Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
890 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 890 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 |
|---|---|---|
| 15. #11716898 | C4 | semidirect |
| 18. C5×#3968 | C4 | semidirect |
| 19. #11716602 | C4 | semidirect |
| 90. #3968 | AGL(1,𝔽5) | semidirect |
| 101. #1043 | #101 | semidirect |
| 210. C52 | C4×#101 | semidirect |
| 291. C5 | AGL(1,𝔽5)×#101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#1043 | 2 |
| #13104927 | 2 |
| #13103905 | 2 |
| #13101808 | 2 |
| #13099912 | 2 |
| AGL(1,𝔽5)×#101 | 5 |