Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
182 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 42 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 | C2×M16 | C2×C4×C5 |
| Frattini, cosocle | #407 | C22×C5 |
| socle | C2×C5 | #1352 |
| prime radical | C24×C5 | Q16 |
| LCS | G ▷ C2×M16 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C5 ◁ C2×C4×C5 ◁ C22×C4×C5 ◁ C5×#407 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. #7433 | C5 | direct (N × H) |
| 142. C5 | #7433 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2091 | 2 |
| C5×#1320 | 2 |
| C5×#1298 | 2 |
| #7433 | 5 |