Subgroups — C₃×C₅×A₄×C₂₉ #19104891

Order 5220.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×C₂₉	C₃	1	1	yes	maximal, characteristic, complemented
2	C₅×A₄×C₂₉	C₃	1	3	yes	maximal, direct product factor
3	C₃²×C₅×C₂₉	—	4	1	no	maximal, Hall
4	C₃×A₄×C₂₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₅×C₂₉	—	3	1	no	—
6	C₂²×C₅×C₂₉	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×C₂₉	—	4	3	no	—
8	C₃×C₅×C₂₉	A₄	1	1	yes	characteristic, direct product factor
9	C₂²×C₃×C₂₉	C₃×C₅	1	1	yes	characteristic, complemented
10	A₄×C₂₉	C₃×C₅	1	3	yes	direct product factor
11	C₂×C₅×C₂₉	—	3	1	no	—
12	C₃²×C₂₉	—	4	1	no	Hall
13	C₃×C₅×A₄	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₃×C₂₉	—	3	1	no	—
15	C₅×C₂₉	C₃×A₄	1	1	yes	characteristic, direct product factor, Hall
16	C₂²×C₂₉	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
17	C₃×C₂₉	—	4	3	no	—
18	C₃×C₂₉	C₅×A₄	1	1	yes	characteristic, direct product factor
19	C₂²×C₃×C₅	C₃×C₂₉	1	1	yes	characteristic, complemented
20	C₅×A₄	C₃×C₂₉	1	3	yes	direct product factor
21	C₂×C₂₉	—	3	1	no	—
22	C₃²×C₅	—	4	1	no	Hall
23	C₃×A₄	C₅×C₂₉	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₃×C₅	—	3	1	no	—
25	C₂₉	C₃×C₅×A₄	1	1	yes	characteristic, direct product factor, Sylow
26	C₂²×C₅	C₃²×C₂₉	1	1	yes	characteristic, complemented, Hall
27	C₃×C₅	—	4	3	no	—
28	C₃×C₅	A₄×C₂₉	1	1	yes	characteristic, direct product factor
29	C₂²×C₃	C₃×C₅×C₂₉	1	1	yes	characteristic, complemented
30	A₄	C₃×C₅×C₂₉	1	3	yes	direct product factor
31	C₂×C₅	—	3	1	no	—
32	C₃²	—	4	1	no	Sylow
33	C₂×C₃	—	3	1	no	—
34	C₅	C₃×A₄×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
35	C₂²	C₃²×C₅×C₂₉	1	1	yes	characteristic, complemented, Sylow
36	C₃	—	4	3	no	—
37	C₃	C₅×A₄×C₂₉	1	1	yes	characteristic, direct product factor
38	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₅×C₂₉	A₄
commutator, hypocenter	C₂²	C₃²×C₅×C₂₉
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₅×C₂₉	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃×C₅×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×C₂₉	C₃	semidirect
2. C₅×A₄×C₂₉	C₃	direct (N × H)
4. C₃×A₄×C₂₉	C₅	direct (N × H)
6. C₂²×C₅×C₂₉	C₃²	semidirect
8. C₃×C₅×C₂₉	A₄	direct (N × H)
9. C₂²×C₃×C₂₉	C₃×C₅	semidirect
10. A₄×C₂₉	C₃×C₅	direct (N × H)
13. C₃×C₅×A₄	C₂₉	direct (N × H)
15. C₅×C₂₉	C₃×A₄	direct (N × H)
16. C₂²×C₂₉	C₃²×C₅	semidirect
18. C₃×C₂₉	C₅×A₄	direct (N × H)
19. C₂²×C₃×C₅	C₃×C₂₉	semidirect
20. C₅×A₄	C₃×C₂₉	direct (N × H)
23. C₃×A₄	C₅×C₂₉	direct (N × H)
25. C₂₉	C₃×C₅×A₄	direct (N × H)
26. C₂²×C₅	C₃²×C₂₉	semidirect
28. C₃×C₅	A₄×C₂₉	direct (N × H)
29. C₂²×C₃	C₃×C₅×C₂₉	semidirect
30. A₄	C₃×C₅×C₂₉	direct (N × H)
34. C₅	C₃×A₄×C₂₉	direct (N × H)
35. C₂²	C₃²×C₅×C₂₉	semidirect
37. C₃	C₅×A₄×C₂₉	direct (N × H)

Subgroups — C3×C5×A4×C29 #19104891

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₅×A₄×C₂₉ #19104891