Finite Group DatabasebetaFinite Group DatabasebetaOrder 3600.
264 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | A4×#1044 |
| commutator, hypocenter | C22×C52 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C52 | C3×C4 |
| prime radical | C3×A4×C5⋊D5 | C2 |
| cosocle | C22×C5⋊D5 | C2×C32 |
| LCS | G ▷ C22×C52 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C3×#1044 | C3 | semidirect |
| 3. A4×#1044 | C3 | direct (N × H) |
| 4. C3×C52×A4 | C4 | semidirect |
| 12. C22×#1044 | C32 | semidirect |
| 15. C22×C3×C52 | C3×C4 | semidirect |
| 18. C52×A4 | C3×C4 | semidirect |
| 21. C3×#1044 | A4 | direct (N × H) |
| 29. C3×C5×A4 | AGL(1,𝔽5) | semidirect |
| 42. C22×C52 | C32×C4 | semidirect |
| 46. #1044 | C3×A4 | direct (N × H) |
| 51. C3×C52 | C4×A4 | semidirect |
| 54. C22×C3×C5 | C3×AGL(1,𝔽5) | semidirect |
| 60. C5×A4 | C3×AGL(1,𝔽5) | semidirect |
| 75. C3×A4 | #1044 | direct (N × H) |
| 85. C52 | C3×C4×A4 | semidirect |
| 91. C22×C5 | C32×AGL(1,𝔽5) | semidirect |
| 103. C3×C5 | A4×AGL(1,𝔽5) | semidirect |
| 106. C22×C3 | C3×#1044 | semidirect |
| 107. A4 | C3×#1044 | direct (N × H) |
| 126. C5 | C3×A4×AGL(1,𝔽5) | semidirect |
| 129. C22 | C32×#1044 | semidirect |
| 133. C3 | A4×#1044 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×A4×C5⋊D5 | 2 |
| C22×C3×#1044 | 3 |
| A4×#1044 | 3 |
| C32×#1044 | 4 |
| C3×A4×AGL(1,𝔽5) | 5 |