Finite Group DatabasebetaFinite Group DatabasebetaOrder 26100.
128 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | #3874⋊D3 |
| commutator, cosocle, hypocenter | C3×C52⋊C3 | C22×C29 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C29 | C2×D3 |
| LCS | G ▷ C3×C52⋊C3 | |
| UCS | C1 ◁ C29 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×C3⋊((C5⋊D5)⋊C3) | C2 | semidirect |
| 2. C29×C3⋊#3874 | C2 | semidirect |
| 3. C3×C29×#3874 | C2 | semidirect |
| 6. C3×C29×C52⋊C3 | C22 | semidirect |
| 7. C29×C3⋊(C5⋊D5) | D3 | semidirect |
| 13. C29×#3874 | D3 | semidirect |
| 16. C29×C52⋊C3 | C2×D3 | semidirect |
| 17. C3×C52×C29 | C2×D3 | semidirect |
| 24. #3874⋊D3 | C29 | direct (N × H) |
| 31. C52×C29 | D32 | semidirect |
| 37. C3⋊((C5⋊D5)⋊C3) | C2×C29 | semidirect |
| 38. C3⋊#3874 | C2×C29 | semidirect |
| 39. C3×#3874 | C2×C29 | semidirect |
| 53. C3×C52⋊C3 | C22×C29 | semidirect |
| 61. C3⋊(C5⋊D5) | D3×C29 | semidirect |
| 67. #3874 | D3×C29 | semidirect |
| 74. C3×C29 | #3874⋊C2 | semidirect |
| 75. C3×C52 | C2×D3×C29 | semidirect |
| 77. C52⋊C3 | C2×D3×C29 | semidirect |
| 93. C29 | #3874⋊D3 | direct (N × H) |
| 94. C52 | D32×C29 | semidirect |
| 123. C3 | C29×#3874⋊C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×C3⋊((C5⋊D5)⋊C3) | 2 |
| C29×C3⋊#3874 | 2 |
| C3×C29×#3874 | 2 |
| D5×C29×D15 | 3 |
| C29×#3874⋊C2 | 3 |
| D32×C29 | 25 |
| #3874⋊D3 | 29 |