Subgroups — C₂³×C₅×C₁₉×C₂₉ #72199546

Order 22040.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₉×C₂₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂²×C₅×C₁₉×C₂₉	C₂	1	7	yes	maximal, direct product factor
3	C₂×C₅×C₁₉×C₂₉	C₂²	1	7	yes	direct product factor
4	C₅×C₁₉×C₂₉	C₂³	1	1	yes	characteristic, direct product factor, Hall
5	C₂²×C₁₉×C₂₉	C₂×C₅	1	7	yes	direct product factor
6	C₂³×C₅×C₂₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₉×C₂₉	C₂²×C₅	1	7	yes	direct product factor
8	C₂³×C₅×C₁₉	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₅×C₂₉	C₂×C₁₉	1	7	yes	direct product factor
10	C₁₉×C₂₉	C₂³×C₅	1	1	yes	characteristic, direct product factor, Hall
11	C₂²×C₅×C₁₉	C₂×C₂₉	1	7	yes	direct product factor
12	C₂×C₅×C₂₉	C₂²×C₁₉	1	7	yes	direct product factor
13	C₂³×C₂₉	C₅×C₁₉	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₅×C₁₉	C₂²×C₂₉	1	7	yes	direct product factor
15	C₂³×C₁₉	C₅×C₂₉	1	1	yes	characteristic, direct product factor, Hall
16	C₅×C₂₉	C₂³×C₁₉	1	1	yes	characteristic, direct product factor, Hall
17	C₂²×C₂₉	C₂×C₅×C₁₉	1	7	yes	direct product factor
18	C₅×C₁₉	C₂³×C₂₉	1	1	yes	characteristic, direct product factor, Hall
19	C₂²×C₁₉	C₂×C₅×C₂₉	1	7	yes	direct product factor
20	C₂×C₂₉	C₂²×C₅×C₁₉	1	7	yes	direct product factor
21	C₂³×C₅	C₁₉×C₂₉	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₁₉	C₂²×C₅×C₂₉	1	7	yes	direct product factor
23	C₂₉	C₂³×C₅×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
24	C₂²×C₅	C₂×C₁₉×C₂₉	1	7	yes	direct product factor
25	C₁₉	C₂³×C₅×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₅	C₂²×C₁₉×C₂₉	1	7	yes	direct product factor
27	C₂³	C₅×C₁₉×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₅	C₂³×C₁₉×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
29	C₂²	C₂×C₅×C₁₉×C₂₉	1	7	yes	direct product factor
30	C₂	C₂²×C₅×C₁₉×C₂₉	1	7	yes	direct product factor

	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. C₂³×C₁₉×C₂₉	C₅	direct (N × H)
2. C₂²×C₅×C₁₉×C₂₉	C₂	direct (N × H)
3. C₂×C₅×C₁₉×C₂₉	C₂²	direct (N × H)
4. C₅×C₁₉×C₂₉	C₂³	direct (N × H)
5. C₂²×C₁₉×C₂₉	C₂×C₅	direct (N × H)
6. C₂³×C₅×C₂₉	C₁₉	direct (N × H)
7. C₂×C₁₉×C₂₉	C₂²×C₅	direct (N × H)
8. C₂³×C₅×C₁₉	C₂₉	direct (N × H)
9. C₂²×C₅×C₂₉	C₂×C₁₉	direct (N × H)
10. C₁₉×C₂₉	C₂³×C₅	direct (N × H)
11. C₂²×C₅×C₁₉	C₂×C₂₉	direct (N × H)
12. C₂×C₅×C₂₉	C₂²×C₁₉	direct (N × H)
13. C₂³×C₂₉	C₅×C₁₉	direct (N × H)
14. C₂×C₅×C₁₉	C₂²×C₂₉	direct (N × H)
15. C₂³×C₁₉	C₅×C₂₉	direct (N × H)
16. C₅×C₂₉	C₂³×C₁₉	direct (N × H)
17. C₂²×C₂₉	C₂×C₅×C₁₉	direct (N × H)
18. C₅×C₁₉	C₂³×C₂₉	direct (N × H)
19. C₂²×C₁₉	C₂×C₅×C₂₉	direct (N × H)
20. C₂×C₂₉	C₂²×C₅×C₁₉	direct (N × H)
21. C₂³×C₅	C₁₉×C₂₉	direct (N × H)
22. C₂×C₁₉	C₂²×C₅×C₂₉	direct (N × H)
23. C₂₉	C₂³×C₅×C₁₉	direct (N × H)
24. C₂²×C₅	C₂×C₁₉×C₂₉	direct (N × H)
25. C₁₉	C₂³×C₅×C₂₉	direct (N × H)
26. C₂×C₅	C₂²×C₁₉×C₂₉	direct (N × H)
27. C₂³	C₅×C₁₉×C₂₉	direct (N × H)
28. C₅	C₂³×C₁₉×C₂₉	direct (N × H)
29. C₂²	C₂×C₅×C₁₉×C₂₉	direct (N × H)
30. C₂	C₂²×C₅×C₁₉×C₂₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₁₉×C₂₉	5
C₂²×C₅×C₁₉×C₂₉	2
C₂³×C₅×C₂₉	19
C₂³×C₅×C₁₉	29

Subgroups — C23×C5×C19×C29 #72199546

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₅×C₁₉×C₂₉ #72199546