Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
368 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 82 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 | #447 |
| commutator, Frattini, cosocle | C4×C8 | C23×C5 |
| prime radical | C5×#3277 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#436 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#2251 | C2 | semidirect |
| 3. C5×#2209 | C2 | semidirect |
| 4. C5×#1689 | C2 | semidirect |
| 5. C5×#1360 | C2 | semidirect |
| 6. C5×#1334 | C2 | semidirect |
| 7. C5×#1330 | C2 | semidirect |
| 27. #12327 | C5 | direct (N × H) |
| 67. #2251 | C2×C5 | semidirect |
| 68. #2209 | C2×C5 | semidirect |
| 69. #1689 | C2×C5 | semidirect |
| 70. #1360 | C2×C5 | semidirect |
| 71. #1334 | C2×C5 | semidirect |
| 72. #1330 | C2×C5 | semidirect |
| 309. C5 | #12327 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3277 | 2 |
| C5×#2251 | 2 |
| C5×#2209 | 2 |
| C5×#1689 | 2 |
| C5×#1360 | 2 |
| C5×#1334 | 2 |
| C5×#1330 | 2 |
| #12327 | 5 |