Finite Group DatabasebetaFinite Group DatabasebetaOrder 26100.
128 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 30 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×C3 | C29⋊#3874 |
| commutator, cosocle, hypocenter | C29×C52⋊C3 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C52×C29 | D3 |
| LCS | G ▷ C29×C52⋊C3 | |
| UCS | C1 ◁ C2×C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×C29×C52⋊C3 | C2 | semidirect |
| 2. C3×C29⋊#3874 | C2 | direct (N × H) |
| 4. C2×C29⋊#3874 | C3 | direct (N × H) |
| 5. C3×C29×C52⋊C3 | C22 | semidirect |
| 8. C2×C29×C52⋊C3 | C2×C3 | semidirect |
| 9. C29⋊#3874 | C2×C3 | direct (N × H) |
| 10. C2×C3×C52×C29 | D3 | semidirect |
| 13. C29×C52⋊C3 | C22×C3 | semidirect |
| 14. C3×C52×C29 | C2×D3 | semidirect |
| 17. C2×C52×C29 | C3×D3 | semidirect |
| 25. C52×C29 | C2×C3×D3 | semidirect |
| 30. C2×C3×C52⋊C3 | D29 | semidirect |
| 43. C3×C52⋊C3 | C2×D29 | semidirect |
| 46. C2×C3×C29 | #3874 | semidirect |
| 49. C2×C3×C52 | D87 | semidirect |
| 52. C2×C52⋊C3 | C3×D29 | semidirect |
| 60. C3×C29 | C2×#3874 | semidirect |
| 61. C3×C52 | C2×D87 | semidirect |
| 63. C52⋊C3 | C2×C3×D29 | semidirect |
| 66. C2×C29 | C3×#3874 | semidirect |
| 68. C2×C52 | C3×D87 | semidirect |
| 75. C29 | C2×C3×#3874 | semidirect |
| 76. C52 | C2×C3×D87 | semidirect |
| 93. C2×C3 | C29⋊#3874 | direct (N × H) |
| 100. C3 | C2×C29⋊#3874 | direct (N × H) |
| 102. C2 | C3×C29⋊#3874 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C29×C52⋊C3 | 2 |
| C3×C29⋊#3874 | 2 |
| C2×C3×C5×D145 | 3 |
| C2×C29⋊#3874 | 3 |
| C2×C3×D87 | 25 |
| C2×C3×#3874 | 29 |