Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
286 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 286 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 | C23 | C22×D5 |
| commutator | C22×C5 | C22×C4 |
| Fitting | C23×C4×C5 | C2 |
| socle, cosocle | C23×C5 | C23 |
| prime radical | C22×C22⋊D5 | C2 |
| hypercenter | C23×C4 | D5 |
| hypocenter | C5 | #386 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ C23×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C4×C5 | C2 | semidirect |
| 3. C2×C22⋊Dic5 | C2 | semidirect |
| 4. C2×#685 | C2 | semidirect |
| 5. #3963 | C2 | semidirect |
| 13. C2×C22⋊D5 | C4 | semidirect |
| 29. C22×D5 | C2×C4 | semidirect |
| 33. C2×C4×C5 | D4 | semidirect |
| 40. C2×Dic5 | C2×C4 | semidirect |
| 42. C23×C4 | D5 | semidirect |
| 50. C22×C5 | C22⋊C4 | semidirect |
| 104. C2×C4 | C22⋊D5 | semidirect |
| 105. C5 | #386 | semidirect |
| 115. C22 | #685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×C5 | 2 |
| C22×C22⋊D5 | 2 |
| C2×C22⋊Dic5 | 2 |
| C2×#685 | 2 |
| #3963 | 2 |
| #386 | 5 |