Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
190 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D5 |
| commutator | C22×C5 | C22×C4 |
| Fitting | C2×C42×C5 | C2 |
| socle, cosocle | C23×C5 | C23 |
| prime radical | C23×D5 | C22 |
| hypercenter | C2×C42 | D5 |
| hypocenter | C5 | #388 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C42×C5 | C2 | semidirect |
| 5. C2×#683 | C2 | semidirect |
| 6. #3963 | C2 | semidirect |
| 7. #3963 | C2 | semidirect |
| 18. #685 | C4 | semidirect |
| 51. C2×C42 | D5 | semidirect |
| 120. C5 | #388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×C5 | 2 |
| C2×#685 | 2 |
| C2×#683 | 2 |
| #3963 | 2 |
| #388 | 5 |