Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
218 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 134 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C5×C16 | D4 |
| commutator | C4 | C22×C5×C16 |
| Frattini, cosocle | C4×C8 | C23×C5 |
| socle, prime radical | C22×C5 | C8×D4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C5×C16 ◁ C4×C5×C16 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 16. C16×Q16 | C5 | direct (N × H) |
| 37. C5×Q16 | C16 | direct (N × H) |
| 51. C5×C16 | Q16 | direct (N × H) |
| 99. Q16 | C5×C16 | direct (N × H) |
| 113. C16 | C5×Q16 | direct (N × H) |
| 131. C5 | C16×Q16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×C16 | 2 |
| C5×C8×Q16 | 2 |
| C5×#1370 | 2 |
| C5×Q8⋊C16 | 2 |
| C5×C8×C16 | 2 |
| C16×Q16 | 5 |