Finite Group DatabasebetaFinite Group DatabasebetaOrder 7920.
39 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10624296 | — | 11 | 1 | no | maximal, Hall |
| 2 | PSL(2,𝔽11) | — | 12 | 1 | no | maximal |
| 3 | A6 | — | 11 | 1 | no | — |
| 4 | AΓL(1,𝔽9) | — | 55 | 1 | no | maximal, Hall |
| 5 | S5 | — | 66 | 1 | no | maximal |
| 6 | PSU(3,𝔽2) | — | 55 | 1 | no | — |
| 7 | GO+(4,𝔽2) | — | 55 | 1 | no | — |
| 8 | AGL(1,𝔽9) | — | 55 | 1 | no | — |
| 9 | A5 | — | 66 | 1 | no | — |
| 10 | A5 | — | 132 | 1 | no | — |
| 11 | C11⋊C5 | — | 144 | 1 | no | Hall |
| 12 | GL(2,𝔽3) | — | 165 | 1 | no | maximal |
| 13 | D32 | — | 110 | 1 | no | — |
| 14 | #157 | — | 55 | 1 | no | — |
| 15 | #157 | — | 110 | 1 | no | — |
| 16 | S4 | — | 330 | 1 | no | — |
| 17 | SL(2,𝔽3) | — | 165 | 1 | no | — |
| 18 | AGL(1,𝔽5) | — | 396 | 1 | no | — |
| 19 | C3⋊D3 | — | 55 | 1 | no | — |
| 20 | C3×D3 | — | 220 | 1 | no | — |
| 21 | SD16 | — | 495 | 1 | no | Sylow |
| 22 | C2×D3 | — | 660 | 1 | no | — |
| 23 | A4 | — | 330 | 1 | no | — |
| 24 | C11 | — | 144 | 1 | no | Sylow |
| 25 | D5 | — | 396 | 1 | no | — |
| 26 | C32 | — | 55 | 1 | no | Sylow |
| 27 | Q8 | — | 165 | 1 | no | — |
| 28 | D4 | — | 495 | 1 | no | — |
| 29 | C8 | — | 495 | 1 | no | — |
| 30 | C2×C3 | — | 660 | 1 | no | — |
| 31 | D3 | — | 660 | 1 | no | — |
| 32 | D3 | — | 220 | 1 | no | — |
| 33 | C5 | — | 396 | 1 | no | Sylow |
| 34 | C22 | — | 330 | 1 | no | — |
| 35 | C4 | — | 495 | 1 | no | — |
| 36 | C3 | — | 220 | 1 | no | — |
| 37 | C2 | — | 165 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | G | C1 |
| LCS | G | |
| UCS | C1 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624296 | 11 |
| PSL(2,𝔽11) | 12 |
| AΓL(1,𝔽9) | 55 |
| S5 | 66 |
| GL(2,𝔽3) | 165 |