Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
386 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 58 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 | #2196 |
| commutator, Frattini, cosocle | #124 | C23×C5 |
| prime radical | C5×#3288 | C2 |
| LCS | G ▷ #124 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C5 ◁ C22×C5 ◁ C2×C4×C5 ◁ C5×#124 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#2203 | C2 | semidirect |
| 3. C5×#2201 | C2 | semidirect |
| 4. C5×#1657 | C2 | semidirect |
| 5. C5×#1406 | C2 | semidirect |
| 6. C5×#1404 | C2 | semidirect |
| 7. C5×#1403 | C2 | semidirect |
| 10. C5×#563 | C22 | semidirect |
| 22. C5×#355 | C22 | semidirect |
| 23. C5×#354 | C22 | semidirect |
| 26. C5×#329 | C22 | semidirect |
| 27. #13679 | C5 | direct (N × H) |
| 72. #2203 | C2×C5 | semidirect |
| 73. #2201 | C2×C5 | semidirect |
| 74. #1657 | C2×C5 | semidirect |
| 75. #1406 | C2×C5 | semidirect |
| 76. #1404 | C2×C5 | semidirect |
| 77. #1403 | C2×C5 | semidirect |
| 139. #563 | C22×C5 | semidirect |
| 151. #355 | C22×C5 | semidirect |
| 152. #354 | C22×C5 | semidirect |
| 155. #329 | C22×C5 | semidirect |
| 359. C5 | #13679 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3288 | 2 |
| C5×#2203 | 2 |
| C5×#2201 | 2 |
| C5×#1657 | 2 |
| C5×#1406 | 2 |
| C5×#1404 | 2 |
| C5×#1403 | 2 |
| #13679 | 5 |