Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1068 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 106 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 | C2×#99 |
| commutator | C22×C4 | C22×C4×C5 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C5 |
| prime radical | C2×C5×#392 | C2 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C24×C5 ◁ C22×C5×C22⋊C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#1819 | C2 | semidirect |
| 3. C5×#1462 | C2 | semidirect |
| 4. C5×#1343 | C2 | semidirect |
| 6. C23×C5×D4 | C4 | semidirect |
| 12. C5×#392 | C4 | semidirect |
| 15. C2×C5×#95 | C4 | semidirect |
| 17. C5×#342 | C22 | semidirect |
| 19. C5×#323 | C22 | semidirect |
| 20. #11796 | C5 | direct (N × H) |
| 54. #1819 | C2×C5 | semidirect |
| 55. #1462 | C2×C5 | semidirect |
| 56. #1343 | C2×C5 | semidirect |
| 117. C23×D4 | C4×C5 | semidirect |
| 123. #392 | C4×C5 | semidirect |
| 126. C2×#95 | C4×C5 | semidirect |
| 128. #342 | C22×C5 | semidirect |
| 130. #323 | C22×C5 | semidirect |
| 406. C5 | #11796 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#392 | 2 |
| C5×#1819 | 2 |
| C5×#1462 | 2 |
| C5×#1343 | 2 |
| #11796 | 5 |