Subgroups — C₃×C₁₃×C₁₉×C₅⋊D₅ #49150323

Order 37050.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×C₁₉×C₅⋊D₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₅×C₁₃×C₁₉	—	5	6	no	maximal
4	C₅²×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₁₃×C₁₉	D₅	1	6	yes	complemented
6	C₃×C₁₉×C₅⋊D₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	D₅×C₁₃×C₁₉	—	5	6	no	—
8	C₃×C₁₃×C₅⋊D₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₁₃×C₁₉	—	25	1	no	Hall
10	C₃×C₅²×C₁₉	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
11	C₅×C₁₃×C₁₉	C₃×D₅	1	6	yes	complemented
12	C₃×C₅²×C₁₃	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
13	C₁₉×C₅⋊D₅	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₁₃×C₁₉	C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
15	C₁₃×C₅⋊D₅	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
16	C₃×D₅×C₁₉	—	5	6	no	—
17	C₂×C₁₃×C₁₉	—	25	1	no	Hall
18	C₅²×C₁₉	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
19	C₃×D₅×C₁₃	—	5	6	no	—
20	C₅²×C₁₃	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
21	C₃×C₅×C₁₉	D₅×C₁₃	1	6	yes	complemented
22	C₁₃×C₁₉	C₃×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₅×C₁₃	D₅×C₁₉	1	6	yes	complemented
24	D₅×C₁₉	—	5	6	no	—
25	C₃×C₅⋊D₅	C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
26	D₅×C₁₃	—	5	6	no	—
27	C₂×C₃×C₁₉	—	25	1	no	Hall
28	C₅×C₁₉	C₃×D₅×C₁₃	1	6	yes	complemented
29	C₂×C₃×C₁₃	—	25	1	no	Hall
30	C₃×C₅²	C₂×C₁₃×C₁₉	1	1	yes	characteristic, complemented, Hall
31	C₅×C₁₃	C₃×D₅×C₁₉	1	6	yes	complemented
32	C₃×C₁₉	C₁₃×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
33	C₅⋊D₅	C₃×C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
34	C₃×C₁₃	C₁₉×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
35	C₂×C₁₉	—	25	1	no	Hall
36	C₃×D₅	—	5	6	no	—
37	C₂×C₁₃	—	25	1	no	Hall
38	C₅²	C₂×C₃×C₁₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
39	C₁₉	C₃×C₁₃×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
40	C₃×C₅	D₅×C₁₃×C₁₉	1	6	yes	complemented
41	C₁₃	C₃×C₁₉×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
42	D₅	—	5	6	no	—
43	C₂×C₃	—	25	1	no	Hall
44	C₅	C₃×D₅×C₁₃×C₁₉	1	6	yes	complemented
45	C₃	C₁₃×C₁₉×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₃×C₁₉	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂×C₃×C₁₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₃×C₁₉	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃×C₁₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₁₃×C₁₉	C₂	semidirect
2. C₁₃×C₁₉×C₅⋊D₅	C₃	direct (N × H)
4. C₅²×C₁₃×C₁₉	C₂×C₃	semidirect
5. C₃×C₅×C₁₃×C₁₉	D₅	semidirect
6. C₃×C₁₉×C₅⋊D₅	C₁₃	direct (N × H)
8. C₃×C₁₃×C₅⋊D₅	C₁₉	direct (N × H)
10. C₃×C₅²×C₁₉	C₂×C₁₃	semidirect
11. C₅×C₁₃×C₁₉	C₃×D₅	semidirect
12. C₃×C₅²×C₁₃	C₂×C₁₉	semidirect
13. C₁₉×C₅⋊D₅	C₃×C₁₃	direct (N × H)
14. C₃×C₁₃×C₁₉	C₅⋊D₅	direct (N × H)
15. C₁₃×C₅⋊D₅	C₃×C₁₉	direct (N × H)
18. C₅²×C₁₉	C₂×C₃×C₁₃	semidirect
20. C₅²×C₁₃	C₂×C₃×C₁₉	semidirect
21. C₃×C₅×C₁₉	D₅×C₁₃	semidirect
22. C₁₃×C₁₉	C₃×C₅⋊D₅	direct (N × H)
23. C₃×C₅×C₁₃	D₅×C₁₉	semidirect
25. C₃×C₅⋊D₅	C₁₃×C₁₉	direct (N × H)
28. C₅×C₁₉	C₃×D₅×C₁₃	semidirect
30. C₃×C₅²	C₂×C₁₃×C₁₉	semidirect
31. C₅×C₁₃	C₃×D₅×C₁₉	semidirect
32. C₃×C₁₉	C₁₃×C₅⋊D₅	direct (N × H)
33. C₅⋊D₅	C₃×C₁₃×C₁₉	direct (N × H)
34. C₃×C₁₃	C₁₉×C₅⋊D₅	direct (N × H)
38. C₅²	C₂×C₃×C₁₃×C₁₉	semidirect
39. C₁₉	C₃×C₁₃×C₅⋊D₅	direct (N × H)
40. C₃×C₅	D₅×C₁₃×C₁₉	semidirect
41. C₁₃	C₃×C₁₉×C₅⋊D₅	direct (N × H)
44. C₅	C₃×D₅×C₁₃×C₁₉	semidirect
45. C₃	C₁₃×C₁₉×C₅⋊D₅	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅²×C₁₃×C₁₉	2
C₁₃×C₁₉×C₅⋊D₅	3
C₃×D₅×C₁₃×C₁₉	5
C₃×C₁₉×C₅⋊D₅	13
C₃×C₁₃×C₅⋊D₅	19

Subgroups — C3×C13×C19×C5⋊D5 #49150323

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₃×C₁₉×C₅⋊D₅ #49150323