Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1130 conjugacy classes of subgroups; only the 366 normal subgroups are shown.
This group has 1130 conjugacy classes of subgroups — too many to draw. Only its 366 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 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C5 |
| Frattini, cosocle | C24 | C24×C5 |
| prime radical | C25×C5 | C23 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C22×C5×C22⋊C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C5×#1996 | C2 | semidirect |
| 6. C2×C5×C22⋊Q8 | C4 | semidirect |
| 15. #21827 | C5 | direct (N × H) |
| 38. #1996 | C2×C5 | semidirect |
| 65. C2×C22⋊Q8 | C4×C5 | semidirect |
| 181. C5 | #21827 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#543 | 2 |
| C5×#2312 | 2 |
| C5×#1996 | 2 |
| C5×#1819 | 2 |
| #21827 | 5 |