Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
862 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 862 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. M16×#1043 | C2 | semidirect |
| 4. #13103905 | C2 | semidirect |
| 6. #13100369 | C2 | semidirect |
| 7. #13099913 | C2 | semidirect |
| 23. #11716781 | C4 | semidirect |
| 26. C5×#3955 | C4 | semidirect |
| 27. #11716599 | C4 | semidirect |
| 43. #87867 | C2×C4 | semidirect |
| 48. #87860 | C2×C4 | semidirect |
| 57. C52×M16 | C2×C4 | semidirect |
| 58. #87804 | C2×C4 | semidirect |
| 61. C5×#681 | C2×C4 | semidirect |
| 129. #3955 | AGL(1,𝔽5) | semidirect |
| 145. #1043 | #100 | semidirect |
| 191. C5×M16 | C2×AGL(1,𝔽5) | semidirect |
| 194. #681 | C2×AGL(1,𝔽5) | semidirect |
| 285. C52 | C4×#100 | semidirect |
| 342. M16 | D5⋊AGL(1,𝔽5) | semidirect |
| 399. C5 | AGL(1,𝔽5)×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11717363 | 2 |
| M16×#1043 | 2 |
| #13103927 | 2 |
| #13103905 | 2 |
| #13101182 | 2 |
| #13100369 | 2 |
| #13099913 | 2 |
| AGL(1,𝔽5)×#100 | 5 |