Finite Group DatabasebetaFinite Group DatabasebetaOrder 6400.
984 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 984 conjugacy classes of subgroups — too many to draw. Only its 221 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. #72253081 | C2 | semidirect |
| 2. C52×#1333 | C2 | semidirect |
| 3. #72253069 | C2 | semidirect |
| 4. #72253065 | C2 | semidirect |
| 6. #72242180 | C2 | semidirect |
| 7. #72242123 | C2 | semidirect |
| 36. #11716693 | C8 | semidirect |
| 48. C5×#1333 | D5 | semidirect |
| 57. C52×D8 | C2×C8 | semidirect |
| 71. #87801 | C2×C8 | semidirect |
| 75. #87756 | C2×C8 | semidirect |
| 140. #1333 | C5⋊D5 | semidirect |
| 160. C5×D8 | C8×D5 | semidirect |
| 242. C52 | #12067 | semidirect |
| 263. D8 | C8×C5⋊D5 | semidirect |
| 307. C5 | #12011182 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72253081 | 2 |
| C52×#1333 | 2 |
| #72253069 | 2 |
| #72253065 | 2 |
| #72242274 | 2 |
| #72242180 | 2 |
| #72242123 | 2 |
| #12011182 | 5 |