Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
584 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. C52×#101 | C2 | semidirect |
| 4. #11716703 | C2 | semidirect |
| 5. #11716691 | C2 | semidirect |
| 34. C5×#101 | D5 | semidirect |
| 60. C5⋊D5 | #101 | direct (N × H) |
| 79. #101 | C5⋊D5 | direct (N × H) |
| 80. C52 | C2×#101 | semidirect |
| 118. C5 | D5×#101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C5⋊D5 | 2 |
| M16×C5⋊D5 | 2 |
| C52×#101 | 2 |
| #11716703 | 2 |
| #11716691 | 2 |
| D5×#101 | 5 |