Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
606 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 606 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 | C2×C4×C5 | #99 |
| commutator | C22×C4 | C22×C4×C5 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C5 |
| socle | C22×C5 | C2×#99 |
| prime radical | C5×#2397 | C2 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C5 ◁ C22×C4×C5 ◁ C2×C4×C5×D4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×C5×#99 | C2 | semidirect |
| 3. C5×#1459 | C2 | semidirect |
| 4. C5×#1352 | C2 | semidirect |
| 5. C5×#1343 | C2 | semidirect |
| 8. C2×C4×C5×D4 | C4 | semidirect |
| 13. C5×#399 | C4 | semidirect |
| 16. C5×#392 | C4 | semidirect |
| 19. C5×#376 | C4 | semidirect |
| 23. #11726 | C5 | direct (N × H) |
| 61. C4×#99 | C2×C5 | semidirect |
| 62. #1459 | C2×C5 | semidirect |
| 63. #1352 | C2×C5 | semidirect |
| 64. #1343 | C2×C5 | semidirect |
| 119. C2×C4×D4 | C4×C5 | semidirect |
| 124. #399 | C4×C5 | semidirect |
| 127. #392 | C4×C5 | semidirect |
| 130. #376 | C4×C5 | semidirect |
| 370. C5 | #11726 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2397 | 2 |
| C4×C5×#99 | 2 |
| C5×#1459 | 2 |
| C5×#1352 | 2 |
| C5×#1343 | 2 |
| #11726 | 5 |