Finite Group DatabasebetaFinite Group DatabasebetaOrder 3600.
288 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C5×C3⋊#168 | C2 | semidirect |
| 7. #10623820 | C5 | direct (N × H) |
| 11. C5×C3⋊#168 | D3 | semidirect |
| 19. C3×C3⋊#168 | C2×C5 | semidirect |
| 29. C32×C52 | M16 | semidirect |
| 53. C3⋊#168 | C5×D3 | semidirect |
| 68. C3×C52 | ΓL(1,𝔽25) | semidirect |
| 93. C32×C5 | #681 | semidirect |
| 94. C32×C5 | C5×M16 | semidirect |
| 115. C52 | #3712 | semidirect |
| 136. C3×C5 | #6650 | semidirect |
| 137. C3×C5 | C5×ΓL(1,𝔽25) | semidirect |
| 150. C32 | C5×#681 | semidirect |
| 158. C5 | C5×#3712 | semidirect |
| 159. C5 | #10623820 | direct (N × H) |
| 164. C3 | C5×#6650 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C52×C3⋊D3 | 2 |
| C3×C5×C3⋊#168 | 2 |
| C5×#6650 | 3 |
| #10623820 | 5 |
| C5×#3712 | 5 |