Finite Group DatabasebetaFinite Group DatabasebetaOrder 9477.
5490 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #15691698 | C3 | 1 | 80 | yes | maximal, complemented |
| 2 | C3×#11760452 | C3 | 1 | 40 | yes | maximal, complemented |
| 3 | C13×H(5,𝔽3) | C3 | 1 | 1 | yes | maximal, characteristic |
| 4 | #11760452 | C32 | 1 | 90 | yes | complemented |
| 5 | #11760452 | C32 | 1 | 720 | yes | complemented |
| 6 | C3×#66851 | C32 | 1 | 320 | yes | complemented |
| 7 | C32×C13⋊C9 | C32 | 1 | 40 | yes | complemented |
| 8 | C3×C13×H(3,𝔽3) | C32 | 1 | 40 | yes | — |
| 9 | #10624943 | — | 13 | 1 | no | maximal, Sylow |
| 10 | C33×C13 | C33 | 1 | 40 | yes | — |
| 11 | C13×H(3,𝔽3) | C33 | 1 | 90 | yes | — |
| 12 | #66851 | C33 | 1 | 720 | yes | — |
| 13 | C3×C13⋊C9 | C33 | 1 | 40 | yes | — |
| 14 | C3×C13⋊C9 | C33 | 1 | 320 | yes | — |
| 15 | 3−1+4 | — | 13 | 80 | no | — |
| 16 | H(5,𝔽3) | C13⋊C3 | 1 | 1 | yes | characteristic |
| 17 | C3×#737 | — | 13 | 40 | no | — |
| 18 | C32×C13 | — | 9 | 40 | no | — |
| 19 | C32×C13 | C34 | 1 | 40 | yes | — |
| 20 | C13⋊C9 | C34 | 1 | 1 | yes | characteristic |
| 21 | C13⋊C9 | C34 | 1 | 80 | yes | — |
| 22 | #737 | — | 13 | 90 | no | — |
| 23 | #737 | — | 13 | 720 | no | — |
| 24 | C3×3−1+2 | — | 13 | 320 | no | — |
| 25 | C3×H(3,𝔽3) | C3×C13⋊C3 | 1 | 40 | yes | — |
| 26 | C32×C9 | — | 13 | 40 | no | — |
| 27 | C3×C13 | — | 3 | 40 | no | — |
| 28 | C3×C13 | C35 | 1 | 1 | yes | characteristic |
| 29 | C33 | C32×C13⋊C3 | 1 | 40 | yes | — |
| 30 | 3−1+2 | — | 13 | 720 | no | — |
| 31 | H(3,𝔽3) | C32×C13⋊C3 | 1 | 90 | yes | — |
| 32 | C3×C9 | — | 13 | 40 | no | — |
| 33 | C3×C9 | — | 13 | 320 | no | — |
| 34 | C13 | #10624943 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 35 | C32 | — | 9 | 40 | no | — |
| 36 | C32 | C33×C13⋊C3 | 1 | 40 | yes | — |
| 37 | C9 | — | 13 | 1 | no | — |
| 38 | C9 | — | 13 | 80 | no | — |
| 39 | C3 | — | 3 | 40 | no | — |
| 40 | C3 | C34×C13⋊C3 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C34×C13⋊C3 |
| commutator, socle, cosocle | C3×C13 | C35 |
| Fitting, prime radical | C13×H(5,𝔽3) | C3 |
| hypercenter | H(5,𝔽3) | C13⋊C3 |
| hypocenter | C13 | #10624943 |
| LCS | G ▷ C3×C13 ▷ C13 | |
| UCS | C1 ◁ C3 ◁ H(5,𝔽3) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15691698 | C3 | semidirect |
| 2. C3×#11760452 | C3 | semidirect |
| 4. #11760452 | C32 | semidirect |
| 5. #11760452 | C32 | semidirect |
| 6. C3×#66851 | C32 | semidirect |
| 7. C32×C13⋊C9 | C32 | semidirect |
| 34. C13 | #10624943 | semidirect |