Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
672 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 111 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. #11717522 | C2 | semidirect |
| 2. C52×AGL(1,ℤ/8) | C2 | semidirect |
| 3. #11717260 | C2 | semidirect |
| 4. #11717252 | C2 | semidirect |
| 5. #11716704 | C2 | semidirect |
| 6. #11716692 | C2 | semidirect |
| 7. #11716690 | C2 | semidirect |
| 9. C2×C52×D4 | C22 | semidirect |
| 20. C52×M16 | C22 | semidirect |
| 23. C4×#1039 | C22 | semidirect |
| 24. #87804 | C22 | semidirect |
| 29. C52×Q8 | D4 | semidirect |
| 33. C52×D4 | D4 | semidirect |
| 43. C4⋊(C5⋊D5) | D4 | semidirect |
| 46. #6045 | D4 | semidirect |
| 50. C5×AGL(1,ℤ/8) | D5 | semidirect |
| 70. C2×C5×D4 | C2×D5 | semidirect |
| 81. C5×M16 | C2×D5 | semidirect |
| 96. C5×Q8 | C22⋊D5 | semidirect |
| 100. C5×D4 | C22⋊D5 | semidirect |
| 118. AGL(1,ℤ/8) | C5⋊D5 | semidirect |
| 123. C52 | #453 | semidirect |
| 146. C2×D4 | C2×C5⋊D5 | semidirect |
| 152. M16 | C2×C5⋊D5 | semidirect |
| 164. Q8 | C22⋊(C5⋊D5) | semidirect |
| 175. D4 | C22⋊(C5⋊D5) | semidirect |
| 183. C5 | #65487 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717522 | 2 |
| C52×AGL(1,ℤ/8) | 2 |
| #11717260 | 2 |
| #11717252 | 2 |
| #11716704 | 2 |
| #11716692 | 2 |
| #11716690 | 2 |
| #65487 | 5 |