Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
290 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C5 | #353 |
| commutator | C42 | C42×C5 |
| Frattini, cosocle | #532 | C22×C5 |
| socle | C2×C5 | #1393 |
| prime radical | C5×#532 | C22 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C5 ◁ C2×C4×C5 ◁ C22×C4×C5 ◁ C5×#532 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C5×#423 | C4 | semidirect |
| 10. C43×C5 | C4 | semidirect |
| 11. C5×#356 | C4 | semidirect |
| 14. C5×#353 | C4 | semidirect |
| 15. #7497 | C5 | direct (N × H) |
| 75. #423 | C4×C5 | semidirect |
| 80. C43 | C4×C5 | semidirect |
| 81. #356 | C4×C5 | semidirect |
| 84. #353 | C4×C5 | semidirect |
| 217. C5 | #7497 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2132 | 2 |
| C5×#2126 | 2 |
| C5×#1962 | 2 |
| #7497 | 5 |