Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 99 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 | C2×C5 | C2×C42 |
| Fitting | C5×#95 | C2 |
| socle, cosocle | C23×C5 | C23 |
| prime radical | C23×D5 | C22 |
| hypercenter | #95 | D5 |
| hypocenter | C5 | C4×C22⋊C4 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C4×Dic5 | C2 | semidirect |
| 4. C5×#95 | C2 | semidirect |
| 5. #3963 | C2 | semidirect |
| 12. C2×C4×D5 | C4 | semidirect |
| 13. #685 | C4 | semidirect |
| 26. C2×C4×C5 | C2×C4 | semidirect |
| 30. C2×Dic5 | C2×C4 | semidirect |
| 37. #95 | D5 | semidirect |
| 47. C2×D5 | C42 | semidirect |
| 51. Dic5 | C22⋊C4 | semidirect |
| 83. C2×C4 | C4×D5 | semidirect |
| 84. C5 | C4×C22⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D5 | 2 |
| C2×#685 | 2 |
| C2×C4×Dic5 | 2 |
| C5×#95 | 2 |
| #3963 | 2 |
| C4×C22⋊C4 | 5 |