Finite Group DatabasebetaFinite Group DatabasebetaOrder 15300.
224 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 43 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 | C32×C52×C17 | C22 |
| LCS | G ▷ C32×C52×C17 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C17×C3⋊(C3⋊(C5⋊D5)) | C2 | semidirect |
| 2. C3×C5×D255 | C2 | semidirect |
| 4. C32×C52×C17 | C22 | semidirect |
| 8. C5×D255 | D3 | semidirect |
| 13. C3×D255 | D5 | semidirect |
| 16. C3×C52×C17 | C2×D3 | semidirect |
| 23. C32×C5×C17 | C2×D5 | semidirect |
| 25. D255 | D15 | semidirect |
| 34. C3⋊(C3⋊(C5⋊D5)) | D17 | semidirect |
| 36. C52×C17 | D32 | semidirect |
| 44. C3×C5×C17 | D3×D5 | semidirect |
| 45. C3×C5×C17 | C2×D15 | semidirect |
| 46. C32×C52 | C2×D17 | semidirect |
| 53. C32×C17 | D52 | semidirect |
| 68. C5×C17 | D3×D15 | semidirect |
| 70. C3×C52 | D3×D17 | semidirect |
| 75. C3×C17 | D5×D15 | semidirect |
| 79. C32×C5 | D5×D17 | semidirect |
| 92. C52 | (C3⋊D3)⋊D17 | semidirect |
| 96. C17 | D152 | semidirect |
| 100. C3×C5 | D15×D17 | semidirect |
| 101. C3×C5 | D15⋊D17 | semidirect |
| 107. C32 | (C5⋊D5)⋊D17 | semidirect |
| 113. C5 | D51⋊D15 | semidirect |
| 116. C3 | D85⋊D15 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×C3⋊(C3⋊(C5⋊D5)) | 2 |
| C3×C5×D255 | 2 |
| D85⋊D15 | 3 |
| D51⋊D15 | 5 |
| D152 | 17 |