Subgroups — C₂²×C₅×C₇×C₁₃×C₁₇ #44525867

Order 30940.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₇×C₁₃×C₁₇	C₂	1	3	yes	maximal, direct product factor
2	C₅×C₇×C₁₃×C₁₇	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₇×C₁₃×C₁₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₅×C₁₃×C₁₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₇×C₁₃×C₁₇	C₂×C₅	1	3	yes	direct product factor
6	C₂²×C₅×C₇×C₁₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₅×C₁₃×C₁₇	C₂×C₇	1	3	yes	direct product factor
8	C₂²×C₅×C₇×C₁₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇×C₁₃×C₁₇	C₂²×C₅	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₅×C₇×C₁₇	C₂×C₁₃	1	3	yes	direct product factor
11	C₅×C₁₃×C₁₇	C₂²×C₇	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₅×C₇×C₁₃	C₂×C₁₇	1	3	yes	direct product factor
13	C₂²×C₁₃×C₁₇	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
14	C₅×C₇×C₁₇	C₂²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
15	C₂²×C₇×C₁₇	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
16	C₅×C₇×C₁₃	C₂²×C₁₇	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₁₃×C₁₇	C₂×C₅×C₇	1	3	yes	direct product factor
18	C₂²×C₇×C₁₃	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
19	C₂²×C₅×C₁₇	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
20	C₂²×C₅×C₁₃	C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₇×C₁₇	C₂×C₅×C₁₃	1	3	yes	direct product factor
22	C₁₃×C₁₇	C₂²×C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₇×C₁₃	C₂×C₅×C₁₇	1	3	yes	direct product factor
24	C₂×C₅×C₁₇	C₂×C₇×C₁₃	1	3	yes	direct product factor
25	C₂²×C₅×C₇	C₁₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₅×C₁₃	C₂×C₇×C₁₇	1	3	yes	direct product factor
27	C₇×C₁₇	C₂²×C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
28	C₇×C₁₃	C₂²×C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
29	C₅×C₁₇	C₂²×C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₅×C₇	C₂×C₁₃×C₁₇	1	3	yes	direct product factor
31	C₂²×C₁₇	C₅×C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
32	C₅×C₁₃	C₂²×C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
33	C₂²×C₁₃	C₅×C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
34	C₅×C₇	C₂²×C₁₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
35	C₂×C₁₇	C₂×C₅×C₇×C₁₃	1	3	yes	direct product factor
36	C₂²×C₇	C₅×C₁₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
37	C₂×C₁₃	C₂×C₅×C₇×C₁₇	1	3	yes	direct product factor
38	C₂²×C₅	C₇×C₁₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
39	C₁₇	C₂²×C₅×C₇×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₇	C₂×C₅×C₁₃×C₁₇	1	3	yes	direct product factor
41	C₁₃	C₂²×C₅×C₇×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₅	C₂×C₇×C₁₃×C₁₇	1	3	yes	direct product factor
43	C₇	C₂²×C₅×C₁₃×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
44	C₅	C₂²×C₇×C₁₃×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
45	C₂²	C₅×C₇×C₁₃×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₂×C₅×C₇×C₁₃×C₁₇	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×C₅×C₇×C₁₃×C₁₇	C₂	direct (N × H)
2. C₅×C₇×C₁₃×C₁₇	C₂²	direct (N × H)
3. C₂²×C₇×C₁₃×C₁₇	C₅	direct (N × H)
4. C₂²×C₅×C₁₃×C₁₇	C₇	direct (N × H)
5. C₂×C₇×C₁₃×C₁₇	C₂×C₅	direct (N × H)
6. C₂²×C₅×C₇×C₁₇	C₁₃	direct (N × H)
7. C₂×C₅×C₁₃×C₁₇	C₂×C₇	direct (N × H)
8. C₂²×C₅×C₇×C₁₃	C₁₇	direct (N × H)
9. C₇×C₁₃×C₁₇	C₂²×C₅	direct (N × H)
10. C₂×C₅×C₇×C₁₇	C₂×C₁₃	direct (N × H)
11. C₅×C₁₃×C₁₇	C₂²×C₇	direct (N × H)
12. C₂×C₅×C₇×C₁₃	C₂×C₁₇	direct (N × H)
13. C₂²×C₁₃×C₁₇	C₅×C₇	direct (N × H)
14. C₅×C₇×C₁₇	C₂²×C₁₃	direct (N × H)
15. C₂²×C₇×C₁₇	C₅×C₁₃	direct (N × H)
16. C₅×C₇×C₁₃	C₂²×C₁₇	direct (N × H)
17. C₂×C₁₃×C₁₇	C₂×C₅×C₇	direct (N × H)
18. C₂²×C₇×C₁₃	C₅×C₁₇	direct (N × H)
19. C₂²×C₅×C₁₇	C₇×C₁₃	direct (N × H)
20. C₂²×C₅×C₁₃	C₇×C₁₇	direct (N × H)
21. C₂×C₇×C₁₇	C₂×C₅×C₁₃	direct (N × H)
22. C₁₃×C₁₇	C₂²×C₅×C₇	direct (N × H)
23. C₂×C₇×C₁₃	C₂×C₅×C₁₇	direct (N × H)
24. C₂×C₅×C₁₇	C₂×C₇×C₁₃	direct (N × H)
25. C₂²×C₅×C₇	C₁₃×C₁₇	direct (N × H)
26. C₂×C₅×C₁₃	C₂×C₇×C₁₇	direct (N × H)
27. C₇×C₁₇	C₂²×C₅×C₁₃	direct (N × H)
28. C₇×C₁₃	C₂²×C₅×C₁₇	direct (N × H)
29. C₅×C₁₇	C₂²×C₇×C₁₃	direct (N × H)
30. C₂×C₅×C₇	C₂×C₁₃×C₁₇	direct (N × H)
31. C₂²×C₁₇	C₅×C₇×C₁₃	direct (N × H)
32. C₅×C₁₃	C₂²×C₇×C₁₇	direct (N × H)
33. C₂²×C₁₃	C₅×C₇×C₁₇	direct (N × H)
34. C₅×C₇	C₂²×C₁₃×C₁₇	direct (N × H)
35. C₂×C₁₇	C₂×C₅×C₇×C₁₃	direct (N × H)
36. C₂²×C₇	C₅×C₁₃×C₁₇	direct (N × H)
37. C₂×C₁₃	C₂×C₅×C₇×C₁₇	direct (N × H)
38. C₂²×C₅	C₇×C₁₃×C₁₇	direct (N × H)
39. C₁₇	C₂²×C₅×C₇×C₁₃	direct (N × H)
40. C₂×C₇	C₂×C₅×C₁₃×C₁₇	direct (N × H)
41. C₁₃	C₂²×C₅×C₇×C₁₇	direct (N × H)
42. C₂×C₅	C₂×C₇×C₁₃×C₁₇	direct (N × H)
43. C₇	C₂²×C₅×C₁₃×C₁₇	direct (N × H)
44. C₅	C₂²×C₇×C₁₃×C₁₇	direct (N × H)
45. C₂²	C₅×C₇×C₁₃×C₁₇	direct (N × H)
46. C₂	C₂×C₅×C₇×C₁₃×C₁₇	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×C₅×C₇×C₁₃×C₁₇	2
C₂²×C₇×C₁₃×C₁₇	5
C₂²×C₅×C₁₃×C₁₇	7
C₂²×C₅×C₇×C₁₇	13
C₂²×C₅×C₇×C₁₃	17

Subgroups — C22×C5×C7×C13×C17 #44525867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×C₇×C₁₃×C₁₇ #44525867