Finite Group DatabasebetaFinite Group DatabasebetaOrder 15300.
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 | C17 | #3874⋊D3 |
| commutator, cosocle, hypocenter | C3×C52⋊C3 | C22×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C17 | C2×D3 |
| LCS | G ▷ C3×C52⋊C3 | |
| UCS | C1 ◁ C17 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C17×C3⋊((C5⋊D5)⋊C3) | C2 | semidirect |
| 2. C17×C3⋊#3874 | C2 | semidirect |
| 3. C3×C17×#3874 | C2 | semidirect |
| 6. C3×C17×C52⋊C3 | C22 | semidirect |
| 7. C17×C3⋊(C5⋊D5) | D3 | semidirect |
| 13. C17×#3874 | D3 | semidirect |
| 15. C3×C52×C17 | C2×D3 | semidirect |
| 17. C17×C52⋊C3 | C2×D3 | semidirect |
| 20. #3874⋊D3 | C17 | direct (N × H) |
| 31. C3⋊((C5⋊D5)⋊C3) | C2×C17 | semidirect |
| 32. C3⋊#3874 | C2×C17 | semidirect |
| 33. C3×#3874 | C2×C17 | semidirect |
| 34. C52×C17 | D32 | semidirect |
| 44. C3×C52⋊C3 | C22×C17 | semidirect |
| 54. C3⋊(C5⋊D5) | D3×C17 | semidirect |
| 60. #3874 | D3×C17 | semidirect |
| 71. C3×C52 | C2×D3×C17 | semidirect |
| 73. C52⋊C3 | C2×D3×C17 | semidirect |
| 79. C3×C17 | #3874⋊C2 | semidirect |
| 93. C52 | D32×C17 | semidirect |
| 99. C17 | #3874⋊D3 | direct (N × H) |
| 123. C3 | C17×#3874⋊C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×C3⋊((C5⋊D5)⋊C3) | 2 |
| C17×C3⋊#3874 | 2 |
| C3×C17×#3874 | 2 |
| D5×C17×D15 | 3 |
| C17×#3874⋊C2 | 3 |
| #3874⋊D3 | 17 |
| D32×C17 | 25 |