Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
334 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
| hypercenter | C2×C22⋊C4 | D5 |
| hypocenter | C5 | #546 |
| 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. C22×C22⋊D5 | C2 | semidirect |
| 2. C2×#709 | C2 | semidirect |
| 3. C2×C5×C22⋊C4 | C2 | semidirect |
| 4. #4099 | C2 | semidirect |
| 5. #4076 | C2 | semidirect |
| 6. #4075 | C2 | semidirect |
| 7. C4×C22⋊D5 | C2 | semidirect |
| 8. #4031 | C2 | semidirect |
| 9. #4030 | C2 | semidirect |
| 10. #4030 | C2 | semidirect |
| 11. #4029 | C2 | semidirect |
| 12. #4028 | C2 | semidirect |
| 13. #4027 | C2 | semidirect |
| 14. D5×C22⋊C4 | C2 | semidirect |
| 15. #4024 | C2 | semidirect |
| 18. C22×C4×C5 | C22 | semidirect |
| 19. C22×C4×C5 | C22 | semidirect |
| 26. C2×C22⋊D5 | C22 | semidirect |
| 27. C2×C22⋊D5 | C22 | semidirect |
| 30. C2×D20 | C22 | semidirect |
| 31. C2×D20 | C22 | semidirect |
| 32. C2×C4×D5 | C22 | semidirect |
| 33. C2×C4×D5 | C22 | semidirect |
| 34. C2×C4×D5 | C22 | semidirect |
| 35. C2×Dic10 | C22 | semidirect |
| 38. C5×C22⋊C4 | C22 | semidirect |
| 39. C5×C22⋊C4 | C22 | semidirect |
| 41. C22⋊Dic5 | C22 | semidirect |
| 42. C22⋊Dic5 | C22 | semidirect |
| 43. #685 | C22 | semidirect |
| 44. #685 | C22 | semidirect |
| 45. #685 | C22 | semidirect |
| 46. #685 | C22 | semidirect |
| 47. #685 | C22 | semidirect |
| 48. C4⋊Dic5 | C22 | semidirect |
| 49. #683 | C22 | semidirect |
| 50. #683 | C22 | semidirect |
| 51. #683 | C22 | semidirect |
| 52. C4×Dic5 | C22 | semidirect |
| 78. C22⋊D5 | D4 | semidirect |
| 105. C2×C22⋊C4 | D5 | semidirect |
| 115. C22×C5 | #41 | semidirect |
| 154. C22×C4 | C2×D5 | semidirect |
| 155. C22×C4 | C2×D5 | semidirect |
| 170. C22⋊C4 | C2×D5 | semidirect |
| 171. C22⋊C4 | C2×D5 | semidirect |
| 219. C5 | #546 | semidirect |
| 238. C22 | #709 | 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×#709 | 2 |
| C2×C5×C22⋊C4 | 2 |
| #4099 | 2 |
| #4076 | 2 |
| #4075 | 2 |
| C4×C22⋊D5 | 2 |
| #4031 | 2 |
| #4030 | 2 |
| #4029 | 2 |
| #4028 | 2 |
| #4027 | 2 |
| D5×C22⋊C4 | 2 |
| #4024 | 2 |
| #546 | 5 |