Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
216 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 216 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 | C5×C16 | D8 |
| commutator | C8 | C22×C5×C8 |
| Frattini, cosocle | C4×C8 | C23×C5 |
| socle | C2×C5 | C8×D8 |
| prime radical | C5×#508 | C4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C5×C16 ◁ C2×C5×C16 ◁ C4×C5×C16 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#2170 | C2 | semidirect |
| 3. C5×#1373 | C2 | semidirect |
| 4. C5×#1335 | C2 | semidirect |
| 5. C5×C8×C16 | C2 | semidirect |
| 16. #12046 | C5 | direct (N × H) |
| 19. C5×Q32 | C8 | semidirect |
| 20. C5×SD32 | C8 | semidirect |
| 21. C5×D16 | C8 | semidirect |
| 34. #2170 | C2×C5 | semidirect |
| 35. #1373 | C2×C5 | semidirect |
| 36. #1335 | C2×C5 | semidirect |
| 37. C8×C16 | C2×C5 | semidirect |
| 80. Q32 | C5×C8 | semidirect |
| 81. SD32 | C5×C8 | semidirect |
| 82. D16 | C5×C8 | semidirect |
| 133. C5 | #12046 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2178 | 2 |
| C5×#2170 | 2 |
| C5×#1373 | 2 |
| C5×#1335 | 2 |
| C5×C8×C16 | 2 |
| #12046 | 5 |