Finite Group DatabasebetaFinite Group DatabasebetaOrder 17100.
144 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 42 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 | C3 | D5×C5⋊(D19⋊C3) |
| commutator, hypocenter | C52×C19 | C22×C9 |
| Fitting, socle, cosocle | C3×C52×C19 | C22×C3 |
| prime radical | C3×D5×D95 | C3 |
| LCS | G ▷ C52×C19 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5⋊(C5⋊(#4294⋊C2)) | C2 | semidirect |
| 2. C5×D5×#4294 | C2 | semidirect |
| 3. C5×C5⋊(#4294⋊C2) | C2 | semidirect |
| 5. C52×#4294 | C22 | semidirect |
| 11. D5×D95 | C9 | semidirect |
| 16. C5⋊(#4294⋊C2) | D5 | direct (N × H) |
| 17. D5×#4294 | D5 | semidirect |
| 22. C5⋊D95 | C2×C9 | semidirect |
| 23. C5×D95 | C2×C9 | semidirect |
| 24. C5×D5×C19 | C2×C9 | semidirect |
| 27. C5×#4294 | C2×D5 | semidirect |
| 28. C5×#4294 | C2×D5 | semidirect |
| 37. C52×C19 | C22×C9 | semidirect |
| 56. D95 | C9×D5 | semidirect |
| 58. D5×C19 | C9×D5 | semidirect |
| 61. #4294 | D52 | semidirect |
| 70. C5×C19 | C2×C9×D5 | semidirect |
| 71. C5×C19 | C2×C9×D5 | semidirect |
| 86. C5×D5 | #4294⋊C2 | semidirect |
| 101. C52 | C2×#4294⋊C2 | semidirect |
| 104. C19 | C9×D52 | semidirect |
| 118. D5 | C5⋊(#4294⋊C2) | direct (N × H) |
| 124. C5 | D5×#4294⋊C2 | semidirect |
| 125. C5 | C2×C5⋊(#4294⋊C2) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5⋊(C5⋊(#4294⋊C2)) | 2 |
| C5×D5×#4294 | 2 |
| C5×C5⋊(#4294⋊C2) | 2 |
| C3×D5×D95 | 3 |
| C2×C5⋊(#4294⋊C2) | 5 |
| D5×#4294⋊C2 | 5 |
| C9×D52 | 19 |