Subgroups — C₂²×C₃×C₇×C₁₃×C₂₉ #44539766

Order 31668.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₁₃×C₂₉	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₇×C₁₃×C₂₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×C₁₃×C₂₉	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₇×C₁₃×C₂₉	C₂×C₃	1	3	yes	direct product factor
5	C₂²×C₃×C₁₃×C₂₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₁₃×C₂₉	C₂²×C₃	1	1	yes	characteristic, direct product factor, Hall
7	C₂²×C₃×C₇×C₂₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₁₃×C₂₉	C₂×C₇	1	3	yes	direct product factor
9	C₂²×C₁₃×C₂₉	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃×C₇×C₂₉	C₂×C₁₃	1	3	yes	direct product factor
11	C₃×C₁₃×C₂₉	C₂²×C₇	1	1	yes	characteristic, direct product factor, Hall
12	C₂²×C₃×C₇×C₁₃	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₇×C₂₉	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₁₃×C₂₉	C₂×C₃×C₇	1	3	yes	direct product factor
15	C₃×C₇×C₂₉	C₂²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₃×C₇×C₁₃	C₂×C₂₉	1	3	yes	direct product factor
17	C₂×C₇×C₂₉	C₂×C₃×C₁₃	1	3	yes	direct product factor
18	C₁₃×C₂₉	C₂²×C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
19	C₂²×C₇×C₁₃	C₃×C₂₉	1	1	yes	characteristic, direct product factor, Hall
20	C₂²×C₃×C₂₉	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₇×C₁₃	C₂²×C₂₉	1	1	yes	characteristic, direct product factor, Hall
22	C₇×C₂₉	C₂²×C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₇×C₁₃	C₂×C₃×C₂₉	1	3	yes	direct product factor
24	C₂×C₃×C₂₉	C₂×C₇×C₁₃	1	3	yes	direct product factor
25	C₂²×C₃×C₁₃	C₇×C₂₉	1	1	yes	characteristic, direct product factor, Hall
26	C₂²×C₂₉	C₃×C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
27	C₇×C₁₃	C₂²×C₃×C₂₉	1	1	yes	characteristic, direct product factor, Hall
28	C₃×C₂₉	C₂²×C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
29	C₂²×C₃×C₇	C₁₃×C₂₉	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₃×C₁₃	C₂×C₇×C₂₉	1	3	yes	direct product factor
31	C₂×C₂₉	C₂×C₃×C₇×C₁₃	1	3	yes	direct product factor
32	C₂²×C₁₃	C₃×C₇×C₂₉	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₃×C₇	C₂×C₁₃×C₂₉	1	3	yes	direct product factor
34	C₃×C₁₃	C₂²×C₇×C₂₉	1	1	yes	characteristic, direct product factor, Hall
35	C₂₉	C₂²×C₃×C₇×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
36	C₂²×C₇	C₃×C₁₃×C₂₉	1	1	yes	characteristic, direct product factor, Hall
37	C₂×C₁₃	C₂×C₃×C₇×C₂₉	1	3	yes	direct product factor
38	C₃×C₇	C₂²×C₁₃×C₂₉	1	1	yes	characteristic, direct product factor, Hall
