Subgroups — C₂²×C₃×C₅×C₁₇×C₃₁ #44539280

Order 31620.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₁₇×C₃₁	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₅×C₁₇×C₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₇×C₃₁	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂²×C₃×C₁₇×C₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₁₇×C₃₁	C₂×C₃	1	3	yes	direct product factor
6	C₂×C₃×C₁₇×C₃₁	C₂×C₅	1	3	yes	direct product factor
7	C₅×C₁₇×C₃₁	C₂²×C₃	1	1	yes	characteristic, direct product factor, Hall
8	C₂²×C₁₇×C₃₁	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×C₃₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₁₇×C₃₁	C₂²×C₅	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₁₇×C₃₁	C₂×C₃×C₅	1	3	yes	direct product factor
12	C₂²×C₃×C₅×C₁₇	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×C₃₁	C₂×C₁₇	1	3	yes	direct product factor
14	C₂²×C₅×C₃₁	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
15	C₁₇×C₃₁	C₂²×C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₃×C₅×C₁₇	C₂×C₃₁	1	3	yes	direct product factor
17	C₃×C₅×C₃₁	C₂²×C₁₇	1	1	yes	characteristic, direct product factor, Hall
18	C₂²×C₃×C₃₁	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
19	C₂²×C₅×C₁₇	C₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₅×C₃₁	C₂×C₃×C₁₇	1	3	yes	direct product factor
21	C₃×C₅×C₁₇	C₂²×C₃₁	1	1	yes	characteristic, direct product factor, Hall
22	C₂²×C₃×C₁₇	C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃×C₃₁	C₂×C₅×C₁₇	1	3	yes	direct product factor
24	C₂×C₅×C₁₇	C₂×C₃×C₃₁	1	3	yes	direct product factor
25	C₅×C₃₁	C₂²×C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
26	C₂²×C₃₁	C₃×C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₃×C₁₇	C₂×C₅×C₃₁	1	3	yes	direct product factor
28	C₃×C₃₁	C₂²×C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
29	C₅×C₁₇	C₂²×C₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
30	C₂²×C₁₇	C₃×C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
31	C₂×C₃₁	C₂×C₃×C₅×C₁₇	1	3	yes	direct product factor
32	C₂²×C₃×C₅	C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
33	C₃×C₁₇	C₂²×C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
34	C₂×C₁₇	C₂×C₃×C₅×C₃₁	1	3	yes	direct product factor
35	C₃₁	C₂²×C₃×C₅×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₃×C₅	C₂×C₁₇×C₃₁	1	3	yes	direct product factor
37	C₂²×C₅	C₃×C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
38	C₁₇	C₂²×C₃×C₅×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
39	C₃×C₅	C₂²×C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
40	C₂²×C₃	C₅×C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
41	C₂×C₅	C₂×C₃×C₁₇×C₃₁	1	3	yes	direct product factor
42	C₂×C₃	C₂×C₅×C₁₇×C₃₁	1	3	yes	direct product factor
43	C₅	C₂²×C₃×C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
44	C₂²	C₃×C₅×C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₂²×C₅×C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₂×C₃×C₅×C₁₇×C₃₁	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×C₅×C₁₇×C₃₁	C₂	direct (N × H)
2. C₂²×C₅×C₁₇×C₃₁	C₃	direct (N × H)
3. C₃×C₅×C₁₇×C₃₁	C₂²	direct (N × H)
4. C₂²×C₃×C₁₇×C₃₁	C₅	direct (N × H)
5. C₂×C₅×C₁₇×C₃₁	C₂×C₃	direct (N × H)
6. C₂×C₃×C₁₇×C₃₁	C₂×C₅	direct (N × H)
7. C₅×C₁₇×C₃₁	C₂²×C₃	direct (N × H)
8. C₂²×C₁₇×C₃₁	C₃×C₅	direct (N × H)
9. C₂²×C₃×C₅×C₃₁	C₁₇	direct (N × H)
10. C₃×C₁₇×C₃₁	C₂²×C₅	direct (N × H)
11. C₂×C₁₇×C₃₁	C₂×C₃×C₅	direct (N × H)
12. C₂²×C₃×C₅×C₁₇	C₃₁	direct (N × H)
13. C₂×C₃×C₅×C₃₁	C₂×C₁₇	direct (N × H)
14. C₂²×C₅×C₃₁	C₃×C₁₇	direct (N × H)
15. C₁₇×C₃₁	C₂²×C₃×C₅	direct (N × H)
16. C₂×C₃×C₅×C₁₇	C₂×C₃₁	direct (N × H)
17. C₃×C₅×C₃₁	C₂²×C₁₇	direct (N × H)
18. C₂²×C₃×C₃₁	C₅×C₁₇	direct (N × H)
19. C₂²×C₅×C₁₇	C₃×C₃₁	direct (N × H)
20. C₂×C₅×C₃₁	C₂×C₃×C₁₇	direct (N × H)
21. C₃×C₅×C₁₇	C₂²×C₃₁	direct (N × H)
22. C₂²×C₃×C₁₇	C₅×C₃₁	direct (N × H)
23. C₂×C₃×C₃₁	C₂×C₅×C₁₇	direct (N × H)
24. C₂×C₅×C₁₇	C₂×C₃×C₃₁	direct (N × H)
25. C₅×C₃₁	C₂²×C₃×C₁₇	direct (N × H)
26. C₂²×C₃₁	C₃×C₅×C₁₇	direct (N × H)
27. C₂×C₃×C₁₇	C₂×C₅×C₃₁	direct (N × H)
28. C₃×C₃₁	C₂²×C₅×C₁₇	direct (N × H)
29. C₅×C₁₇	C₂²×C₃×C₃₁	direct (N × H)
30. C₂²×C₁₇	C₃×C₅×C₃₁	direct (N × H)
31. C₂×C₃₁	C₂×C₃×C₅×C₁₇	direct (N × H)
32. C₂²×C₃×C₅	C₁₇×C₃₁	direct (N × H)
33. C₃×C₁₇	C₂²×C₅×C₃₁	direct (N × H)
34. C₂×C₁₇	C₂×C₃×C₅×C₃₁	direct (N × H)
35. C₃₁	C₂²×C₃×C₅×C₁₇	direct (N × H)
36. C₂×C₃×C₅	C₂×C₁₇×C₃₁	direct (N × H)
37. C₂²×C₅	C₃×C₁₇×C₃₁	direct (N × H)
38. C₁₇	C₂²×C₃×C₅×C₃₁	direct (N × H)
39. C₃×C₅	C₂²×C₁₇×C₃₁	direct (N × H)
40. C₂²×C₃	C₅×C₁₇×C₃₁	direct (N × H)
41. C₂×C₅	C₂×C₃×C₁₇×C₃₁	direct (N × H)
42. C₂×C₃	C₂×C₅×C₁₇×C₃₁	direct (N × H)
43. C₅	C₂²×C₃×C₁₇×C₃₁	direct (N × H)
44. C₂²	C₃×C₅×C₁₇×C₃₁	direct (N × H)
45. C₃	C₂²×C₅×C₁₇×C₃₁	direct (N × H)
46. C₂	C₂×C₃×C₅×C₁₇×C₃₁	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×C₅×C₁₇×C₃₁	2
C₂²×C₅×C₁₇×C₃₁	3
C₂²×C₃×C₁₇×C₃₁	5
C₂²×C₃×C₅×C₃₁	17
C₂²×C₃×C₅×C₁₇	31

Subgroups — C22×C3×C5×C17×C31 #44539280

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×C₅×C₁₇×C₃₁ #44539280