Finite Group DatabasebetaFinite Group DatabasebetaOrder 15300.
128 conjugacy classes of subgroups; only the 21 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 21 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, cosocle, hypocenter | C3×C17×C52⋊C3 | C22 |
| Fitting, socle | C3×C52×C17 | C2×D3 |
| LCS | G ▷ C3×C17×C52⋊C3 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C52⋊C3×D51 | C2 | semidirect |
| 2. C3⋊(C17⋊#3874) | C2 | semidirect |
| 3. C3×C17×#3874 | C2 | semidirect |
| 6. C3×C17×C52⋊C3 | C22 | semidirect |
| 8. C52×D51 | D3 | semidirect |
| 13. C17×#3874 | D3 | semidirect |
| 15. C3×C52×C17 | C2×D3 | semidirect |
| 17. C17×C52⋊C3 | C2×D3 | semidirect |
| 33. C3×#3874 | D17 | semidirect |
| 34. C52×C17 | D32 | semidirect |
| 44. C3×C52⋊C3 | C2×D17 | semidirect |
| 60. #3874 | D51 | direct (N × H) |
| 65. D51 | #3874 | direct (N × H) |
| 71. C3×C52 | D3×D17 | semidirect |
| 73. C52⋊C3 | C2×D51 | semidirect |
| 79. C3×C17 | C2×#3874 | semidirect |
| 93. C52 | D3×D51 | semidirect |
| 99. C17 | D3×#3874 | semidirect |
| 123. C3 | D17×#3874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52⋊C3×D51 | 2 |
| C3⋊(C17⋊#3874) | 2 |
| C3×C17×#3874 | 2 |
| C5×D5×D51 | 3 |
| D17×#3874 | 3 |
| D3×#3874 | 17 |
| D3×D51 | 25 |