Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
346 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 346 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, Frattini | C22 | C23×D5 |
| commutator, socle, cosocle | C22×C5 | C24 |
| Fitting | C22×C5×D4 | C2 |
| hypercenter | C22×D4 | D5 |
| hypocenter | C5 | #534 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C5×D4 | C2 | semidirect |
| 2. C22×C22⋊D5 | C2 | semidirect |
| 3. #4099 | C2 | semidirect |
| 4. C2×C22⋊Dic5 | C2 | semidirect |
| 5. #4085 | C2 | semidirect |
| 6. #4083 | C2 | semidirect |
| 7. #4081 | C2 | semidirect |
| 8. #4075 | C2 | semidirect |
| 10. C24×C5 | C22 | semidirect |
| 11. C23×D5 | C22 | semidirect |
| 14. C2×C5×D4 | C22 | semidirect |
| 15. C22×C4×C5 | C22 | semidirect |
| 18. C2×C22⋊D5 | C22 | semidirect |
| 19. C2×C22⋊D5 | C22 | semidirect |
| 20. C22×Dic5 | C22 | semidirect |
| 21. C22×Dic5 | C22 | semidirect |
| 22. C22⋊Dic5 | C22 | semidirect |
| 23. C22⋊Dic5 | C22 | semidirect |
| 24. C22⋊Dic5 | C22 | semidirect |
| 25. #685 | C22 | semidirect |
| 26. #683 | C22 | semidirect |
| 31. C23×C5 | D4 | semidirect |
| 51. C22×D4 | D5 | semidirect |
| 77. C24 | C2×D5 | semidirect |
| 84. C2×D4 | C2×D5 | semidirect |
| 87. C22×C4 | C2×D5 | semidirect |
| 106. C23 | C22⋊D5 | semidirect |
| 122. C5 | #534 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D4 | 2 |
| C22×C22⋊D5 | 2 |
| #4099 | 2 |
| C2×C22⋊Dic5 | 2 |
| #4085 | 2 |
| #4083 | 2 |
| #4081 | 2 |
| #4075 | 2 |
| #534 | 5 |