Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
166 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | C5⋊S4 |
| commutator, cosocle, hypocenter | C5×SL(2,𝔽3) | C22×C3 |
| Frattini | C2 | C2×C3×C5⋊S4 |
| Fitting | C3×C5×#41 | D3 |
| socle | C2×C3×C5 | C2×S4 |
| LCS | G ▷ C5×SL(2,𝔽3) | |
| UCS | C1 ◁ C3×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×#41⋊C3 | C2 | semidirect |
| 2. C3×C5⋊GL(2,𝔽3) | C2 | semidirect |
| 3. C3×C5⋊#226 | C2 | semidirect |
| 4. #91955 | C3 | direct (N × H) |
| 9. C3×C5×#41 | D3 | semidirect |
| 12. C5×#41⋊C3 | C2×C3 | semidirect |
| 13. C5⋊GL(2,𝔽3) | C2×C3 | semidirect |
| 14. C5⋊#226 | C2×C3 | semidirect |
| 24. C3×#41⋊C3 | D5 | semidirect |
| 43. C5×#41 | C3×D3 | semidirect |
| 62. C3×#41 | D15 | semidirect |
| 64. #41⋊C3 | C3×D5 | semidirect |
| 112. #41 | C3×D15 | semidirect |
| 120. C3×C5 | #985 | semidirect |
| 149. C5 | C3×#985 | semidirect |
| 157. C3 | #91955 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#41⋊C3 | 2 |
| C3×C5⋊GL(2,𝔽3) | 2 |
| C3×C5⋊#226 | 2 |
| #91955 | 3 |
| C3×#4096 | 3 |
| C3×C4×D15 | 4 |
| C3×#985 | 5 |