Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1630 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 1630 conjugacy classes of subgroups — too many to draw. Only its 283 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #21426750 | C2 | semidirect |
| 3. #21424504 | C2 | semidirect |
| 4. #21424377 | C2 | semidirect |
| 5. #21424044 | C2 | semidirect |
| 6. C4×#14273642 | C2 | semidirect |
| 7. C4×H(5,𝔽2)×C59 | C2 | semidirect |
| 9. C22×(C2×D59)⋊C4 | C22 | semidirect |
| 10. #16837589 | C4 | semidirect |
| 18. #16837274 | C22 | semidirect |
| 19. #16837257 | C22 | semidirect |
| 20. C4×C22⋊Dic59 | C22 | semidirect |
| 21. #16837169 | C22 | semidirect |
| 33. #14273695 | C2×C4 | semidirect |
| 45. #14273642 | C2×C4 | semidirect |
| 55. C23×C4×C59 | D4 | semidirect |
| 69. C2×C4⋊C4×C59 | D4 | semidirect |
| 72. C2×C22⋊C4×C59 | D4 | semidirect |
| 75. C2×C42×C59 | D4 | semidirect |
| 83. C23×D59 | C22×C4 | semidirect |
| 126. C22⋊Dic59 | C22×C4 | semidirect |
| 215. C4×H(5,𝔽2) | D59 | semidirect |
| 250. C59 | #21482 | semidirect |
| 260. C23×C4 | C22⋊D59 | semidirect |
| 277. C2×C4⋊C4 | C22⋊D59 | semidirect |
| 288. C2×C22⋊C4 | C22⋊D59 | semidirect |
| 292. C2×C42 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837589 | 2 |
| #21426750 | 2 |
| #21424504 | 2 |
| #21424377 | 2 |
| #21424044 | 2 |
| C4×#14273642 | 2 |
| C4×H(5,𝔽2)×C59 | 2 |
| #21482 | 59 |