Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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 | C2×C5×C22⋊C4 | C2 |
| prime radical | #4099 | C2 |
| hypercenter | C2×C22⋊C4 | D5 |
| hypocenter | C5 | #551 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×C22⋊C4 | C2 | semidirect |
| 3. C2×C22⋊Dic5 | C2 | semidirect |
| 4. #4075 | C2 | semidirect |
| 5. C4×C22⋊D5 | C2 | semidirect |
| 6. #4072 | C2 | semidirect |
| 7. #4070 | C2 | semidirect |
| 8. #4032 | C2 | semidirect |
| 9. #4031 | C2 | semidirect |
| 10. #4029 | C2 | semidirect |
| 11. #4027 | C2 | semidirect |
| 12. #4025 | C2 | semidirect |
| 13. #4025 | C2 | semidirect |
| 14. #4024 | C2 | semidirect |
| 15. #4023 | C2 | semidirect |
| 24. C2×C4×D5 | C22 | semidirect |
| 25. C2×Dic10 | C22 | semidirect |
| 37. #685 | C22 | semidirect |
| 38. #685 | C22 | semidirect |
| 39. #685 | C22 | semidirect |
| 40. C4⋊Dic5 | C22 | semidirect |
| 41. C4⋊Dic5 | C22 | semidirect |
| 42. C4⋊Dic5 | C22 | semidirect |
| 43. #683 | C22 | semidirect |
| 44. #683 | C22 | semidirect |
| 45. #683 | C22 | semidirect |
| 46. #683 | C22 | semidirect |
| 47. #683 | C22 | semidirect |
| 48. C4×Dic5 | C22 | semidirect |
| 49. C4×Dic5 | C22 | semidirect |
| 50. C4×Dic5 | C22 | semidirect |
| 93. C2×C22⋊C4 | D5 | semidirect |
| 188. C5 | #551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C22⋊C4 | 2 |
| #4099 | 2 |
| C2×C22⋊Dic5 | 2 |
| #4075 | 2 |
| C4×C22⋊D5 | 2 |
| #4072 | 2 |
| #4070 | 2 |
| #4032 | 2 |
| #4031 | 2 |
| #4029 | 2 |
| #4027 | 2 |
| #4025 | 2 |
| #4024 | 2 |
| #4023 | 2 |
| #551 | 5 |