Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
356 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 70 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 | #1598 |
| commutator, Frattini, cosocle | C2×M16 | C23×C5 |
| LCS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C2×C5×M16 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#3259 | C2 | semidirect |
| 2. C5×#2190 | C2 | semidirect |
| 3. C5×#2053 | C2 | semidirect |
| 4. C5×#1339 | C2 | semidirect |
| 5. C5×#1328 | C2 | semidirect |
| 19. #12170 | C5 | direct (N × H) |
| 47. #3259 | C2×C5 | semidirect |
| 48. #2190 | C2×C5 | semidirect |
| 49. #2053 | C2×C5 | semidirect |
| 50. #1339 | C2×C5 | semidirect |
| 51. #1328 | C2×C5 | semidirect |
| 230. C5 | #12170 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3259 | 2 |
| C5×#2190 | 2 |
| C5×#2053 | 2 |
| C5×#1339 | 2 |
| C5×#1328 | 2 |
| #12170 | 5 |