Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 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×#121 | C2 |
| hypercenter | #121 | D5 |
| hypocenter | C5 | #525 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#711 | C2 | semidirect |
| 2. C22×C4×D5 | C2 | semidirect |
| 3. C5×#121 | C2 | semidirect |
| 4. #4084 | C2 | semidirect |
| 5. #4083 | C2 | semidirect |
| 6. D4×Dic5 | C2 | semidirect |
| 7. #4070 | C2 | semidirect |
| 8. #4043 | C2 | semidirect |
| 9. #4038 | C2 | semidirect |
| 10. #4029 | C2 | semidirect |
| 11. #4027 | C2 | semidirect |
| 14. C2×C5×D4 | C22 | semidirect |
| 19. C22×Dic5 | C22 | semidirect |
| 26. C2×Dic10 | C22 | semidirect |
| 27. C5×C4⋊C4 | C22 | semidirect |
| 28. C5×C22⋊C4 | C22 | semidirect |
| 30. C22⋊Dic5 | C22 | semidirect |
| 33. C4⋊Dic5 | C22 | semidirect |
| 34. C4⋊Dic5 | C22 | semidirect |
| 35. #683 | C22 | semidirect |
| 36. C4×Dic5 | C22 | semidirect |
| 62. C4×D5 | D4 | semidirect |
| 70. #121 | D5 | semidirect |
| 80. C22×C5 | #41 | semidirect |
| 88. C2×D5 | #41 | semidirect |
| 102. C2×D4 | C2×D5 | semidirect |
| 114. C4⋊C4 | C2×D5 | semidirect |
| 119. C22⋊C4 | C2×D5 | semidirect |
| 154. C5 | #525 | semidirect |
| 167. C22 | #711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#711 | 2 |
| C22×C4×D5 | 2 |
| C5×#121 | 2 |
| #4084 | 2 |
| #4083 | 2 |
| D4×Dic5 | 2 |
| #4070 | 2 |
| #4043 | 2 |
| #4038 | 2 |
| #4029 | 2 |
| #4027 | 2 |
| #525 | 5 |