Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
628 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 162 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 | C2×C4 | C2×C42×C5 |
| Frattini, cosocle | C22×D4 | C23×C5 |
| prime radical | C2×C5×#127 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C4×C5×D4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C4×C5×#99 | C2 | semidirect |
| 4. C5×#1393 | C2 | semidirect |
| 6. C2×C4×C5×D4 | C4 | semidirect |
| 9. C5×#390 | C4 | semidirect |
| 13. C5×#382 | C4 | semidirect |
| 15. C5×#376 | C4 | semidirect |
| 16. C5×#353 | C4 | semidirect |
| 18. #12628 | C5 | direct (N × H) |
| 40. C5×#99 | C2×C4 | semidirect |
| 47. C4×#99 | C2×C5 | semidirect |
| 48. #1393 | C2×C5 | semidirect |
| 59. C2×C5×D4 | C42 | semidirect |
| 87. C42×C5 | C42 | semidirect |
| 89. C2×C4×D4 | C4×C5 | semidirect |
| 92. #390 | C4×C5 | semidirect |
| 96. #382 | C4×C5 | semidirect |
| 98. #376 | C4×C5 | semidirect |
| 99. #353 | C4×C5 | semidirect |
| 162. #99 | C2×C4×C5 | semidirect |
| 201. C2×D4 | C42×C5 | semidirect |
| 229. C42 | C42×C5 | semidirect |
| 277. C5 | #12628 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2328 | 2 |
| C2×C5×#353 | 2 |
| C4×C5×#99 | 2 |
| C5×#1393 | 2 |
| #12628 | 5 |