Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
1324 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 1324 conjugacy classes of subgroups — too many to draw. Only its 224 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D3×D5 |
| commutator, cosocle | C22×C3×C5 | C24 |
| Frattini | C22 | C22×D3×D5 |
| Fitting | C24×C3×C5 | C22 |
| socle | C23×C3×C5 | C23 |
| hypercenter | C24 | D3×D5 |
| hypocenter | C3×C5 | C2×#120 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C23 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×C3×D5 | C2 | semidirect |
| 2. C22×#1220 | C2 | semidirect |
| 3. C22×#1202 | C2 | semidirect |
| 4. C2×C5×#217 | C2 | semidirect |
| 5. #91564 | C2 | direct (N × H) |
| 6. C2×#6665 | C2 | semidirect |
| 9. C23×D15 | C22 | semidirect |
| 13. C23×C3×D5 | C22 | semidirect |
| 15. C2×#1220 | C22 | semidirect |
| 16. C22×Dic15 | C22 | semidirect |
| 17. C22×C5×Dic3 | C22 | semidirect |
| 19. C2×#1202 | C22 | semidirect |
| 20. C5×#217 | C22 | semidirect |
| 21. #6665 | C22 | semidirect |
| 23. C24×D5 | D3 | semidirect |
| 30. C23×C3×C5 | D4 | semidirect |
| 35. C22×D15 | C23 | semidirect |
| 41. C22×C3×D5 | D4 | semidirect |
| 45. C2×Dic15 | C23 | semidirect |
| 47. C2×C5×Dic3 | C23 | semidirect |
| 54. C2×#217 | D5 | semidirect |
| 60. C23×D5 | C2×D3 | semidirect |
| 74. C22×C3×C5 | C2×D4 | semidirect |
| 83. C2×C3×D5 | C2×D4 | semidirect |
| 97. C22×Dic3 | C2×D5 | semidirect |
| 99. #217 | C2×D5 | semidirect |
| 101. C23×C5 | #67 | semidirect |
| 112. C22×D5 | #67 | semidirect |
| 127. C2×C3×C5 | #120 | semidirect |
| 140. C23×C3 | D20 | semidirect |
| 151. C2×Dic3 | C22×D5 | semidirect |
| 156. C22×C5 | C2×#67 | semidirect |
| 165. C2×D5 | C2×#67 | semidirect |
| 182. C3×C5 | C2×#120 | semidirect |
| 191. C22×C3 | C2×D20 | semidirect |
| 200. C2×C5 | #953 | semidirect |
| 216. C23 | #1202 | semidirect |
| 227. C2×C3 | #4028 | semidirect |
| 231. C5 | C2×#953 | semidirect |
| 243. C22 | C2×#1202 | semidirect |
| 248. C3 | C2×#4028 | semidirect |
| 252. C2 | #91564 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C3×D5 | 2 |
| C22×#1220 | 2 |
| C22×#1202 | 2 |
| C2×C5×#217 | 2 |
| #91564 | 2 |
| C2×#6665 | 2 |
| C2×#4028 | 3 |
| C2×#953 | 5 |