Finite Group DatabasebetaFinite Group DatabasebetaOrder 3600.
304 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 62 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 | C4 | D152 |
| commutator, hypocenter | C32×C52 | C2×C8 |
| Fitting, cosocle | C32×C4×C52 | C22 |
| socle | C2×C32×C52 | C2×C4 |
| prime radical | C2×C3⋊(C3⋊(C5⋊D5)) | C4 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C5×C3⋊#168 | C2 | semidirect |
| 10. C5×C3⋊#168 | D3 | semidirect |
| 13. C3⋊(C3⋊(C5⋊D5)) | C8 | semidirect |
| 17. C3×C3⋊#168 | D5 | semidirect |
| 27. C32×C52 | C2×C8 | semidirect |
| 47. C3⋊#168 | D15 | semidirect |
| 59. C3×C52 | D3×C8 | semidirect |
| 81. C32×C5 | C8×D5 | semidirect |
| 99. C52 | #3710 | semidirect |
| 116. C3×C5 | #6648 | semidirect |
| 117. C3×C5 | C8×D15 | semidirect |
| 128. C32 | #87767 | semidirect |
| 136. C5 | #10623794 | semidirect |
| 141. C3 | #11925126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C3⋊(C3⋊(C5⋊D5)) | 2 |
| C3×C5×C3⋊#168 | 2 |
| #11925126 | 3 |
| #10623794 | 5 |