 | C2 | semidirect |
| 11. C22×C5×SD16 | C22 | semidirect |
| 12. C2×C5×C22⋊Q8 | C22 | semidirect |
| 14. C2×C5×#102 | C22 | semidirect |
| 15. C2×C5×C22⋊C8 | C22 | semidirect |
| 17. C5×#380 | C22 | semidirect |
| 19. #32881 | C5 | direct (N × H) |
| 25. C22×C5×Q8 | C23 | semidirect |
| 38. C22×C5×C8 | C23 | semidirect |
| 41. C2×C5×C4⋊C4 | C23 | semidirect |
| 48. C2×#450 | C2×C5 | semidirect |
| 49. #2848 | C2×C5 | semidirect |
| 50. #1786 | C2×C5 | semidirect |
| 51. #1779 | C2×C5 | semidirect |
| 63. C24×C5 | SD16 | semidirect |
| 93. C22×SD16 | C22×C5 | semidirect |
| 94. C2×C22⋊Q8 | C22×C5 | semidirect |
| 96. C2×#102 | C22×C5 | semidirect |
| 97. C2×C22⋊C8 | C22×C5 | semidirect |
| 99. #380 | C22×C5 | semidirect |
| 137. C22×Q8 | C23×C5 | semidirect |
| 150. C22×C8 | C23×C5 | semidirect |
| 153. C2×C4⋊C4 | C23×C5 | semidirect |
| 168. C22×C5 | #450 | semidirect |
| 187. C24 | C5×SD16 | semidirect |
| 248. C5 | #32881 | direct (N × H) |
| 258. C22 | C5×#450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C5×D4 | 2 |
| C2×C5×#450 | 2 |
| C5×#2848 | 2 |
| C5×#1786 | 2 |
| C5×#1779 | 2 |
| #32881 | 5 |