Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
434 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C5 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C5×C4⋊C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#3245 | C2 | semidirect |
| 2. C5×#2184 | C2 | semidirect |
| 3. C5×#2054 | C2 | semidirect |
| 4. C5×#1347 | C2 | semidirect |
| 5. C5×#1322 | C2 | semidirect |
| 19. #12158 | C5 | direct (N × H) |
| 47. #3245 | C2×C5 | semidirect |
| 48. #2184 | C2×C5 | semidirect |
| 49. #2054 | C2×C5 | semidirect |
| 50. #1347 | C2×C5 | semidirect |
| 51. #1322 | C2×C5 | semidirect |
| 134. C2×C4×C5 | D16 | semidirect |
| 264. C2×C4 | C5×D16 | semidirect |
| 269. C5 | #12158 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3245 | 2 |
| C5×#2184 | 2 |
| C5×#2054 | 2 |
| C5×#1347 | 2 |
| C5×#1322 | 2 |
| #12158 | 5 |