Finite Group DatabasebetaFinite Group DatabasebetaOrder 5913.
100 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×#10620323 | C3 | 1 | 12 | yes | maximal, direct product factor |
| 2 | C32×C73⋊C3 | C3 | 1 | 1 | yes | maximal, characteristic |
| 3 | C32×C73 | C9 | 1 | 1 | yes | characteristic, complemented |
| 4 | C3×C73⋊C3 | C9 | 1 | 8 | yes | complemented |
| 5 | C3×C73⋊C3 | C32 | 1 | 4 | yes | — |
| 6 | #10620323 | C32 | 1 | 9 | yes | direct product factor |
| 7 | C3×C73 | C3×C9 | 1 | 4 | yes | complemented |
| 8 | C73⋊C3 | C3×C9 | 1 | 8 | yes | complemented |
| 9 | C73⋊C3 | C33 | 1 | 1 | yes | characteristic |
| 10 | C32×C9 | — | 73 | 1 | no | maximal, Sylow |
| 11 | C73 | C32×C9 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | C33 | — | 73 | 1 | no | — |
| 13 | C3×C9 | — | 73 | 12 | no | — |
| 14 | C32 | — | 73 | 4 | no | — |
| 15 | C32 | — | 73 | 8 | no | — |
| 16 | C32 | #10620323 | 1 | 1 | yes | characteristic, direct product factor |
| 17 | C9 | — | 73 | 9 | no | — |
| 18 | C3 | — | 73 | 1 | no | — |
| 19 | C3 | — | 73 | 8 | no | — |
| 20 | C3 | C3×#10620323 | 1 | 4 | yes | direct product factor |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #10620323 |
| commutator, hypocenter | C73 | C32×C9 |
| Frattini | C1 | G |
| Fitting, socle | C32×C73 | C9 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#10620323 | C3 | direct (N × H) |
| 3. C32×C73 | C9 | semidirect |
| 4. C3×C73⋊C3 | C9 | semidirect |
| 6. #10620323 | C32 | direct (N × H) |
| 7. C3×C73 | C3×C9 | semidirect |
| 8. C73⋊C3 | C3×C9 | semidirect |
| 11. C73 | C32×C9 | semidirect |
| 16. C32 | #10620323 | direct (N × H) |
| 20. C3 | C3×#10620323 | direct (N × H) |