39	C₂×C₇	C₂×C₃×C₁₃×C₂₉	1	3	yes	direct product factor
40	C₁₃	C₂²×C₃×C₇×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₂²×C₃	C₇×C₁₃×C₂₉	1	1	yes	characteristic, direct product factor, Hall
42	C₇	C₂²×C₃×C₁₃×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	C₂×C₇×C₁₃×C₂₉	1	3	yes	direct product factor
44	C₂²	C₃×C₇×C₁₃×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₂²×C₇×C₁₃×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₂×C₃×C₇×C₁₃×C₂₉	1	3	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. C₂×C₃×C₇×C₁₃×C₂₉	C₂	direct (N × H)
2. C₂²×C₇×C₁₃×C₂₉	C₃	direct (N × H)
3. C₃×C₇×C₁₃×C₂₉	C₂²	direct (N × H)
4. C₂×C₇×C₁₃×C₂₉	C₂×C₃	direct (N × H)
5. C₂²×C₃×C₁₃×C₂₉	C₇	direct (N × H)
6. C₇×C₁₃×C₂₉	C₂²×C₃	direct (N × H)
7. C₂²×C₃×C₇×C₂₉	C₁₃	direct (N × H)
8. C₂×C₃×C₁₃×C₂₉	C₂×C₇	direct (N × H)
9. C₂²×C₁₃×C₂₉	C₃×C₇	direct (N × H)
10. C₂×C₃×C₇×C₂₉	C₂×C₁₃	direct (N × H)
11. C₃×C₁₃×C₂₉	C₂²×C₇	direct (N × H)
12. C₂²×C₃×C₇×C₁₃	C₂₉	direct (N × H)
13. C₂²×C₇×C₂₉	C₃×C₁₃	direct (N × H)
14. C₂×C₁₃×C₂₉	C₂×C₃×C₇	direct (N × H)
15. C₃×C₇×C₂₉	C₂²×C₁₃	direct (N × H)
16. C₂×C₃×C₇×C₁₃	C₂×C₂₉	direct (N × H)
17. C₂×C₇×C₂₉	C₂×C₃×C₁₃	direct (N × H)
18. C₁₃×C₂₉	C₂²×C₃×C₇	direct (N × H)
19. C₂²×C₇×C₁₃	C₃×C₂₉	direct (N × H)
20. C₂²×C₃×C₂₉	C₇×C₁₃	direct (N × H)
21. C₃×C₇×C₁₃	C₂²×C₂₉	direct (N × H)
22. C₇×C₂₉	C₂²×C₃×C₁₃	direct (N × H)
23. C₂×C₇×C₁₃	C₂×C₃×C₂₉	direct (N × H)
24. C₂×C₃×C₂₉	C₂×C₇×C₁₃	direct (N × H)
25. C₂²×C₃×C₁₃	C₇×C₂₉	direct (N × H)
26. C₂²×C₂₉	C₃×C₇×C₁₃	direct (N × H)
27. C₇×C₁₃	C₂²×C₃×C₂₉	direct (N × H)
28. C₃×C₂₉	C₂²×C₇×C₁₃	direct (N × H)
29. C₂²×C₃×C₇	C₁₃×C₂₉	direct (N × H)
30. C₂×C₃×C₁₃	C₂×C₇×C₂₉	direct (N × H)
31. C₂×C₂₉	C₂×C₃×C₇×C₁₃	direct (N × H)
32. C₂²×C₁₃	C₃×C₇×C₂₉	direct (N × H)
33. C₂×C₃×C₇	C₂×C₁₃×C₂₉	direct (N × H)
34. C₃×C₁₃	C₂²×C₇×C₂₉	direct (N × H)
35. C₂₉	C₂²×C₃×C₇×C₁₃	direct (N × H)
36. C₂²×C₇	C₃×C₁₃×C₂₉	direct (N × H)
37. C₂×C₁₃	C₂×C₃×C₇×C₂₉	direct (N × H)
38. C₃×C₇	C₂²×C₁₃×C₂₉	direct (N × H)
39. C₂×C₇	C₂×C₃×C₁₃×C₂₉	direct (N × H)
40. C₁₃	C₂²×C₃×C₇×C₂₉	direct (N × H)
41. C₂²×C₃	C₇×C₁₃×C₂₉	direct (N × H)
42. C₇	C₂²×C₃×C₁₃×C₂₉	direct (N × H)
43. C₂×C₃	C₂×C₇×C₁₃×C₂₉	direct (N × H)
44. C₂²	C₃×C₇×C₁₃×C₂₉	direct (N × H)
45. C₃	C₂²×C₇×C₁₃×C₂₉	direct (N × H)
46. C₂	C₂×C₃×C₇×C₁₃×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
C₂×C₃×C₇×C₁₃×C₂₉	2
C₂²×C₇×C₁₃×C₂₉	3
C₂²×C₃×C₁₃×C₂₉	7
C₂²×C₃×C₇×C₂₉	13
C₂²×C₃×C₇×C₁₃	29

Subgroups — C22×C3×C7×C13×C29 #44539766

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×C₇×C₁₃×C₂₉ #44539766