Finite Group DatabasebetaFinite Group DatabasebetaOrder 26100.
128 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 27 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 | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C52×C29 | C22×C3 |
| LCS | G ▷ C3×C52×C29 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C52⋊C3×D87 | C2 | semidirect |
| 2. C3⋊(C29⋊((C5⋊D5)⋊C3)) | C2 | semidirect |
| 3. C3×C29×(C5⋊D5)⋊C3 | C2 | semidirect |
| 4. C5⋊D5×D87 | C3 | semidirect |
| 6. C3×C29×C52⋊C3 | C22 | semidirect |
| 7. C3⋊(C5⋊D145) | C2×C3 | semidirect |
| 8. C52×D87 | C2×C3 | semidirect |
| 9. C3×C29×C5⋊D5 | C2×C3 | semidirect |
| 13. C29×(C5⋊D5)⋊C3 | D3 | semidirect |
| 16. C29×C52⋊C3 | C2×D3 | semidirect |
| 17. C3×C52×C29 | C22×C3 | semidirect |
| 20. C29×C5⋊D5 | C3×D3 | semidirect |
| 27. C52×C29 | C2×C3×D3 | semidirect |
| 34. C3×(C5⋊D5)⋊C3 | D29 | semidirect |
| 44. C3×C52⋊C3 | C2×D29 | semidirect |
| 49. D87 | (C5⋊D5)⋊C3 | direct (N × H) |
| 54. C3×C5⋊D5 | C3×D29 | semidirect |
| 58. (C5⋊D5)⋊C3 | D87 | direct (N × H) |
| 64. C3×C29 | C2×(C5⋊D5)⋊C3 | semidirect |
| 65. C3×C52 | C2×C3×D29 | semidirect |
| 67. C52⋊C3 | C2×D87 | semidirect |
| 74. C5⋊D5 | C3×D87 | semidirect |
| 79. C29 | D3×(C5⋊D5)⋊C3 | semidirect |
| 80. C52 | C2×C3×D87 | semidirect |
| 103. C3 | D29×(C5⋊D5)⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52⋊C3×D87 | 2 |
| C3⋊(C29⋊((C5⋊D5)⋊C3)) | 2 |
| C3×C29×(C5⋊D5)⋊C3 | 2 |
| C5⋊D5×D87 | 3 |
| D29×(C5⋊D5)⋊C3 | 3 |
| C2×C3×D87 | 25 |
| D3×(C5⋊D5)⋊C3 | 29 |