Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
168 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C3×C4×C5 | D8 |
| commutator, Frattini, cosocle | C8 | C23×C3×C5 |
| socle | C2×C3×C5 | C2×D8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C3×C4×C5 ◁ C2×C3×C4×C5 ◁ C2×C3×C5×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×#135 | C2 | semidirect |
| 2. C3×C5×Q32 | C2 | semidirect |
| 3. C3×C5×SD32 | C2 | semidirect |
| 4. C3×C5×D16 | C2 | semidirect |
| 5. C2×C3×C5×C16 | C2 | semidirect |
| 6. C5×#508 | C3 | direct (N × H) |
| 14. C3×#508 | C5 | direct (N × H) |
| 15. C5×#135 | C2×C3 | semidirect |
| 16. C5×Q32 | C2×C3 | semidirect |
| 17. C5×SD32 | C2×C3 | semidirect |
| 18. C5×D16 | C2×C3 | semidirect |
| 19. C2×C5×C16 | C2×C3 | semidirect |
| 27. C3×#135 | C2×C5 | semidirect |
| 28. C3×Q32 | C2×C5 | semidirect |
| 29. C3×SD32 | C2×C5 | semidirect |
| 30. C3×D16 | C2×C5 | semidirect |
| 31. C2×C3×C16 | C2×C5 | semidirect |
| 39. #508 | C3×C5 | direct (N × H) |
| 59. #135 | C2×C3×C5 | semidirect |
| 60. Q32 | C2×C3×C5 | semidirect |
| 61. SD32 | C2×C3×C5 | semidirect |
| 62. D16 | C2×C3×C5 | semidirect |
| 63. C2×C16 | C2×C3×C5 | semidirect |
| 86. C3×C5 | #508 | direct (N × H) |
| 105. C5 | C3×#508 | direct (N × H) |
| 111. C3 | C5×#508 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#135 | 2 |
| C3×C5×Q32 | 2 |
| C3×C5×SD32 | 2 |
| C3×C5×D16 | 2 |
| C2×C3×C5×C16 | 2 |
| C5×#508 | 3 |
| C3×#508 | 5 |