Finite Group DatabasebetaFinite Group DatabasebetaOrder 4320.
328 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #11724027 |
| commutator, cosocle, hypocenter | (C22⋊A4)⋊C9 | C2×C5 |
| Frattini | C3 | C5×A4⋊S4 |
| Fitting, socle | C24×C3×C5 | C3⋊D3 |
| LCS | G ▷ (C22⋊A4)⋊C9 | |
| UCS | C1 ◁ C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×(C22⋊A4)⋊C9 | C2 | semidirect |
| 6. #11724027 | C5 | direct (N × H) |
| 8. C5×C22⋊(C22⋊C9) | D3 | semidirect |
| 9. C22×C5×C22⋊C9 | D3 | semidirect |
| 15. (C22⋊A4)⋊C9 | C2×C5 | semidirect |
| 28. C5×C22⋊A4 | D9 | semidirect |
| 40. C5×C22⋊C9 | S4 | semidirect |
| 44. C22⋊(C22⋊C9) | C5×D3 | semidirect |
| 45. C22×C22⋊C9 | C5×D3 | semidirect |
| 67. C24×C5 | C3⋊D9 | semidirect |
| 92. C22⋊A4 | C5×D9 | semidirect |
| 115. C22⋊C9 | C5×S4 | semidirect |
| 140. C22×C5 | C9⋊S4 | semidirect |
| 147. C24 | C5×C3⋊D9 | semidirect |
| 184. C5 | #11724027 | direct (N × H) |
| 191. C22 | C5×C9⋊S4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×(C22⋊A4)⋊C9 | 2 |
| C5×C3⋊#1020 | 3 |
| C5×#64188 | 3 |
| C5×#63694 | 3 |
| C5×C9⋊S4 | 4 |
| #11724027 | 5 |