Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
1324 conjugacy classes of subgroups; only the 318 normal subgroups are shown.
This group has 1324 conjugacy classes of subgroups — too many to draw. Only its 318 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23×C5 | C22×D3 |
| commutator, cosocle | C22×C3 | C24×C5 |
| Frattini | C22 | C23×C5×D3 |
| Fitting | C25×C3×C5 | C2 |
| socle | C23×C3×C5 | C23 |
| hypercenter | C25×C5 | D3 |
| hypocenter | C3 | C2×C5×#120 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C23×C5 ◁ C25×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C25×C3×C5 | C2 | semidirect |
| 2. C22×C5×#67 | C2 | semidirect |
| 3. C5×#953 | C2 | direct (N × H) |
| 4. C2×C5×#217 | C2 | semidirect |
| 8. C24×C3×C5 | C22 | semidirect |
| 9. C23×C5×D3 | C22 | semidirect |
| 11. C2×C5×#67 | C22 | semidirect |
| 12. C22×C5×Dic3 | C22 | semidirect |
| 13. C5×#217 | C22 | semidirect |
| 14. C2×#953 | C5 | direct (N × H) |
| 15. C25×C5 | D3 | semidirect |
| 22. C23×C3×C5 | D4 | semidirect |
| 26. C22×C5×D3 | C23 | semidirect |
| 29. C2×C5×Dic3 | C23 | semidirect |
| 30. C25×C3 | C2×C5 | semidirect |
| 31. C22×#67 | C2×C5 | semidirect |
| 32. #953 | C2×C5 | direct (N × H) |
| 33. C2×#217 | C2×C5 | semidirect |
| 37. C24×C5 | C2×D3 | semidirect |
| 47. C22×C3×C5 | C2×D4 | semidirect |
| 54. C24×C3 | C22×C5 | semidirect |
| 55. C23×D3 | C22×C5 | semidirect |
| 57. C2×#67 | C22×C5 | semidirect |
| 58. C22×Dic3 | C22×C5 | semidirect |
| 59. #217 | C22×C5 | semidirect |
| 65. C23×C5 | #67 | semidirect |
| 71. C25 | C5×D3 | semidirect |
| 76. C2×C3×C5 | #120 | semidirect |
| 82. C23×C3 | C5×D4 | semidirect |
| 86. C22×D3 | C23×C5 | semidirect |
| 89. C2×Dic3 | C23×C5 | semidirect |
| 96. C22×C5 | C2×#67 | semidirect |
| 102. C24 | C2×C5×D3 | semidirect |
| 107. C3×C5 | C2×#120 | semidirect |
| 112. C22×C3 | C2×C5×D4 | semidirect |
| 119. C2×C5 | #953 | direct (N × H) |
| 126. C23 | C5×#67 | semidirect |
| 133. C2×C3 | C5×#120 | semidirect |
| 136. C5 | C2×#953 | direct (N × H) |
| 143. C22 | C2×C5×#67 | semidirect |
| 146. C3 | C2×C5×#120 | semidirect |
| 149. C2 | C5×#953 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C3×C5 | 2 |
| C22×C5×#67 | 2 |
| C5×#953 | 2 |
| C2×C5×#217 | 2 |
| C2×C5×#120 | 3 |
| C2×#953 | 5 |