Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
372 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C3×C5 | C23 |
| commutator, Frattini, cosocle | C23 | C23×C3×C5 |
| prime radical | C24×C3×C5 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C3×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×C5×C4⋊C4 | C2 | semidirect |
| 3. C3×C5×#95 | C2 | semidirect |
| 4. C5×#396 | C3 | direct (N × H) |
| 10. C3×#396 | C5 | direct (N × H) |
| 11. C2×C5×C4⋊C4 | C2×C3 | semidirect |
| 13. C5×#95 | C2×C3 | semidirect |
| 24. C2×C3×C4⋊C4 | C2×C5 | semidirect |
| 26. C3×#95 | C2×C5 | semidirect |
| 32. #396 | C3×C5 | direct (N × H) |
| 56. C2×C4⋊C4 | C2×C3×C5 | semidirect |
| 58. #95 | C2×C3×C5 | semidirect |
| 86. C3×C5 | #396 | direct (N × H) |
| 113. C5 | C3×#396 | direct (N × H) |
| 122. C3 | C5×#396 | 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×C4⋊C4 | 2 |
| C2×C3×C5×C22⋊C4 | 2 |
| C3×C5×#95 | 2 |
| C5×#396 | 3 |
| C3×#396 | 5 |