Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
540 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 126 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 | C22×C4 | C22×C4×C5 |
| Frattini, cosocle | C22×Q8 | C23×C5 |
| prime radical | C2×C5×#127 | C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C4×C5×Q8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C5×#355 | C2 | semidirect |
| 3. C5×#1801 | C2 | semidirect |
| 4. C4×C5×#101 | C2 | semidirect |
| 21. #13226 | C5 | direct (N × H) |
| 50. C5×#101 | D4 | semidirect |
| 55. C2×#355 | C2×C5 | semidirect |
| 56. #1801 | C2×C5 | semidirect |
| 57. C4×#101 | C2×C5 | semidirect |
| 184. #101 | C5×D4 | semidirect |
| 209. C4×C5 | #355 | semidirect |
| 298. C5 | #13226 | direct (N × H) |
| 320. C4 | C5×#355 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2548 | 2 |
| C2×C5×#355 | 2 |
| C5×#1801 | 2 |
| C4×C5×#101 | 2 |
| #13226 | 5 |