Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
938 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 938 conjugacy classes of subgroups — too many to draw. Only its 222 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 |
| prime radical | C2×C5×#562 | C2 |
| 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 |
|---|---|---|
| 2. C5×#3215 | C2 | semidirect |
| 3. C5×#3166 | C2 | semidirect |
| 4. C5×#1661 | C2 | semidirect |
| 5. C5×#1534 | C2 | semidirect |
| 6. C5×#1527 | C2 | semidirect |
| 16. C5×#501 | C22 | semidirect |
| 18. C5×#497 | C22 | semidirect |
| 19. C5×#489 | C22 | semidirect |
| 26. C5×#330 | C22 | semidirect |
| 27. C5×#329 | C22 | semidirect |
| 28. #19006 | C5 | direct (N × H) |
| 71. #3215 | C2×C5 | semidirect |
| 72. #3166 | C2×C5 | semidirect |
| 73. #1661 | C2×C5 | semidirect |
| 74. #1534 | C2×C5 | semidirect |
| 75. #1527 | C2×C5 | semidirect |
| 124. #501 | C22×C5 | semidirect |
| 126. #497 | C22×C5 | semidirect |
| 127. #489 | C22×C5 | semidirect |
| 134. #330 | C22×C5 | semidirect |
| 135. #329 | C22×C5 | semidirect |
| 284. C5 | #19006 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#562 | 2 |
| C5×#3215 | 2 |
| C5×#3166 | 2 |
| C5×#1661 | 2 |
| C5×#1534 | 2 |
| C5×#1527 | 2 |
| #19006 | 5 |