Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
386 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 94 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 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C5 |
| prime radical | C5×#532 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#1843 | C2 | semidirect |
| 3. C5×#1552 | C2 | semidirect |
| 5. C5×#1506 | C2 | semidirect |
| 7. C5×#1290 | C2 | semidirect |
| 27. #10514 | C5 | direct (N × H) |
| 66. #1843 | C2×C5 | semidirect |
| 67. #1552 | C2×C5 | semidirect |
| 69. #1506 | C2×C5 | semidirect |
| 71. #1290 | C2×C5 | semidirect |
| 291. C5 | #10514 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3246 | 2 |
| C5×#1843 | 2 |
| C5×#1552 | 2 |
| C5×#1551 | 2 |
| C5×#1506 | 2 |
| C5×#1505 | 2 |
| C5×#1290 | 2 |
| #10514 | 5 |