Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
380 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 380 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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D4×C3⋊(C5⋊D5) | C2 | semidirect |
| 2. #11925624 | C2 | semidirect |
| 3. C5×#6716 | C2 | semidirect |
| 4. C3×C5×#686 | C2 | semidirect |
| 5. #11925136 | C2 | semidirect |
| 6. #11925132 | C2 | semidirect |
| 7. #11925129 | C2 | semidirect |
| 14. C5×Dic30 | C22 | semidirect |
| 15. C3×C5×D20 | C22 | semidirect |
| 18. C5×C3⋊#168 | C22 | semidirect |
| 19. C3×C5×#168 | C22 | semidirect |
| 25. C5×#686 | D3 | semidirect |
| 43. #6716 | D5 | semidirect |
| 48. C3×#686 | D5 | semidirect |
| 57. C5×D20 | C2×D3 | semidirect |
| 62. C5×#168 | C2×D3 | semidirect |
| 90. Dic30 | C2×D5 | semidirect |
| 92. C3×D20 | C2×D5 | semidirect |
| 96. C3⋊#168 | C2×D5 | semidirect |
| 97. C3×#168 | C2×D5 | semidirect |
| 118. #686 | D15 | semidirect |
| 123. C3×C52 | AGL(1,ℤ/8) | semidirect |
| 180. D20 | C2×D15 | semidirect |
| 189. #168 | C2×D15 | semidirect |
| 208. C52 | #911 | semidirect |
| 253. C3×C5 | #4057 | semidirect |
| 254. C3×C5 | #4060 | semidirect |
| 297. C5 | #91498 | semidirect |
| 298. C5 | #91800 | semidirect |
| 307. C3 | #11717055 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×C3⋊(C5⋊D5) | 2 |
| #11925624 | 2 |
| C5×#6716 | 2 |
| C3×C5×#686 | 2 |
| #11925136 | 2 |
| #11925132 | 2 |
| #11925129 | 2 |
| #11717055 | 3 |
| #91800 | 5 |
| #91498 | 5 |