Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
524 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 524 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×H(3,𝔽4) | C2 | semidirect |
| 2. C3×C5×#496 | C2 | semidirect |
| 3. C3×C5×#329 | C2 | semidirect |
| 4. C5×#1655 | C3 | direct (N × H) |
| 7. C3×C5×#127 | C22 | semidirect |
| 11. C3×C5×#97 | C22 | semidirect |
| 12. C3×#1655 | C5 | direct (N × H) |
| 13. C5×H(3,𝔽4) | C2×C3 | semidirect |
| 14. C5×#496 | C2×C3 | semidirect |
| 15. C5×#329 | C2×C3 | semidirect |
| 28. C3×H(3,𝔽4) | C2×C5 | semidirect |
| 29. C3×#496 | C2×C5 | semidirect |
| 30. C3×#329 | C2×C5 | semidirect |
| 33. C5×#127 | C22×C3 | semidirect |
| 37. C5×#97 | C22×C3 | semidirect |
| 38. #1655 | C3×C5 | direct (N × H) |
| 52. C3×#127 | C22×C5 | semidirect |
| 56. C3×#97 | C22×C5 | semidirect |
| 69. H(3,𝔽4) | C2×C3×C5 | semidirect |
| 70. #496 | C2×C3×C5 | semidirect |
| 71. #329 | C2×C3×C5 | semidirect |
| 104. #127 | C22×C3×C5 | semidirect |
| 108. #97 | C22×C3×C5 | semidirect |
| 142. C3×C5 | #1655 | direct (N × H) |
| 167. C5 | C3×#1655 | direct (N × H) |
| 175. C3 | C5×#1655 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×H(3,𝔽4) | 2 |
| C3×C5×#496 | 2 |
| C3×C5×#329 | 2 |
| C5×#1655 | 3 |
| C3×#1655 | 5 |