Finite Group DatabasebetaFinite Group DatabasebetaOrder 4800.
664 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 664 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | A4×D5⋊AGL(1,𝔽5) |
| commutator, hypocenter | C22×C52 | C3×C42 |
| Fitting, socle | C23×C52 | C2×C3×C4 |
| prime radical | C2×A4×C5⋊D5 | C22 |
| cosocle | C23×C5⋊D5 | C22×C3 |
| LCS | G ▷ C22×C52 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C22×#87830 | C3 | semidirect |
| 6. A4×#1044 | C4 | semidirect |
| 7. A4×#1043 | C4 | semidirect |
| 8. C5×A4×Dic5 | C4 | semidirect |
| 32. C22×#1044 | C3×C4 | semidirect |
| 36. C22×#1043 | C3×C4 | semidirect |
| 37. C22×C5×Dic5 | C3×C4 | semidirect |
| 45. #87830 | A4 | direct (N × H) |
| 48. C52×A4 | C42 | semidirect |
| 59. A4×Dic5 | AGL(1,𝔽5) | semidirect |
| 109. C22×C52 | C3×C42 | semidirect |
| 120. #1044 | C4×A4 | semidirect |
| 122. #1043 | C4×A4 | semidirect |
| 124. C5×Dic5 | C4×A4 | semidirect |
| 143. C22×Dic5 | C3×AGL(1,𝔽5) | semidirect |
| 158. C5×A4 | C4×AGL(1,𝔽5) | semidirect |
| 230. C52 | C42×A4 | semidirect |
| 242. C22×C5 | C3×C4×AGL(1,𝔽5) | semidirect |
| 270. Dic5 | A4×AGL(1,𝔽5) | semidirect |
| 292. A4 | #87830 | direct (N × H) |
| 339. C5 | C4×A4×AGL(1,𝔽5) | semidirect |
| 351. C22 | C3×#87830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×A4×#1044 | 2 |
| A4×#6036 | 2 |
| C2×A4×#1043 | 2 |
| C22×#87830 | 3 |
| C3×#87830 | 4 |
| C4×A4×AGL(1,𝔽5) | 5 |