Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
520 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 131 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×D15 |
| commutator, socle, cosocle | C22×C3×C5 | C24 |
| Fitting | C3×C5×#120 | C2 |
| hypercenter | #120 | D15 |
| hypocenter | C3×C5 | H(3,𝔽4) |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ #120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×#120 | C2 | semidirect |
| 2. #91842 | C2 | semidirect |
| 3. #91826 | C2 | semidirect |
| 4. #91825 | C2 | semidirect |
| 5. #91774 | C2 | semidirect |
| 7. C24×C3×C5 | C22 | semidirect |
| 8. C23×D15 | C22 | semidirect |
| 11. C2×Dic30 | C22 | semidirect |
| 12. C3×C5×C22⋊C4 | C22 | semidirect |
| 13. #6719 | C22 | semidirect |
| 14. #6719 | C22 | semidirect |
| 15. #6714 | C22 | semidirect |
| 16. C4×Dic15 | C22 | semidirect |
| 18. C5×#120 | D3 | semidirect |
| 33. C3×#120 | D5 | semidirect |
| 38. C24×C5 | C2×D3 | semidirect |
| 43. C5×C22⋊C4 | C2×D3 | semidirect |
| 58. C24×C3 | C2×D5 | semidirect |
| 63. C3×C22⋊C4 | C2×D5 | semidirect |
| 82. #120 | D15 | semidirect |
| 107. C24 | C2×D15 | semidirect |
| 114. C22⋊C4 | C2×D15 | semidirect |
| 116. C3×C5 | H(3,𝔽4) | semidirect |
| 144. C5 | #5594 | semidirect |
| 154. C3 | #65928 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#120 | 2 |
| #91842 | 2 |
| #91826 | 2 |
| #91825 | 2 |
| #91774 | 2 |
| #65928 | 3 |
| #5594 | 5 |