Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
2816 conjugacy classes of subgroups; only the 601 normal subgroups are shown.
This group has 2816 conjugacy classes of subgroups — too many to draw. Only its 601 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 | C24×D15 |
| commutator, socle, cosocle | C22×C3×C5 | C25 |
| Fitting | C3×C5×H(3,𝔽4) | C2 |
| hypercenter | H(3,𝔽4) | D15 |
| hypocenter | C3×C5 | C2×H(3,𝔽4) |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ H(3,𝔽4) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×H(3,𝔽4) | C2 | semidirect |
| 2. #11756442 | C2 | semidirect |
| 3. D15×#124 | C2 | semidirect |
| 4. #11756353 | C2 | semidirect |
| 5. D15×#120 | C2 | semidirect |
| 7. C24×D15 | C22 | semidirect |
| 8. C2×Q8×D15 | C22 | semidirect |
| 10. C3×C5×#124 | C22 | semidirect |
| 11. C3×C5×#120 | C22 | semidirect |
| 12. #91842 | C22 | semidirect |
| 13. #91836 | C22 | semidirect |
| 14. #91826 | C22 | semidirect |
| 15. #91825 | C22 | semidirect |
| 16. #91774 | C22 | semidirect |
| 17. #91771 | C22 | semidirect |
| 18. C22⋊C4×D15 | C22 | semidirect |
| 19. #91764 | C22 | semidirect |
| 20. C42×D15 | C22 | semidirect |
| 22. C5×H(3,𝔽4) | D3 | semidirect |
| 27. C24×C3×C5 | C23 | semidirect |
| 30. C23×D15 | C23 | semidirect |
| 31. C2×C3×C5×Q8 | C23 | semidirect |
| 38. C2×Dic30 | C23 | semidirect |
| 39. C3×C5×C22⋊C4 | C23 | semidirect |
| 40. C3×C42×C5 | C23 | semidirect |
| 41. #6719 | C23 | semidirect |
| 42. #6714 | C23 | semidirect |
| 43. C4×Dic15 | C23 | semidirect |
| 44. C3×H(3,𝔽4) | D5 | semidirect |
| 52. C5×#124 | C2×D3 | semidirect |
| 53. C5×#120 | C2×D3 | semidirect |
| 82. C3×#124 | C2×D5 | semidirect |
| 83. C3×#120 | C2×D5 | semidirect |
| 93. C24×C5 | C22×D3 | semidirect |
| 97. C2×C5×Q8 | C22×D3 | semidirect |
| 105. C5×C22⋊C4 | C22×D3 | semidirect |
| 106. C42×C5 | C22×D3 | semidirect |
| 112. H(3,𝔽4) | D15 | direct (N × H) |
| 124. C24×C3 | C22×D5 | semidirect |
| 128. C2×C3×Q8 | C22×D5 | semidirect |
| 136. C3×C22⋊C4 | C22×D5 | semidirect |
| 137. C3×C42 | C22×D5 | semidirect |
| 163. #124 | C2×D15 | semidirect |
| 167. #120 | C2×D15 | semidirect |
| 173. D15 | H(3,𝔽4) | direct (N × H) |
| 201. C24 | C22×D15 | semidirect |
| 204. C2×Q8 | C22×D15 | semidirect |
| 212. C22⋊C4 | C22×D15 | semidirect |
| 214. C42 | C22×D15 | semidirect |
| 215. C3×C5 | C2×H(3,𝔽4) | semidirect |
| 248. C5 | D3×H(3,𝔽4) | semidirect |
| 258. C3 | D5×H(3,𝔽4) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×H(3,𝔽4) | 2 |
| #11756442 | 2 |
| D15×#124 | 2 |
| #11756353 | 2 |
| D15×#120 | 2 |
| D5×H(3,𝔽4) | 3 |
| D3×H(3,𝔽4) | 5 |