Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
194 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 194 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, Frattini, hypercenter | C2 | D3×D5×A4 |
| commutator, Fitting, cosocle, hypocenter | C3×C5×Q8 | C22×C3 |
| socle | C2×C3×C5 | C22×A4 |
| LCS | G ▷ C3×C5×Q8 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. SL(2,𝔽3)×D15 | C2 | semidirect |
| 2. C5×D3×SL(2,𝔽3) | C2 | semidirect |
| 3. C3×C5⋊(#41⋊C3) | C2 | semidirect |
| 4. #92028 | C3 | semidirect |
| 9. Q8×D15 | C2×C3 | semidirect |
| 10. C5×D3×Q8 | C2×C3 | semidirect |
| 11. C3×#713 | C2×C3 | semidirect |
| 19. C5⋊(#41⋊C3) | D3 | semidirect |
| 26. D3×SL(2,𝔽3) | D5 | semidirect |
| 49. #713 | C3×D3 | semidirect |
| 69. D3×Q8 | C3×D5 | semidirect |
| 137. C3×C5 | 2−1+4⋊C3 | semidirect |
| 174. C5 | #1010⋊C3 | semidirect |
| 184. C3 | #4147⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| SL(2,𝔽3)×D15 | 2 |
| C5×D3×SL(2,𝔽3) | 2 |
| C3×C5⋊(#41⋊C3) | 2 |
| #92028 | 3 |
| #4147⋊C3 | 3 |
| C3×#1203 | 4 |
| #1010⋊C3 | 5 |