Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
294 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D5 |
| commutator | C2×C5 | C23×C4 |
| Fitting | C5×#117 | C2 |
| socle, cosocle | C22×C5 | C24 |
| prime radical | C2×#709 | C2 |
| hypercenter | #117 | D5 |
| hypocenter | C5 | #520 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#117 | C2 | semidirect |
| 3. C2×C4⋊Dic5 | C2 | semidirect |
| 4. #4038 | C2 | semidirect |
| 5. D5×C4⋊C4 | C2 | semidirect |
| 6. #4027 | C2 | semidirect |
| 7. C4×D20 | C2 | semidirect |
| 8. C4×Dic10 | C2 | semidirect |
| 12. #709 | C4 | semidirect |
| 29. C2×C4×C5 | C2×C4 | semidirect |
| 34. C22⋊D5 | C2×C4 | semidirect |
| 38. D20 | C2×C4 | semidirect |
| 40. C4×D5 | C2×C4 | semidirect |
| 41. Dic10 | C2×C4 | semidirect |
| 47. #117 | D5 | semidirect |
| 95. C2×C4 | C4×D5 | semidirect |
| 100. C5 | #520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#709 | 2 |
| C5×#117 | 2 |
| C2×C4⋊Dic5 | 2 |
| #4038 | 2 |
| D5×C4⋊C4 | 2 |
| #4027 | 2 |
| C4×D20 | 2 |
| C4×Dic10 | 2 |
| #520 | 5 |