Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
158 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C16 | C22×D5 |
| commutator, socle, prime radical | C22×C5 | C22×C16 |
| Fitting | C5×C4⋊C32 | C2 |
| cosocle | C2×C5×C16 | C23 |
| hypercenter | C4⋊C32 | D5 |
| hypocenter | C5 | #13660 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C2×C16 ◁ C4⋊C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 34. #3926 | Q8 | semidirect |
| 138. C5 | #13660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×Dic10 | 2 |
| C5×C4⋊C32 | 2 |
| #10598081 | 2 |
| #10598080 | 2 |
| Dic5×C32 | 2 |
| #10597999 | 2 |
| #13660 | 5 |