Subgroups — C₂²×C₃²×C₅²×C₂₉ #39908021

Order 26100.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₅²×C₂₉	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₅²×C₂₉	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₅²×C₂₉	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂²×C₃²×C₅×C₂₉	C₅	1	6	yes	maximal, direct product factor
5	C₂×C₃×C₅²×C₂₉	C₂×C₃	1	12	yes	direct product factor
6	C₂²×C₅²×C₂₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃²×C₅×C₂₉	C₂×C₅	1	18	yes	direct product factor
8	C₃×C₅²×C₂₉	C₂²×C₃	1	4	yes	direct product factor
9	C₂²×C₃×C₅×C₂₉	C₃×C₅	1	24	yes	direct product factor
10	C₂×C₅²×C₂₉	C₂×C₃²	1	3	yes	direct product factor
11	C₃²×C₅×C₂₉	C₂²×C₅	1	6	yes	direct product factor
12	C₂²×C₃²×C₂₉	C₅²	1	1	yes	characteristic, direct product factor, Hall
13	C₂²×C₃²×C₅²	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₃×C₅×C₂₉	C₂×C₃×C₅	1	72	yes	direct product factor
15	C₅²×C₂₉	C₂²×C₃²	1	1	yes	characteristic, direct product factor, Hall
16	C₂²×C₅×C₂₉	C₃²×C₅	1	6	yes	direct product factor
17	C₂×C₃²×C₂₉	C₂×C₅²	1	3	yes	direct product factor
18	C₂×C₃²×C₅²	C₂×C₂₉	1	3	yes	direct product factor
19	C₃×C₅×C₂₉	C₂²×C₃×C₅	1	24	yes	direct product factor
20	C₂²×C₃×C₂₉	C₃×C₅²	1	4	yes	direct product factor
21	C₂²×C₃×C₅²	C₃×C₂₉	1	4	yes	direct product factor
22	C₂×C₅×C₂₉	C₂×C₃²×C₅	1	18	yes	direct product factor
23	C₃²×C₂₉	C₂²×C₅²	1	1	yes	characteristic, direct product factor, Hall
24	C₃²×C₅²	C₂²×C₂₉	1	1	yes	characteristic, direct product factor, Hall
25	C₂²×C₃²×C₅	C₅×C₂₉	1	6	yes	direct product factor
26	C₂×C₃×C₂₉	C₂×C₃×C₅²	1	12	yes	direct product factor
27	C₂×C₃×C₅²	C₂×C₃×C₂₉	1	12	yes	direct product factor
28	C₅×C₂₉	C₂²×C₃²×C₅	1	6	yes	direct product factor
29	C₂²×C₂₉	C₃²×C₅²	1	1	yes	characteristic, direct product factor, Hall
30	C₂²×C₅²	C₃²×C₂₉	1	1	yes	characteristic, direct product factor, Hall
31	C₂×C₃²×C₅	C₂×C₅×C₂₉	1	18	yes	direct product factor
32	C₃×C₂₉	C₂²×C₃×C₅²	1	4	yes	direct product factor
33	C₃×C₅²	C₂²×C₃×C₂₉	1	4	yes	direct product factor
34	C₂²×C₃×C₅	C₃×C₅×C₂₉	1	24	yes	direct product factor
35	C₂×C₂₉	C₂×C₃²×C₅²	1	3	yes	direct product factor
36	C₂×C₅²	C₂×C₃²×C₂₉	1	3	yes	direct product factor
37	C₃²×C₅	C₂²×C₅×C₂₉	1	6	yes	direct product factor
38	C₂²×C₃²	C₅²×C₂₉	1	1	yes	characteristic, direct product factor, Hall
39	C₂×C₃×C₅	C₂×C₃×C₅×C₂₉	1	72	yes	direct product factor
40	C₂₉	C₂²×C₃²×C₅²	1	1	yes	characteristic, direct product factor, Sylow
41	C₅²	C₂²×C₃²×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
42	C₂²×C₅	C₃²×C₅×C₂₉	1	6	yes	direct product factor
43	C₂×C₃²	C₂×C₅²×C₂₉	1	3	yes	direct product factor
44	C₃×C₅	C₂²×C₃×C₅×C₂₉	1	24	yes	direct product factor
