Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
534 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C5 |
| prime radical | C5×#2819 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ C2×C42×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#1959 | C2 | semidirect |
| 3. C5×#1847 | C2 | semidirect |
| 4. C2×C5×#329 | C2 | semidirect |
| 5. C5×#1295 | C2 | semidirect |
| 20. #10424 | C5 | direct (N × H) |
| 47. C5×#97 | D4 | semidirect |
| 52. #1959 | C2×C5 | semidirect |
| 53. #1847 | C2×C5 | semidirect |
| 54. C2×#329 | C2×C5 | semidirect |
| 55. #1295 | C2×C5 | semidirect |
| 169. #97 | C5×D4 | semidirect |
| 272. C5 | #10424 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2819 | 2 |
| C5×#1959 | 2 |
| C5×#1847 | 2 |
| C2×C5×#329 | 2 |
| C5×#1295 | 2 |
| #10424 | 5 |