Finite Group DatabasebetaFinite Group DatabasebetaOrder 4800.
3984 conjugacy classes of subgroups; only the 614 normal subgroups are shown.
This group has 3984 conjugacy classes of subgroups — too many to draw. Only its 614 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×D3×C5⋊D5 |
| commutator, socle, cosocle | C22×C3×C52 | C24 |
| Fitting | C3×C42×C52 | C22 |
| hypercenter | C42 | D3×C5⋊D5 |
| hypocenter | C3×C52 | C2×#127 |
| LCS | G ▷ C22×C3×C52 ▷ C3×C52 | |
| UCS | C1 ◁ C22 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72230985 | C2 | semidirect |
| 2. #72229734 | C2 | semidirect |
| 3. C3×#11717194 | C2 | semidirect |
| 4. C42×C52×D3 | C2 | semidirect |
| 5. C2×D3×C4⋊(C5⋊D5) | C2 | semidirect |
| 8. C2×C4⋊(C3⋊(C5⋊D5)) | C22 | semidirect |
| 10. C2×C3×C4⋊(C5⋊D5) | C22 | semidirect |
| 11. C2×#10597115 | C22 | semidirect |
| 13. C3×C42×C52 | C22 | semidirect |
| 14. C4×C52×Dic3 | C22 | semidirect |
| 20. #11717194 | D3 | direct (N × H) |
| 28. C4×C52×D3 | D4 | semidirect |
| 33. C42×C5×D3 | D5 | semidirect |
| 41. C2×C4⋊(C5⋊D5) | C2×D3 | semidirect |
| 43. C42×C52 | C2×D3 | semidirect |
| 50. C3×C4×C52 | C2×D4 | semidirect |
| 51. C52×Dic3 | C2×D4 | semidirect |
| 58. C3×C42×C5 | C2×D5 | semidirect |
| 59. C4×C5×Dic3 | C2×D5 | semidirect |
| 78. C52×D3 | #127 | semidirect |
| 87. C4×C5×D3 | D20 | semidirect |
| 96. C4×C52 | D3×D4 | semidirect |
| 101. C42×D3 | C5⋊D5 | semidirect |
| 109. C42×C5 | D3×D5 | semidirect |
| 110. C3×C52 | C2×#127 | semidirect |
| 117. C3×C4×C5 | C2×D20 | semidirect |
| 118. C5×Dic3 | C2×D20 | semidirect |
| 129. C3×C42 | C2×C5⋊D5 | semidirect |
| 130. C4×Dic3 | C2×C5⋊D5 | semidirect |
| 149. C5×D3 | #4020 | semidirect |
| 150. C52 | D3×#127 | semidirect |
| 160. C4×D3 | C4⋊(C5⋊D5) | semidirect |
| 167. C4×C5 | D3×D20 | semidirect |
| 175. C42 | D3×C5⋊D5 | semidirect |
| 176. C3×C5 | C2×#4020 | semidirect |
| 182. C3×C4 | C2×C4⋊(C5⋊D5) | semidirect |
| 183. Dic3 | C2×C4⋊(C5⋊D5) | semidirect |
| 201. D3 | #11717194 | direct (N × H) |
| 202. C5 | D3×#4020 | semidirect |
| 209. C4 | D3×C4⋊(C5⋊D5) | semidirect |
| 210. C3 | C2×#11717194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72230985 | 2 |
| #72229734 | 2 |
| C3×#11717194 | 2 |
| C42×C52×D3 | 2 |
| C2×D3×C4⋊(C5⋊D5) | 2 |
| C2×#11717194 | 3 |
| D3×#4020 | 5 |