Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
228 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 107 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, socle, cosocle | C22×C5 | C24 |
| Fitting | C2×C5×C4⋊C4 | C2 |
| prime radical | C2×C22⋊D5 | C22 |
| hypercenter | C2×C4⋊C4 | D5 |
| hypocenter | C5 | #554 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C2×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×C4⋊C4 | C2 | semidirect |
| 4. #4070 | C2 | semidirect |
| 5. #4070 | C2 | semidirect |
| 6. #4043 | C2 | semidirect |
| 7. #4042 | C2 | semidirect |
| 8. D5×C4⋊C4 | C2 | semidirect |
| 9. #4035 | C2 | semidirect |
| 10. #4034 | C2 | semidirect |
| 11. #4033 | C2 | semidirect |
| 44. C22⋊D5 | Q8 | semidirect |
| 64. C2×C4⋊C4 | D5 | semidirect |
| 127. C5 | #554 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C4⋊C4 | 2 |
| C4×C22⋊D5 | 2 |
| #4070 | 2 |
| #4043 | 2 |
| #4042 | 2 |
| D5×C4⋊C4 | 2 |
| #4035 | 2 |
| #4034 | 2 |
| #4033 | 2 |
| #554 | 5 |