Finite Group DatabasebetaFinite Group Databasebeta← D41×C3⋊((C5⋊D5)⋊C3) #49147015
Order 36900.
128 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 26 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×C41 | C22×C3 |
| LCS | G ▷ C3×C52×C41 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3⋊(C41⋊((C5⋊D5)⋊C3)) | C2 | semidirect |
| 2. C41×C3⋊((C5⋊D5)⋊C3) | C2 | semidirect |
| 3. C3×C52⋊C3×D41 | C2 | semidirect |
| 4. D41×C3⋊(C5⋊D5) | C3 | semidirect |
| 6. C3×C41×C52⋊C3 | C22 | semidirect |
| 7. C3⋊(C5⋊D205) | C2×C3 | semidirect |
| 8. C41×C3⋊(C5⋊D5) | C2×C3 | semidirect |
| 9. C3×C52×D41 | C2×C3 | semidirect |
| 11. C52⋊C3×D41 | D3 | semidirect |
| 16. C41×C52⋊C3 | C2×D3 | semidirect |
| 17. C3×C52×C41 | C22×C3 | semidirect |
| 21. C52×D41 | C3×D3 | semidirect |
| 26. C52×C41 | C2×C3×D3 | semidirect |
| 37. C3⋊((C5⋊D5)⋊C3) | D41 | direct (N × H) |
| 49. C3×D41 | (C5⋊D5)⋊C3 | semidirect |
| 51. C3×C52⋊C3 | C2×D41 | semidirect |
| 56. C3⋊(C5⋊D5) | C3×D41 | semidirect |
| 63. C3×C41 | C2×(C5⋊D5)⋊C3 | semidirect |
| 67. D41 | C3⋊((C5⋊D5)⋊C3) | direct (N × H) |
| 68. C3×C52 | C2×C3×D41 | semidirect |
| 70. C52⋊C3 | D3×D41 | semidirect |
| 75. C41 | C2×C3⋊((C5⋊D5)⋊C3) | semidirect |
| 80. C52 | C3×D3×D41 | semidirect |
| 103. C3 | D41×(C5⋊D5)⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊(C41⋊((C5⋊D5)⋊C3)) | 2 |
| C41×C3⋊((C5⋊D5)⋊C3) | 2 |
| C3×C52⋊C3×D41 | 2 |
| D41×C3⋊(C5⋊D5) | 3 |
| D41×(C5⋊D5)⋊C3 | 3 |
| C3×D3×D41 | 25 |
| C2×C3⋊((C5⋊D5)⋊C3) | 41 |