Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
360 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 360 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 | C4×C5 | #418 |
| commutator | C2×C8 | C22×C4×C5 |
| Frattini, cosocle | C4×C8 | C23×C5 |
| socle | C2×C5 | #1490 |
| prime radical | C5×#575 | C4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C5 ◁ C2×C5×C8 ◁ C4×C5×M16 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#2165 | C2 | semidirect |
| 3. C5×#1455 | C2 | semidirect |
| 4. C5×#1336 | C2 | semidirect |
| 5. C5×#1335 | C2 | semidirect |
| 16. C5×#364 | C22 | semidirect |
| 20. C5×#322 | C22 | semidirect |
| 21. C5×C82 | C22 | semidirect |
| 22. #11669 | C5 | direct (N × H) |
| 50. #2165 | C2×C5 | semidirect |
| 51. #1455 | C2×C5 | semidirect |
| 52. #1336 | C2×C5 | semidirect |
| 53. #1335 | C2×C5 | semidirect |
| 65. C5×Q16 | M16 | semidirect |
| 69. C5×D8 | M16 | semidirect |
| 100. #364 | C22×C5 | semidirect |
| 104. #322 | C22×C5 | semidirect |
| 105. C82 | C22×C5 | semidirect |
| 179. Q16 | C5×M16 | semidirect |
| 183. D8 | C5×M16 | semidirect |
| 233. C5 | #11669 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2956 | 2 |
| C5×#2165 | 2 |
| C5×#1455 | 2 |
| C5×#1336 | 2 |
| C5×#1335 | 2 |
| #11669 | 5 |