Subgroups — C₅²×C₁₃×D₁₉⋊C₃ #49150263

Order 37050.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₃×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅²×C₁₃×D₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₁₃×D₁₉⋊C₃	C₅	1	6	yes	maximal, direct product factor
4	C₅²×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅×C₁₃×C₁₉⋊C₃	C₂×C₅	1	6	yes	complemented
6	C₅²×D₁₉⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₁₃×D₁₉	C₃×C₅	1	6	yes	complemented
8	C₂×C₃×C₅²×C₁₃	—	19	1	no	maximal, Hall
9	C₁₃×D₁₉⋊C₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
10	C₅²×C₁₉⋊C₃	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
11	C₅×C₁₃×C₁₉	C₂×C₃×C₅	1	6	yes	complemented
12	C₃×C₅²×C₁₃	—	19	1	no	Hall
13	C₅²×D₁₉	C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
14	C₁₃×C₁₉⋊C₃	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
15	C₂×C₅²×C₁₃	—	19	1	no	Hall
16	C₅×D₁₉⋊C₃	C₅×C₁₃	1	6	yes	direct product factor
17	C₁₃×D₁₉	C₃×C₅²	1	1	yes	characteristic, complemented, Hall
18	C₅²×C₁₉	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×C₅×C₁₃	—	19	6	no	—
20	C₅²×C₁₃	D₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
21	C₅×C₁₉⋊C₃	C₂×C₅×C₁₃	1	6	yes	complemented
22	C₁₃×C₁₉	C₂×C₃×C₅²	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₁₃	—	19	6	no	—
24	C₅×D₁₉	C₃×C₅×C₁₃	1	6	yes	complemented
25	C₂×C₃×C₅²	—	19	1	no	Hall
26	C₂×C₅×C₁₃	—	19	6	no	—
27	D₁₉⋊C₃	C₅²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
28	C₅×C₁₉	C₂×C₃×C₅×C₁₃	1	6	yes	complemented
29	C₂×C₃×C₁₃	—	19	1	no	Hall
30	C₃×C₅²	—	19	1	no	Hall
31	C₅×C₁₃	C₅×D₁₉⋊C₃	1	6	yes	direct product factor
32	C₁₉⋊C₃	C₂×C₅²×C₁₃	1	1	yes	characteristic, complemented, Hall
33	C₂×C₅²	—	19	1	no	Hall
34	C₃×C₁₃	—	19	1	no	Hall
35	D₁₉	C₃×C₅²×C₁₃	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃×C₅	—	19	6	no	—
37	C₂×C₁₃	—	19	1	no	Hall
38	C₅²	C₁₃×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
39	C₁₉	C₂×C₃×C₅²×C₁₃	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₅	—	19	6	no	—
41	C₁₃	C₅²×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₅	—	19	6	no	—
43	C₂×C₃	—	19	1	no	Hall
44	C₅	C₅×C₁₃×D₁₉⋊C₃	1	6	yes	direct product factor
45	C₃	—	19	1	no	Sylow
46	C₂	—	19	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²×C₁₃	D₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₂×C₃×C₅²×C₁₃
Frattini	C₁	G
Fitting, socle	C₅²×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₅²×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₅²×C₁₃×C₁₉⋊C₃	C₂	semidirect
2. C₅²×C₁₃×D₁₉	C₃	semidirect
3. C₅×C₁₃×D₁₉⋊C₃	C₅	direct (N × H)
4. C₅²×C₁₃×C₁₉	C₂×C₃	semidirect
5. C₅×C₁₃×C₁₉⋊C₃	C₂×C₅	semidirect
6. C₅²×D₁₉⋊C₃	C₁₃	direct (N × H)
7. C₅×C₁₃×D₁₉	C₃×C₅	semidirect
9. C₁₃×D₁₉⋊C₃	C₅²	direct (N × H)
10. C₅²×C₁₉⋊C₃	C₂×C₁₃	semidirect
11. C₅×C₁₃×C₁₉	C₂×C₃×C₅	semidirect
13. C₅²×D₁₉	C₃×C₁₃	semidirect
14. C₁₃×C₁₉⋊C₃	C₂×C₅²	semidirect
16. C₅×D₁₉⋊C₃	C₅×C₁₃	direct (N × H)
17. C₁₃×D₁₉	C₃×C₅²	semidirect
18. C₅²×C₁₉	C₂×C₃×C₁₃	semidirect
20. C₅²×C₁₃	D₁₉⋊C₃	direct (N × H)
21. C₅×C₁₉⋊C₃	C₂×C₅×C₁₃	semidirect
22. C₁₃×C₁₉	C₂×C₃×C₅²	semidirect
24. C₅×D₁₉	C₃×C₅×C₁₃	semidirect
27. D₁₉⋊C₃	C₅²×C₁₃	direct (N × H)
28. C₅×C₁₉	C₂×C₃×C₅×C₁₃	semidirect
31. C₅×C₁₃	C₅×D₁₉⋊C₃	direct (N × H)
32. C₁₉⋊C₃	C₂×C₅²×C₁₃	semidirect
35. D₁₉	C₃×C₅²×C₁₃	semidirect
38. C₅²	C₁₃×D₁₉⋊C₃	direct (N × H)
39. C₁₉	C₂×C₃×C₅²×C₁₃	semidirect
41. C₁₃	C₅²×D₁₉⋊C₃	direct (N × H)
44. C₅	C₅×C₁₃×D₁₉⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×C₁₃×C₁₉⋊C₃	2
C₅²×C₁₃×D₁₉	3
C₅×C₁₃×D₁₉⋊C₃	5
C₅²×D₁₉⋊C₃	13
C₂×C₃×C₅²×C₁₃	19

Subgroups — C52×C13×D19⋊C3 #49150263

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×C₁₃×D₁₉⋊C₃ #49150263