Finite Group DatabasebetaFinite Group DatabasebetaOrder 17100.
144 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C52×C9×C19 | C22 |
| Frattini | C3 | D95⋊D15 |
| socle | C3×C52×C19 | C2×D3 |
| LCS | G ▷ C52×C9×C19 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C19×C5⋊D45 | C2 | semidirect |
| 2. C5×D855 | C2 | semidirect |
| 3. C5×C9×D95 | C2 | semidirect |
| 5. C52×C9×C19 | C22 | semidirect |
| 12. D855 | D5 | semidirect |
| 17. C9×D95 | D5 | semidirect |
| 24. C5×D95 | D9 | semidirect |
| 27. C5×C9×C19 | C2×D5 | semidirect |
| 28. C5×C9×C19 | C2×D5 | semidirect |
| 37. C52×C19 | C2×D9 | semidirect |
| 38. C5⋊D45 | D19 | semidirect |
| 51. C52×C9 | C2×D19 | semidirect |
| 53. D95 | D45 | semidirect |
| 61. C9×C19 | D52 | semidirect |
| 70. C5×C19 | D5×D9 | semidirect |
| 71. C5×C19 | C2×D45 | semidirect |
| 88. C5×C9 | D5×D19 | semidirect |
| 89. C5×C9 | D5×D19 | semidirect |
| 101. C52 | D9×D19 | semidirect |
| 104. C19 | D5×D45 | semidirect |
| 119. C9 | (C5⋊D5)⋊D19 | semidirect |
| 124. C5 | D19×D45 | semidirect |
| 125. C5 | D45⋊D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×C5⋊D45 | 2 |
| C5×D855 | 2 |
| C5×C9×D95 | 2 |
| D95⋊D15 | 3 |
| D45⋊D19 | 5 |
| D19×D45 | 5 |
| D5×D45 | 19 |