Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1252 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 230 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 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C5 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#3549 | C2 | semidirect |
| 2. C5×#3151 | C2 | semidirect |
| 3. C5×#1655 | C2 | semidirect |
| 4. C5×#1525 | C2 | semidirect |
| 6. C5×H(3,𝔽4) | C22 | semidirect |
| 11. C2×C5×#127 | C22 | semidirect |
| 12. C5×#496 | C22 | semidirect |
| 15. C4×C5×M16 | C22 | semidirect |
| 16. C5×#329 | C22 | semidirect |
| 17. #19073 | C5 | direct (N × H) |
| 41. #3549 | C2×C5 | semidirect |
| 42. #3151 | C2×C5 | semidirect |
| 43. #1655 | C2×C5 | semidirect |
| 44. #1525 | C2×C5 | semidirect |
| 70. H(3,𝔽4) | C22×C5 | semidirect |
| 75. C2×#127 | C22×C5 | semidirect |
| 76. #496 | C22×C5 | semidirect |
| 79. C4×M16 | C22×C5 | semidirect |
| 80. #329 | C22×C5 | semidirect |
| 178. C5 | #19073 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3549 | 2 |
| C5×#3151 | 2 |
| C5×#1655 | 2 |
| C5×#1525 | 2 |
| #19073 | 5 |