Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
192 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 192 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×#477 | C3 | direct (N × H) |
| 16. C3×#477 | C5 | direct (N × H) |
| 24. C3×C5×Q8 | Q8 | semidirect |
| 46. #477 | C3×C5 | direct (N × H) |
| 66. C5×Q8 | C3×Q8 | semidirect |
| 84. C3×Q8 | C5×Q8 | semidirect |
| 109. C3×C5 | #477 | direct (N × H) |
| 123. Q8 | C3×C5×Q8 | semidirect |
| 134. C5 | C3×#477 | direct (N × H) |
| 143. C3 | C5×#477 | 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×C4×C5×Q8 | 2 |
| C3×C5×#107 | 2 |
| C3×C5×C4⋊C8 | 2 |
| C3×C5×#103 | 2 |
| C5×#477 | 3 |
| C3×#477 | 5 |