Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
334 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 103 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 | C5×#120 | C2 |
| hypercenter | #120 | D5 |
| hypocenter | C5 | #535 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ #120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C22⋊D5 | C2 | semidirect |
| 2. C2×#711 | C2 | semidirect |
| 3. C5×#120 | C2 | semidirect |
| 4. #4099 | C2 | semidirect |
| 5. #4086 | C2 | semidirect |
| 6. #4085 | C2 | semidirect |
| 7. #4083 | C2 | semidirect |
| 8. #4031 | C2 | semidirect |
| 9. #4030 | C2 | semidirect |
| 10. #4028 | C2 | semidirect |
| 11. #4023 | C2 | semidirect |
| 15. C2×C5×D4 | C22 | semidirect |
| 20. C2×C22⋊D5 | C22 | semidirect |
| 21. C2×C22⋊D5 | C22 | semidirect |
| 22. C2×C22⋊D5 | C22 | semidirect |
| 24. C22×Dic5 | C22 | semidirect |
| 26. C2×D20 | C22 | semidirect |
| 27. C2×C4×D5 | C22 | semidirect |
| 28. C2×Dic10 | C22 | semidirect |
| 30. C5×C22⋊C4 | C22 | semidirect |
| 32. C22⋊Dic5 | C22 | semidirect |
| 33. #685 | C22 | semidirect |
| 34. #685 | C22 | semidirect |
| 35. #683 | C22 | semidirect |
| 36. C4×Dic5 | C22 | semidirect |
| 58. C2×Dic5 | D4 | semidirect |
| 75. #120 | D5 | semidirect |
| 111. C2×D4 | C2×D5 | semidirect |
| 121. C22⋊C4 | C2×D5 | semidirect |
| 158. C5 | #535 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊D5 | 2 |
| C2×#711 | 2 |
| C5×#120 | 2 |
| #4099 | 2 |
| #4086 | 2 |
| #4085 | 2 |
| #4083 | 2 |
| #4031 | 2 |
| #4030 | 2 |
| #4028 | 2 |
| #4023 | 2 |
| #535 | 5 |