Finite Group DatabasebetaFinite Group DatabasebetaOrder 15300.
224 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C17 | (C3⋊D3)⋊D5 |
| commutator, cosocle, hypocenter | C32×C5 | C22×C5×C17 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C17 | C22 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C5×C17 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C52×C17×C3⋊D3 | C2 | semidirect |
| 2. C3×C5×C17×D15 | C2 | semidirect |
| 4. C32×C52×C17 | C22 | semidirect |
| 5. C17×(C3⋊D3)⋊D5 | C5 | direct (N × H) |
| 7. C5×C17×D15 | D3 | semidirect |
| 13. C5×C17×C3⋊D3 | D5 | semidirect |
| 14. C5×C17×C3⋊D3 | C2×C5 | semidirect |
| 15. C3×C17×D15 | C2×C5 | semidirect |
| 18. C3×C52×C17 | C2×D3 | semidirect |
| 21. C5×(C3⋊D3)⋊D5 | C17 | direct (N × H) |
| 25. C32×C5×C17 | C2×D5 | semidirect |
| 26. C32×C5×C17 | C22×C5 | semidirect |
| 29. C17×D15 | C5×D3 | semidirect |
| 38. C52×C3⋊D3 | C2×C17 | semidirect |
| 39. C3×C5×D15 | C2×C17 | semidirect |
| 40. C52×C17 | D32 | semidirect |
| 43. C17×C3⋊D3 | C5×D5 | semidirect |
| 50. C3×C5×C17 | D3×D5 | semidirect |
| 51. C3×C5×C17 | C2×C5×D3 | semidirect |
| 52. C32×C52 | C22×C17 | semidirect |
| 54. (C3⋊D3)⋊D5 | C5×C17 | direct (N × H) |
| 61. C32×C17 | C2×C5×D5 | semidirect |
| 62. C5×D15 | D3×C17 | semidirect |
| 72. C5×C3⋊D3 | D5×C17 | semidirect |
| 73. C5×C3⋊D3 | C2×C5×C17 | semidirect |
| 74. C3×D15 | C2×C5×C17 | semidirect |
| 77. C5×C17 | C5×D32 | semidirect |
| 78. C5×C17 | (C3⋊D3)⋊D5 | direct (N × H) |
| 80. C3×C52 | C2×D3×C17 | semidirect |
| 85. C3×C17 | C5×D3×D5 | semidirect |
| 89. C32×C5 | C2×D5×C17 | semidirect |
| 90. C32×C5 | C22×C5×C17 | semidirect |
| 95. D15 | C5×D3×C17 | semidirect |
| 104. C52 | D32×C17 | semidirect |
| 107. C3⋊D3 | C5×D5×C17 | semidirect |
| 109. C17 | C5×(C3⋊D3)⋊D5 | direct (N × H) |
| 114. C3×C5 | D3×D5×C17 | semidirect |
| 115. C3×C5 | C2×C5×D3×C17 | semidirect |
| 122. C32 | C2×C5×D5×C17 | semidirect |
| 128. C5 | C5×D32×C17 | semidirect |
| 129. C5 | C17×(C3⋊D3)⋊D5 | direct (N × H) |
| 132. C3 | C5×D3×D5×C17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×C17×C3⋊D3 | 2 |
| C3×C5×C17×D15 | 2 |
| C5×D3×D5×C17 | 3 |
| C17×(C3⋊D3)⋊D5 | 5 |
| C5×D32×C17 | 5 |
| C5×(C3⋊D3)⋊D5 | 17 |