Finite Group DatabasebetaFinite Group DatabasebetaOrder 20032.
310 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D313 |
| commutator, socle, cosocle | C22×C313 | C24 |
| Frattini | C22 | C23×D313 |
| Fitting | C4×D4×C313 | C2 |
| hypercenter | C4×D4 | D313 |
| hypocenter | C313 | #532 |
| LCS | G ▷ C22×C313 ▷ C313 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19097561 | C2 | semidirect |
| 2. #23756496 | C2 | semidirect |
| 3. #23756493 | C2 | semidirect |
| 4. #23756483 | C2 | semidirect |
| 5. #23756472 | C2 | semidirect |
| 6. #23756470 | C2 | semidirect |
| 7. #23756468 | C2 | semidirect |
| 8. C4×D1252 | C2 | semidirect |
| 9. C4×C22⋊D313 | C2 | semidirect |
| 10. C42×D313 | C2 | semidirect |
| 11. C4×D4×C313 | C2 | semidirect |
| 51. C4×D313 | D4 | semidirect |
| 72. C4×C313 | #41 | semidirect |
| 76. Dic313 | #41 | semidirect |
| 83. C313 | #532 | semidirect |
| 94. C4×D4 | D313 | semidirect |
| 160. C4 | #19097561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097561 | 2 |
| #23756496 | 2 |
| #23756493 | 2 |
| #23756483 | 2 |
| #23756472 | 2 |
| #23756470 | 2 |
| #23756468 | 2 |
| C4×D1252 | 2 |
| C4×C22⋊D313 | 2 |
| C42×D313 | 2 |
| C4×D4×C313 | 2 |
| #532 | 313 |