Finite Group DatabasebetaFinite Group DatabasebetaOrder 2880.
117 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13088280 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | SL(2,𝔽9) | C4 | 1 | 1 | yes | characteristic, complemented |
| 3 | #91145 | — | 6 | 2 | no | maximal |
| 4 | C8×#157 | — | 10 | 1 | no | maximal |
| 5 | #6732 | — | 6 | 2 | no | — |
| 6 | #5404 | — | 15 | 2 | no | maximal |
| 7 | C4×#157 | — | 10 | 1 | no | — |
| 8 | #3787 | — | 10 | 1 | no | — |
| 9 | C8×C3⋊D3 | — | 10 | 1 | no | — |
| 10 | SL(2,𝔽5) | — | 6 | 2 | no | — |
| 11 | #985 | — | 15 | 2 | no | — |
| 12 | #131⋊C3 | — | 15 | 2 | no | — |
| 13 | GU(2,𝔽3) | — | 15 | 2 | no | — |
| 14 | C8×D5 | — | 36 | 1 | no | — |
| 15 | C2×#157 | — | 10 | 2 | no | — |
| 16 | C4×C3⋊D3 | — | 10 | 1 | no | — |
| 17 | #622 | — | 10 | 1 | no | — |
| 18 | #622 | — | 10 | 1 | no | — |
| 19 | C32×C8 | — | 10 | 1 | no | — |
| 20 | C3⋊(C3⋊C8) | — | 10 | 1 | no | — |
| 21 | #443 | — | 45 | 1 | no | Sylow |
| 22 | #41⋊C3 | — | 15 | 2 | no | — |
| 23 | GL(2,𝔽3) | — | 15 | 2 | no | — |
| 24 | #226 | — | 15 | 2 | no | — |
| 25 | D3×C8 | — | 60 | 2 | no | — |
| 26 | C4×D5 | — | 36 | 1 | no | — |
| 27 | C5×C8 | — | 36 | 1 | no | — |
| 28 | #168 | — | 36 | 1 | no | — |
| 29 | C2×C3⋊D3 | — | 10 | 1 | no | — |
| 30 | #157 | — | 10 | 4 | no | — |
| 31 | C32×C4 | — | 10 | 1 | no | — |
| 32 | C3⋊Dic3 | — | 10 | 1 | no | — |
| 33 | #135 | — | 45 | 1 | no | — |
| 34 | #131 | — | 15 | 2 | no | — |
| 35 | #108 | — | 45 | 1 | no | — |
| 36 | #104 | — | 45 | 2 | no | — |
| 37 | C4×C8 | — | 45 | 1 | no | — |
| 38 | C4×D3 | — | 60 | 2 | no | — |
| 39 | SL(2,𝔽3) | — | 15 | 2 | no | — |
| 40 | C3×C8 | — | 20 | 2 | no | — |
| 41 | C3⋊C8 | — | 60 | 2 | no | — |
| 42 | C2×D5 | — | 36 | 1 | no | — |
| 43 | C4×C5 | — | 36 | 1 | no | — |
| 44 | Dic5 | — | 36 | 1 | no | — |
| 45 | C2×C32 | — | 10 | 1 | no | — |
| 46 | C3⋊D3 | — | 10 | 2 | no | — |
| 47 | #41 | — | 15 | 2 | no | — |
| 48 | Q16 | — | 45 | 1 | no | — |
| 49 | SD16 | — | 45 | 2 | no | — |
| 50 | D8 | — | 45 | 1 | no | — |
| 51 | M16 | — | 45 | 2 | no | — |
| 52 | C2×C8 | — | 45 | 1 | no | — |
| 53 | C2×C8 | — | 45 | 1 | no | — |
| 54 | C42 | — | 45 | 1 | no | — |
| 55 | C2×D3 | — | 60 | 2 | no | — |
| 56 | C3×C4 | — | 20 | 2 | no | — |
| 57 | Dic3 | — | 60 | 2 | no | — |
| 58 | C2×C5 | — | 36 | 1 | no | — |
| 59 | D5 | — | 36 | 2 | no | — |
| 60 | C32 | — | 10 | 1 | no | Sylow |
| 61 | Q8 | — | 15 | 2 | no | — |
| 62 | D4 | — | 45 | 2 | no | — |
| 63 | C2×C4 | — | 45 | 1 | no | — |
| 64 | C2×C4 | — | 90 | 1 | no | — |
| 65 | C8 | — | 45 | 1 | no | — |
| 66 | C8 | — | 45 | 1 | no | — |
| 67 | C8 | — | 45 | 1 | no | — |
| 68 | C8 | A6 | 1 | 1 | yes | maximal normal, characteristic |
| 69 | C2×C3 | — | 20 | 2 | no | — |
| 70 | D3 | — | 60 | 4 | no | — |
| 71 | C5 | — | 36 | 1 | no | Sylow |
| 72 | C22 | — | 45 | 1 | no | — |
| 73 | C4 | — | 45 | 1 | no | — |
| 74 | C4 | — | 90 | 2 | no | — |
| 75 | C4 | C2×A6 | 1 | 1 | yes | characteristic |
| 76 | C3 | — | 20 | 2 | no | — |
| 77 | C2 | — | 90 | 1 | no | — |
| 78 | C2 | C4×A6 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C8 | A6 |
| commutator, hypocenter | SL(2,𝔽9) | C4 |
| Frattini, cosocle | C4 | C2×A6 |
| socle | C2 | C4×A6 |
| prime radical | #13088280 | C2 |
| LCS | G ▷ SL(2,𝔽9) | |
| UCS | C1 ◁ C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. SL(2,𝔽9) | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13088280 | 2 |
| #91145 | 6 |
| C8×#157 | 10 |
| #5404 | 15 |