Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
734 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 734 conjugacy classes of subgroups — too many to draw. Only its 130 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 | #386 |
| commutator | C22×C4 | C22×C4×C5 |
| Frattini, cosocle | C23×C4 | C23×C5 |
| prime radical | C25×C5 | D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C5×#1826 | C2 | semidirect |
| 5. C5×#1284 | C2 | semidirect |
| 10. C5×#399 | C4 | semidirect |
| 11. C5×#397 | C4 | semidirect |
| 21. #9477 | C5 | direct (N × H) |
| 30. C2×C5×C4⋊C4 | C2×C4 | semidirect |
| 31. C2×C5×C4⋊C4 | C2×C4 | semidirect |
| 52. C5×#95 | C2×C4 | semidirect |
| 55. #1826 | C2×C5 | semidirect |
| 57. #1284 | C2×C5 | semidirect |
| 102. #399 | C4×C5 | semidirect |
| 103. #397 | C4×C5 | semidirect |
| 162. C2×C4⋊C4 | C2×C4×C5 | semidirect |
| 163. C2×C4⋊C4 | C2×C4×C5 | semidirect |
| 184. #95 | C2×C4×C5 | semidirect |
| 299. C5 | #9477 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2482 | 2 |
| C5×#2273 | 2 |
| C5×#1826 | 2 |
| C5×#1462 | 2 |
| C5×#1284 | 2 |
| #9477 | 5 |