Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
30 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | SL(2,𝔽9) | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #3771 | — | 10 | 1 | no | maximal |
| 3 | SL(2,𝔽5) | — | 12 | 1 | no | — |
| 4 | #622 | — | 10 | 1 | no | — |
| 5 | #226 | — | 30 | 1 | no | — |
| 6 | Dic10 | — | 36 | 1 | no | maximal |
| 7 | C3⋊Dic3 | — | 10 | 1 | no | — |
| 8 | Q32 | — | 45 | 1 | no | maximal, Sylow |
| 9 | SL(2,𝔽3) | — | 30 | 1 | no | — |
| 10 | C4×C5 | — | 36 | 1 | no | — |
| 11 | Dic5 | — | 36 | 1 | no | — |
| 12 | Dic5 | — | 36 | 1 | no | — |
| 13 | C2×C32 | — | 10 | 1 | no | — |
| 14 | Q16 | — | 45 | 1 | no | — |
| 15 | Q16 | — | 45 | 1 | no | — |
| 16 | C16 | — | 45 | 1 | no | — |
| 17 | Dic3 | — | 120 | 1 | no | — |
| 18 | C2×C5 | — | 36 | 1 | no | — |
| 19 | C32 | — | 10 | 1 | no | Sylow |
| 20 | Q8 | — | 30 | 1 | no | — |
| 21 | Q8 | — | 90 | 1 | no | — |
| 22 | C8 | — | 45 | 1 | no | — |
| 23 | C2×C3 | — | 40 | 1 | no | — |
| 24 | C5 | — | 36 | 1 | no | Sylow |
| 25 | C4 | — | 36 | 1 | no | — |
| 26 | C4 | — | 45 | 1 | no | — |
| 27 | C3 | — | 40 | 1 | no | — |
| 28 | C2 | PGL(2,𝔽9) | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, Fitting, socle, hypercenter | C2 | PGL(2,𝔽9) |
| commutator, prime radical, cosocle, hypocenter | SL(2,𝔽9) | C2 |
| LCS | G ▷ SL(2,𝔽9) | |
| UCS | C1 ◁ C2 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| SL(2,𝔽9) | 2 |
| #3771 | 10 |
| Dic10 | 36 |
| Q32 | 45 |