Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
216 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C3×C5 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C3×C5 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C5×#462 | C3 | direct (N × H) |
| 17. C3×#462 | C5 | direct (N × H) |
| 49. #462 | C3×C5 | direct (N × H) |
| 55. C3×C4×C5 | Q16 | semidirect |
| 103. C4×C5 | C3×Q16 | semidirect |
| 116. C3×C5 | #462 | direct (N × H) |
| 122. C3×C4 | C5×Q16 | semidirect |
| 142. C5 | C3×#462 | direct (N × H) |
| 148. C4 | C3×C5×Q16 | semidirect |
| 151. C3 | C5×#462 | 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×Q16 | 2 |
| C3×C5×C4⋊Q8 | 2 |
| C3×C4×C5×Q8 | 2 |
| C3×C5×C4⋊C8 | 2 |
| C3×C5×#103 | 2 |
| C5×#462 | 3 |
| C3×#462 | 5 |