Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
456 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 152 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 |
| prime radical | C3×C5×#127 | C22 |
| 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×Q82 | C2 | semidirect |
| 4. C3×C5×#333 | C2 | semidirect |
| 5. C3×C5×Q8⋊C8 | C2 | semidirect |
| 6. C5×#1623 | C3 | direct (N × H) |
| 18. C3×#1623 | C5 | direct (N × H) |
| 19. C5×Q82 | C2×C3 | semidirect |
| 22. C5×#333 | C2×C3 | semidirect |
| 23. C5×Q8⋊C8 | C2×C3 | semidirect |
| 40. C3×Q82 | C2×C5 | semidirect |
| 43. C3×#333 | C2×C5 | semidirect |
| 44. C3×Q8⋊C8 | C2×C5 | semidirect |
| 56. #1623 | C3×C5 | direct (N × H) |
| 61. C3×C5×Q8 | SD16 | semidirect |
| 99. Q82 | C2×C3×C5 | semidirect |
| 102. #333 | C2×C3×C5 | semidirect |
| 103. Q8⋊C8 | C2×C3×C5 | semidirect |
| 133. C5×Q8 | C3×SD16 | semidirect |
| 162. C3×Q8 | C5×SD16 | semidirect |
| 198. C3×C5 | #1623 | direct (N × H) |
| 215. Q8 | C3×C5×SD16 | semidirect |
| 229. C5 | C3×#1623 | direct (N × H) |
| 239. C3 | C5×#1623 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×Q82 | 2 |
| C3×C5×#492 | 2 |
| C3×C5×#460 | 2 |
| C3×C5×#333 | 2 |
| C3×C5×Q8⋊C8 | 2 |
| C5×#1623 | 3 |
| C3×#1623 | 5 |