Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
560 conjugacy classes of subgroups; only the 354 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 354 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C82 | D5 |
| commutator, hypocenter | C5 | C2×C3×C82 |
| Frattini | C42 | C22×C3×D5 |
| Fitting | C3×C5×C82 | C2 |
| socle | C22×C3×C5 | C2×C42 |
| prime radical | C22×C3×D5 | C42 |
| cosocle | C42×C5 | C23×C3 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C3×C82 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C5×C82 | C2 | semidirect |
| 3. C3×C8×#168 | C2 | semidirect |
| 4. C82×D5 | C3 | direct (N × H) |
| 12. C5×C82 | C2×C3 | semidirect |
| 13. C8×#168 | C2×C3 | semidirect |
| 19. C3×C8×D5 | C8 | direct (N × H) |
| 22. C3×C82 | D5 | direct (N × H) |
| 33. C3×C5×C8 | C2×C8 | semidirect |
| 34. C3×#168 | C2×C8 | semidirect |
| 45. C8×D5 | C3×C8 | direct (N × H) |
| 48. C82 | C3×D5 | direct (N × H) |
| 63. C5×C8 | C2×C3×C8 | semidirect |
| 64. #168 | C2×C3×C8 | semidirect |
| 71. C3×D5 | C82 | direct (N × H) |
| 77. C3×C8 | C8×D5 | direct (N × H) |
| 88. C3×C5 | C2×C82 | semidirect |
| 94. D5 | C3×C82 | direct (N × H) |
| 100. C8 | C3×C8×D5 | direct (N × H) |
| 103. C5 | C2×C3×C82 | semidirect |
| 108. C3 | C82×D5 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C8×D5 | 2 |
| C3×C5×C82 | 2 |
| C3×C8×#168 | 2 |
| C82×D5 | 3 |
| C2×C3×C82 | 5 |