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×#127 | C2 |
| hypercenter | #127 | D5 |
| hypocenter | C5 | #535 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ #127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#711 | C2 | semidirect |
| 2. C2×D4×D5 | C2 | semidirect |
| 3. C5×#127 | C2 | semidirect |
| 4. #4086 | C2 | semidirect |
| 5. #4085 | C2 | semidirect |
| 6. #4083 | C2 | semidirect |
| 7. #4082 | C2 | semidirect |
| 8. #4021 | C2 | semidirect |
| 9. #4018 | C2 | semidirect |
| 12. C2×C5×D4 | C22 | semidirect |
| 13. C2×C5×D4 | C22 | semidirect |
| 16. C2×C22⋊D5 | C22 | semidirect |
| 17. C22×Dic5 | C22 | semidirect |
| 22. C2×Dic10 | C22 | semidirect |
| 23. C42×C5 | C22 | semidirect |
| 24. C22⋊Dic5 | C22 | semidirect |
| 26. #685 | C22 | semidirect |
| 27. #683 | C22 | semidirect |
| 28. C4×Dic5 | C22 | semidirect |
| 49. C4×D5 | D4 | semidirect |
| 54. #127 | D5 | semidirect |
| 84. C2×D4 | C2×D5 | semidirect |
| 85. C2×D4 | C2×D5 | semidirect |
| 93. C42 | C2×D5 | semidirect |
| 121. C5 | #535 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#711 | 2 |
| C2×D4×D5 | 2 |
| C5×#127 | 2 |
| #4086 | 2 |
| #4085 | 2 |
| #4083 | 2 |
| #4082 | 2 |
| #4021 | 2 |
| #4018 | 2 |
| #535 | 5 |