Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
260 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C3×C5 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C22×C3×C4×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×C5×D8 | C2 | semidirect |
| 2. C2×C3×C5×M16 | C2 | semidirect |
| 3. C3×C5×#121 | C2 | semidirect |
| 4. C3×C5×#106 | C2 | semidirect |
| 5. C3×C5×#102 | C2 | semidirect |
| 6. C5×#469 | C3 | direct (N × H) |
| 16. C3×#469 | C5 | direct (N × H) |
| 17. C2×C5×D8 | C2×C3 | semidirect |
| 18. C2×C5×M16 | C2×C3 | semidirect |
| 19. C5×#121 | C2×C3 | semidirect |
| 20. C5×#106 | C2×C3 | semidirect |
| 21. C5×#102 | C2×C3 | semidirect |
| 33. C3×C5×C8 | D4 | semidirect |
| 34. C2×C3×D8 | C2×C5 | semidirect |
| 35. C2×C3×M16 | C2×C5 | semidirect |
| 36. C3×#121 | C2×C5 | semidirect |
| 37. C3×#106 | C2×C5 | semidirect |
| 38. C3×#102 | C2×C5 | semidirect |
| 48. #469 | C3×C5 | direct (N × H) |
| 79. C5×C8 | C3×D4 | semidirect |
| 80. C2×D8 | C2×C3×C5 | semidirect |
| 81. C2×M16 | C2×C3×C5 | semidirect |
| 82. #121 | C2×C3×C5 | semidirect |
| 83. #106 | C2×C3×C5 | semidirect |
| 84. #102 | C2×C3×C5 | semidirect |
| 100. C3×C8 | C5×D4 | semidirect |
| 120. C3×C5 | #469 | direct (N × H) |
| 146. C8 | C3×C5×D4 | semidirect |
| 151. C5 | C3×#469 | direct (N × H) |
| 162. C3 | C5×#469 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×D8 | 2 |
| C2×C3×C5×M16 | 2 |
| C3×C5×#121 | 2 |
| C3×C5×#106 | 2 |
| C3×C5×#102 | 2 |
| C5×#469 | 3 |
| C3×#469 | 5 |