Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
330 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | A4⋊#1044 |
| commutator, hypocenter | C52×A4 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C23×C52 | Dic3 |
| prime radical | C2×A4×C5⋊D5 | C2 |
| cosocle | A4×C5⋊D5 | C22 |
| LCS | G ▷ C52×A4 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. A4⋊#1044 | C2 | direct (N × H) |
| 4. C2×C52×A4 | C4 | semidirect |
| 6. A4×C5⋊D5 | C4 | semidirect |
| 15. C52×A4 | C2×C4 | semidirect |
| 20. C23×C52 | Dic3 | semidirect |
| 25. C22×C5⋊D5 | Dic3 | semidirect |
| 38. C2×C5×A4 | AGL(1,𝔽5) | semidirect |
| 46. C22×C52 | C2×Dic3 | semidirect |
| 69. C5×A4 | C2×AGL(1,𝔽5) | semidirect |
| 73. C2×C52 | SL(2,ℤ/4) | semidirect |
| 76. C5⋊D5 | SL(2,ℤ/4) | semidirect |
| 81. C23×C5 | ΓL(1,𝔽16) | semidirect |
| 107. C52 | C2×SL(2,ℤ/4) | semidirect |
| 110. C2×A4 | #1044 | semidirect |
| 117. C22×C5 | C2×ΓL(1,𝔽16) | semidirect |
| 146. A4 | C2×#1044 | semidirect |
| 153. C2×C5 | A4⋊AGL(1,𝔽5) | semidirect |
| 168. C23 | C3⋊#1044 | semidirect |
| 179. C5 | C2×A4⋊AGL(1,𝔽5) | semidirect |
| 191. C22 | C2×C3⋊#1044 | semidirect |
| 201. C2 | A4⋊#1044 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×A4×C5⋊D5 | 2 |
| A4⋊#1044 | 2 |
| C2×C22⋊#1044 | 3 |
| C2×C3⋊#1044 | 4 |
| C2×A4⋊AGL(1,𝔽5) | 5 |