Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
640 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 98 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×#5617 | C2 | semidirect |
| 2. C3×C5×#447 | C2 | semidirect |
| 3. C5×#5223 | C2 | semidirect |
| 4. C5×#5218 | C2 | semidirect |
| 5. C5×#4537 | C2 | semidirect |
| 6. C5×#4468 | C2 | semidirect |
| 7. C5×#4467 | C2 | semidirect |
| 28. #70969 | C5 | direct (N × H) |
| 31. C5×#447 | D3 | semidirect |
| 42. C2×C3×C5×D4 | D4 | semidirect |
| 52. C2×C5×Dic6 | D4 | semidirect |
| 55. C3×C5×C4⋊C4 | D4 | semidirect |
| 66. C5×C4⋊Dic3 | D4 | semidirect |
| 70. #5617 | C2×C5 | semidirect |
| 71. C3×#447 | C2×C5 | semidirect |
| 72. #5223 | C2×C5 | semidirect |
| 73. #5218 | C2×C5 | semidirect |
| 74. #4537 | C2×C5 | semidirect |
| 75. #4468 | C2×C5 | semidirect |
| 76. #4467 | C2×C5 | semidirect |
| 167. C2×C5×D4 | #67 | semidirect |
| 179. C5×C4⋊C4 | #67 | semidirect |
| 191. #447 | C5×D3 | semidirect |
| 229. C2×C3×D4 | C5×D4 | semidirect |
| 239. C2×Dic6 | C5×D4 | semidirect |
| 242. C3×C4⋊C4 | C5×D4 | semidirect |
| 253. C4⋊Dic3 | C5×D4 | semidirect |
| 401. C2×D4 | C5×#67 | semidirect |
| 413. C4⋊C4 | C5×#67 | semidirect |
| 423. C3×C5 | #1600 | semidirect |
| 506. C5 | #70969 | direct (N × H) |
| 534. C3 | C5×#1600 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5617 | 2 |
| C3×C5×#447 | 2 |
| C5×#5223 | 2 |
| C5×#5218 | 2 |
| C5×#4537 | 2 |
| C5×#4468 | 2 |
| C5×#4467 | 2 |
| C5×#1600 | 3 |
| #70969 | 5 |