Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
460 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C5 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C3×C5 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×#562 | C2 | semidirect |
| 2. C3×C5×#496 | C2 | semidirect |
| 3. C3×C5×#490 | C2 | semidirect |
| 4. C3×C5×#330 | C2 | semidirect |
| 5. C3×C5×#329 | C2 | semidirect |
| 6. C5×#1656 | C3 | direct (N × H) |
| 18. C3×#1656 | C5 | direct (N × H) |
| 19. C5×#562 | C2×C3 | semidirect |
| 20. C5×#496 | C2×C3 | semidirect |
| 21. C5×#490 | C2×C3 | semidirect |
| 22. C5×#330 | C2×C3 | semidirect |
| 23. C5×#329 | C2×C3 | semidirect |
| 41. C3×#562 | C2×C5 | semidirect |
| 42. C3×#496 | C2×C5 | semidirect |
| 43. C3×#490 | C2×C5 | semidirect |
| 44. C3×#330 | C2×C5 | semidirect |
| 45. C3×#329 | C2×C5 | semidirect |
| 57. #1656 | C3×C5 | direct (N × H) |
| 101. #562 | C2×C3×C5 | semidirect |
| 102. #496 | C2×C3×C5 | semidirect |
| 103. #490 | C2×C3×C5 | semidirect |
| 104. #330 | C2×C3×C5 | semidirect |
| 105. #329 | C2×C3×C5 | semidirect |
| 205. C3×C5 | #1656 | direct (N × H) |
| 239. C5 | C3×#1656 | direct (N × H) |
| 250. C3 | C5×#1656 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#562 | 2 |
| C3×C5×#496 | 2 |
| C3×C5×#490 | 2 |
| C3×C5×#330 | 2 |
| C3×C5×#329 | 2 |
| C5×#1656 | 3 |
| C3×#1656 | 5 |