Finite Group DatabasebetaFinite Group DatabasebetaOrder 3600.
528 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3×C3⋊#1044 | C2 | semidirect |
| 4. C2×C3⋊(C3⋊(C5⋊D5)) | C4 | semidirect |
| 5. C2×C52×C3⋊D3 | C4 | semidirect |
| 12. C2×C3⋊#1044 | D3 | semidirect |
| 34. C32×C52 | C22⋊C4 | semidirect |
| 40. C2×C5×C3⋊D3 | AGL(1,𝔽5) | semidirect |
| 77. C3×C52 | (C2×D3)⋊C4 | semidirect |
| 106. C32×C5 | C22⋊AGL(1,𝔽5) | semidirect |
| 113. C2×C3⋊D3 | #1044 | semidirect |
| 133. C52 | #3722 | semidirect |
| 155. C3×C5 | (C2×D3)⋊AGL(1,𝔽5) | semidirect |
| 175. C32 | C22⋊#1044 | semidirect |
| 188. C5 | #10623978 | semidirect |
| 195. C3 | (C2×D3)⋊#1044 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3⋊D3×C5⋊D5 | 2 |
| C2×C3×C3⋊#1044 | 2 |
| (C2×D3)⋊#1044 | 3 |
| #10623978 | 5 |