Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
196 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 196 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 |
|---|---|---|
| 5. C5×#487 | C3 | direct (N × H) |
| 14. C3×#487 | C5 | direct (N × H) |
| 39. #487 | C3×C5 | direct (N × H) |
| 91. C3×C5 | #487 | direct (N × H) |
| 112. C5 | C3×#487 | direct (N × H) |
| 119. C3 | C5×#487 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×C4⋊Q8 | 2 |
| C3×C5×#103 | 2 |
| C3×C4×C5×C8 | 2 |
| C5×#487 | 3 |
| C3×#487 | 5 |