Subgroups — C₃×C₅²×C₁₁×C₁₃ #24924331

Order 10725.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₁×C₁₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₅×C₁₁×C₁₃	C₅	1	6	yes	maximal, direct product factor
3	C₃×C₅²×C₁₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅²×C₁₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₁₁×C₁₃	C₃×C₅	1	6	yes	direct product factor
6	C₃×C₁₁×C₁₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
7	C₅²×C₁₃	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
8	C₅²×C₁₁	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₅×C₁₃	C₅×C₁₁	1	6	yes	direct product factor
10	C₃×C₅×C₁₁	C₅×C₁₃	1	6	yes	direct product factor
11	C₁₁×C₁₃	C₃×C₅²	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₅²	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
13	C₅×C₁₃	C₃×C₅×C₁₁	1	6	yes	direct product factor
14	C₅×C₁₁	C₃×C₅×C₁₃	1	6	yes	direct product factor
15	C₃×C₁₃	C₅²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₁₁	C₅²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
17	C₅²	C₃×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×C₅	C₅×C₁₁×C₁₃	1	6	yes	direct product factor
19	C₁₃	C₃×C₅²×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
20	C₁₁	C₃×C₅²×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₅	C₃×C₅×C₁₁×C₁₃	1	6	yes	direct product factor
22	C₃	C₅²×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅²×C₁₁×C₁₃	C₃	direct (N × H)
2. C₃×C₅×C₁₁×C₁₃	C₅	direct (N × H)
3. C₃×C₅²×C₁₃	C₁₁	direct (N × H)
4. C₃×C₅²×C₁₁	C₁₃	direct (N × H)
5. C₅×C₁₁×C₁₃	C₃×C₅	direct (N × H)
6. C₃×C₁₁×C₁₃	C₅²	direct (N × H)
7. C₅²×C₁₃	C₃×C₁₁	direct (N × H)
8. C₅²×C₁₁	C₃×C₁₃	direct (N × H)
9. C₃×C₅×C₁₃	C₅×C₁₁	direct (N × H)
10. C₃×C₅×C₁₁	C₅×C₁₃	direct (N × H)
11. C₁₁×C₁₃	C₃×C₅²	direct (N × H)
12. C₃×C₅²	C₁₁×C₁₃	direct (N × H)
13. C₅×C₁₃	C₃×C₅×C₁₁	direct (N × H)
14. C₅×C₁₁	C₃×C₅×C₁₃	direct (N × H)
15. C₃×C₁₃	C₅²×C₁₁	direct (N × H)
16. C₃×C₁₁	C₅²×C₁₃	direct (N × H)
17. C₅²	C₃×C₁₁×C₁₃	direct (N × H)
18. C₃×C₅	C₅×C₁₁×C₁₃	direct (N × H)
19. C₁₃	C₃×C₅²×C₁₁	direct (N × H)
20. C₁₁	C₃×C₅²×C₁₃	direct (N × H)
21. C₅	C₃×C₅×C₁₁×C₁₃	direct (N × H)
22. C₃	C₅²×C₁₁×C₁₃	direct (N × H)

Subgroups — C3×C52×C11×C13 #24924331

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₅²×C₁₁×C₁₃ #24924331