Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
13646 conjugacy classes of subgroups; only the 1539 normal subgroups are shown.
This group has 13646 conjugacy classes of subgroups — too many to draw. Only its 1539 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C25 | C22×D5 |
| commutator, cosocle | C23×C5 | C25 |
| Frattini | C23 | C24×D5 |
| Fitting | C22×C5×#95 | C2 |
| socle | C25×C5 | C23 |
| hypercenter | C22×#95 | D5 |
| hypocenter | C5 | C22×#392 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C25 ◁ C22×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×D20 | C2 | semidirect |
| 2. C23×#685 | C2 | semidirect |
| 3. C22×C5×#95 | C2 | semidirect |
| 4. C2×#64960 | C2 | direct (N × H) |
| 10. C23×D20 | C22 | semidirect |
| 12. C22×#685 | C22 | semidirect |
| 13. C2×C5×#95 | C22 | semidirect |
| 14. #64960 | C22 | direct (N × H) |
| 21. C24×D5 | D4 | semidirect |
| 24. C23×C4×C5 | D4 | semidirect |
| 31. C22×D20 | C23 | semidirect |
| 33. C2×#685 | C23 | semidirect |
| 34. C5×#95 | C23 | semidirect |
| 38. C22×#95 | D5 | semidirect |
| 52. C23×D5 | C2×D4 | semidirect |
| 56. C22×C4×C5 | C2×D4 | semidirect |
| 74. C2×#95 | C2×D5 | semidirect |
| 92. C22×D5 | C22×D4 | semidirect |
| 95. C2×C4×C5 | C22×D4 | semidirect |
| 113. C23×C4 | D20 | semidirect |
| 117. #95 | C22×D5 | semidirect |
| 118. C22×C5 | #392 | semidirect |
| 156. C22×C4 | C2×D20 | semidirect |
| 159. C2×C5 | C2×#392 | semidirect |
| 187. C2×C4 | C22×D20 | semidirect |
| 188. C5 | C22×#392 | semidirect |
| 195. C22 | #64960 | direct (N × H) |
| 205. C2 | C2×#64960 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×D20 | 2 |
| C23×#685 | 2 |
| C22×C5×#95 | 2 |
| C2×#64960 | 2 |
| C22×#392 | 5 |