Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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. C5×#6817 | C2 | semidirect |
| 2. C2×C3×C4⋊(C5⋊D5) | C2 | semidirect |
| 3. C5×#6710 | C2 | semidirect |
| 4. #11925156 | C2 | semidirect |
| 5. #11925153 | C2 | semidirect |
| 10. C5×D60 | C22 | semidirect |
| 12. C5×Dic30 | C22 | semidirect |
| 15. C5×C3⋊#168 | C22 | semidirect |
| 18. C2×C4⋊(C5⋊D5) | D3 | semidirect |
| 30. #6817 | D5 | semidirect |
| 35. #6710 | D5 | semidirect |
| 64. D60 | C2×D5 | semidirect |
| 66. Dic30 | C2×D5 | semidirect |
| 78. C3⋊#168 | C2×D5 | semidirect |
| 99. C3×C52 | AGL(1,ℤ/8) | semidirect |
| 168. C52 | #932 | semidirect |
| 205. C3×C5 | #4054 | semidirect |
| 206. C3×C5 | #4095 | semidirect |
| 241. C5 | #91298 | semidirect |
| 242. C5 | #91312 | semidirect |
| 250. C3 | #11716943 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#6817 | 2 |
| C2×C3×C4⋊(C5⋊D5) | 2 |
| C5×#6710 | 2 |
| #11925156 | 2 |
| #11925153 | 2 |
| #11716943 | 3 |
| #91312 | 5 |
| #91298 | 5 |