Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
830 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 830 conjugacy classes of subgroups — too many to draw. Only its 206 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C59 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C59×#376 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C59×#2641 | C2 | semidirect |
| 2. C59×#2054 | C2 | semidirect |
| 3. C59×#2025 | C2 | semidirect |
| 4. C59×#2011 | C2 | semidirect |
| 5. C59×#1832 | C2 | semidirect |
| 73. #32814 | C59 | direct (N × H) |
| 87. #2641 | C2×C59 | semidirect |
| 88. #2054 | C2×C59 | semidirect |
| 89. #2025 | C2×C59 | semidirect |
| 90. #2011 | C2×C59 | semidirect |
| 91. #1832 | C2×C59 | semidirect |
| 107. C59 | #32814 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C59×#2641 | 2 |
| C59×#2054 | 2 |
| C59×#2025 | 2 |
| C59×#2011 | 2 |
| C59×#1832 | 2 |
| #32814 | 59 |