45	C₂²×C₃	C₃×C₅²×C₂₉	1	4	yes	direct product factor
46	C₂×C₅	C₂×C₃²×C₅×C₂₉	1	18	yes	direct product factor
47	C₃²	C₂²×C₅²×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
48	C₂×C₃	C₂×C₃×C₅²×C₂₉	1	12	yes	direct product factor
49	C₅	C₂²×C₃²×C₅×C₂₉	1	6	yes	direct product factor
50	C₂²	C₃²×C₅²×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
51	C₃	C₂²×C₃×C₅²×C₂₉	1	4	yes	direct product factor
52	C₂	C₂×C₃²×C₅²×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×C₃²×C₅²×C₂₉	C₂	direct (N × H)
2. C₂²×C₃×C₅²×C₂₉	C₃	direct (N × H)
3. C₃²×C₅²×C₂₉	C₂²	direct (N × H)
4. C₂²×C₃²×C₅×C₂₉	C₅	direct (N × H)
5. C₂×C₃×C₅²×C₂₉	C₂×C₃	direct (N × H)
6. C₂²×C₅²×C₂₉	C₃²	direct (N × H)
7. C₂×C₃²×C₅×C₂₉	C₂×C₅	direct (N × H)
8. C₃×C₅²×C₂₉	C₂²×C₃	direct (N × H)
9. C₂²×C₃×C₅×C₂₉	C₃×C₅	direct (N × H)
10. C₂×C₅²×C₂₉	C₂×C₃²	direct (N × H)
11. C₃²×C₅×C₂₉	C₂²×C₅	direct (N × H)
12. C₂²×C₃²×C₂₉	C₅²	direct (N × H)
13. C₂²×C₃²×C₅²	C₂₉	direct (N × H)
14. C₂×C₃×C₅×C₂₉	C₂×C₃×C₅	direct (N × H)
15. C₅²×C₂₉	C₂²×C₃²	direct (N × H)
16. C₂²×C₅×C₂₉	C₃²×C₅	direct (N × H)
17. C₂×C₃²×C₂₉	C₂×C₅²	direct (N × H)
18. C₂×C₃²×C₅²	C₂×C₂₉	direct (N × H)
19. C₃×C₅×C₂₉	C₂²×C₃×C₅	direct (N × H)
20. C₂²×C₃×C₂₉	C₃×C₅²	direct (N × H)
21. C₂²×C₃×C₅²	C₃×C₂₉	direct (N × H)
22. C₂×C₅×C₂₉	C₂×C₃²×C₅	direct (N × H)
23. C₃²×C₂₉	C₂²×C₅²	direct (N × H)
24. C₃²×C₅²	C₂²×C₂₉	direct (N × H)
25. C₂²×C₃²×C₅	C₅×C₂₉	direct (N × H)
26. C₂×C₃×C₂₉	C₂×C₃×C₅²	direct (N × H)
27. C₂×C₃×C₅²	C₂×C₃×C₂₉	direct (N × H)
28. C₅×C₂₉	C₂²×C₃²×C₅	direct (N × H)
29. C₂²×C₂₉	C₃²×C₅²	direct (N × H)
30. C₂²×C₅²	C₃²×C₂₉	direct (N × H)
31. C₂×C₃²×C₅	C₂×C₅×C₂₉	direct (N × H)
32. C₃×C₂₉	C₂²×C₃×C₅²	direct (N × H)
33. C₃×C₅²	C₂²×C₃×C₂₉	direct (N × H)
34. C₂²×C₃×C₅	C₃×C₅×C₂₉	direct (N × H)
35. C₂×C₂₉	C₂×C₃²×C₅²	direct (N × H)
36. C₂×C₅²	C₂×C₃²×C₂₉	direct (N × H)
37. C₃²×C₅	C₂²×C₅×C₂₉	direct (N × H)
38. C₂²×C₃²	C₅²×C₂₉	direct (N × H)
39. C₂×C₃×C₅	C₂×C₃×C₅×C₂₉	direct (N × H)
40. C₂₉	C₂²×C₃²×C₅²	direct (N × H)
41. C₅²	C₂²×C₃²×C₂₉	direct (N × H)
42. C₂²×C₅	C₃²×C₅×C₂₉	direct (N × H)
43. C₂×C₃²	C₂×C₅²×C₂₉	direct (N × H)
44. C₃×C₅	C₂²×C₃×C₅×C₂₉	direct (N × H)
45. C₂²×C₃	C₃×C₅²×C₂₉	direct (N × H)
46. C₂×C₅	C₂×C₃²×C₅×C₂₉	direct (N × H)
47. C₃²	C₂²×C₅²×C₂₉	direct (N × H)
48. C₂×C₃	C₂×C₃×C₅²×C₂₉	direct (N × H)
49. C₅	C₂²×C₃²×C₅×C₂₉	direct (N × H)
50. C₂²	C₃²×C₅²×C₂₉	direct (N × H)
51. C₃	C₂²×C₃×C₅²×C₂₉	direct (N × H)
52. C₂	C₂×C₃²×C₅²×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×C₃²×C₅²×C₂₉	2
C₂²×C₃×C₅²×C₂₉	3
C₂²×C₃²×C₅×C₂₉	5
C₂²×C₃²×C₅²	29

Subgroups — C22×C32×C52×C29 #39908021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃²×C₅²×C₂₉ #39908021