Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
266 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22⋊D5 |
| commutator, cosocle | C4×C5 | C24 |
| Frattini | C4 | C23×D5 |
| Fitting | C2×C5×#41 | C2 |
| socle | C22×C5 | C2×D4 |
| hypercenter | C2×#41 | D5 |
| hypocenter | C5 | C2×#135 |
| LCS | G ▷ C4×C5 ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×#41 | C2 | semidirect |
| 2. C2×#709 | C2 | semidirect |
| 3. #4096 | C2 | direct (N × H) |
| 4. C2×#689 | C2 | semidirect |
| 5. C2×#688 | C2 | semidirect |
| 6. C2×#687 | C2 | semidirect |
| 7. C2×#686 | C2 | semidirect |
| 8. C22×#168 | C2 | semidirect |
| 10. C5×#41 | C22 | semidirect |
| 18. #709 | C22 | semidirect |
| 22. #689 | C22 | semidirect |
| 23. #688 | C22 | semidirect |
| 24. #687 | C22 | semidirect |
| 25. #686 | C22 | semidirect |
| 28. C2×#168 | C22 | semidirect |
| 54. C2×#41 | D5 | semidirect |
| 76. #41 | C2×D5 | semidirect |
| 95. C2×C5 | #135 | semidirect |
| 121. C5 | C2×#135 | semidirect |
| 137. C2 | #4096 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#41 | 2 |
| C2×#709 | 2 |
| #4096 | 2 |
| C2×#689 | 2 |
| C2×#688 | 2 |
| C2×#687 | 2 |
| C2×#686 | 2 |
| C22×#168 | 2 |
| C2×#135 | 5 |