Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
278 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 278 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, socle | C2×C5 | #1390 |
| commutator | C2×Q8 | C42×C5 |
| Frattini, cosocle | #532 | C22×C5 |
| prime radical | C5×#532 | C22 |
| LCS | G ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×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 |
|---|---|---|
| 4. C5×#568 | C4 | semidirect |
| 9. C5×#410 | C4 | semidirect |
| 10. C5×#354 | C4 | semidirect |
| 13. C5×#333 | C4 | semidirect |
| 15. #7482 | C5 | direct (N × H) |
| 74. #568 | C4×C5 | semidirect |
| 79. #410 | C4×C5 | semidirect |
| 80. #354 | C4×C5 | semidirect |
| 83. #333 | C4×C5 | semidirect |
| 220. C5 | #7482 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2126 | 2 |
| C5×#1884 | 2 |
| C5×#1560 | 2 |
| #7482 | 5 |