Finite Group DatabasebetaFinite Group DatabasebetaOrder 2880.
2988 conjugacy classes of subgroups; only the 476 normal subgroups are shown.
This group has 2988 conjugacy classes of subgroups — too many to draw. Only its 476 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D5×C3⋊D3 |
| commutator, socle, cosocle | C22×C32×C5 | C24 |
| Fitting | C32×C42×C5 | C22 |
| hypercenter | C42 | D5×C3⋊D3 |
| hypocenter | C32×C5 | C2×#127 |
| LCS | G ▷ C22×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D5×C4⋊(C3⋊D3) | C2 | semidirect |
| 2. #13088143 | C2 | semidirect |
| 3. C5×#64083 | C2 | semidirect |
| 4. C32×C42×D5 | C2 | semidirect |
| 5. #13086919 | C2 | semidirect |
| 8. C2×C4⋊(C3⋊D15) | C22 | semidirect |
| 9. C2×C5×C4⋊(C3⋊D3) | C22 | semidirect |
| 11. C2×#67140 | C22 | semidirect |
| 13. C32×C42×C5 | C22 | semidirect |
| 14. C32×C4×Dic5 | C22 | semidirect |
| 19. C3×C42×D5 | D3 | semidirect |
| 29. C32×C4×D5 | D4 | semidirect |
| 36. #64083 | D5 | direct (N × H) |
| 43. C3×C42×C5 | C2×D3 | semidirect |
| 44. C3×C4×Dic5 | C2×D3 | semidirect |
| 51. C32×C4×C5 | C2×D4 | semidirect |
| 52. C32×Dic5 | C2×D4 | semidirect |
| 57. C42×D5 | C3⋊D3 | semidirect |
| 63. C2×C4⋊(C3⋊D3) | C2×D5 | semidirect |
| 65. C32×C42 | C2×D5 | semidirect |
| 74. C3×C4×D5 | D12 | semidirect |
| 84. C32×D5 | #127 | semidirect |
| 91. C42×C5 | C2×C3⋊D3 | semidirect |
| 92. C4×Dic5 | C2×C3⋊D3 | semidirect |
| 109. C3×C4×C5 | C2×D12 | semidirect |
| 110. C3×Dic5 | C2×D12 | semidirect |
| 118. C3×C42 | D3×D5 | semidirect |
| 119. C32×C5 | C2×#127 | semidirect |
| 129. C4×D5 | C4⋊(C3⋊D3) | semidirect |
| 136. C32×C4 | D4×D5 | semidirect |
| 144. C3×D5 | #874 | semidirect |
| 161. C4×C5 | C2×C4⋊(C3⋊D3) | semidirect |
| 162. Dic5 | C2×C4⋊(C3⋊D3) | semidirect |
| 174. C42 | D5×C3⋊D3 | semidirect |
| 175. C3×C5 | C2×#874 | semidirect |
| 182. C3×C4 | D5×D12 | semidirect |
| 186. D5 | #64083 | direct (N × H) |
| 187. C32 | D5×#127 | semidirect |
| 202. C5 | C2×#64083 | semidirect |
| 209. C4 | D5×C4⋊(C3⋊D3) | semidirect |
| 210. C3 | D5×#874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×C4⋊(C3⋊D3) | 2 |
| #13088143 | 2 |
| C5×#64083 | 2 |
| C32×C42×D5 | 2 |
| #13086919 | 2 |
| D5×#874 | 3 |
| C2×#64083 | 5 |