Subgroups — C₂²×C₃×C₅²×C₁₀₇ #44545649

Order 32100.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅²×C₁₀₇	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₅²×C₁₀₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅²×C₁₀₇	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂²×C₃×C₅×C₁₀₇	C₅	1	6	yes	maximal, direct product factor
5	C₂×C₅²×C₁₀₇	C₂×C₃	1	3	yes	direct product factor
6	C₂×C₃×C₅×C₁₀₇	C₂×C₅	1	18	yes	direct product factor
7	C₅²×C₁₀₇	C₂²×C₃	1	1	yes	characteristic, direct product factor, Hall
8	C₂²×C₅×C₁₀₇	C₃×C₅	1	6	yes	direct product factor
9	C₃×C₅×C₁₀₇	C₂²×C₅	1	6	yes	direct product factor
10	C₂²×C₃×C₁₀₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₅×C₁₀₇	C₂×C₃×C₅	1	18	yes	direct product factor
12	C₂×C₃×C₁₀₇	C₂×C₅²	1	3	yes	direct product factor
13	C₅×C₁₀₇	C₂²×C₃×C₅	1	6	yes	direct product factor
14	C₂²×C₁₀₇	C₃×C₅²	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₁₀₇	C₂²×C₅²	1	1	yes	characteristic, direct product factor, Hall
16	C₂²×C₃×C₅²	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₁₀₇	C₂×C₃×C₅²	1	3	yes	direct product factor
18	C₂×C₃×C₅²	C₂×C₁₀₇	1	3	yes	direct product factor
19	C₁₀₇	C₂²×C₃×C₅²	1	1	yes	characteristic, direct product factor, Sylow
20	C₂²×C₅²	C₃×C₁₀₇	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₅²	C₂²×C₁₀₇	1	1	yes	characteristic, direct product factor, Hall
22	C₂²×C₃×C₅	C₅×C₁₀₇	1	6	yes	direct product factor
23	C₂×C₅²	C₂×C₃×C₁₀₇	1	3	yes	direct product factor
24	C₂×C₃×C₅	C₂×C₅×C₁₀₇	1	18	yes	direct product factor
25	C₅²	C₂²×C₃×C₁₀₇	1	1	yes	characteristic, direct product factor, Sylow
26	C₂²×C₅	C₃×C₅×C₁₀₇	1	6	yes	direct product factor
27	C₃×C₅	C₂²×C₅×C₁₀₇	1	6	yes	direct product factor
28	C₂²×C₃	C₅²×C₁₀₇	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₅	C₂×C₃×C₅×C₁₀₇	1	18	yes	direct product factor
30	C₂×C₃	C₂×C₅²×C₁₀₇	1	3	yes	direct product factor
31	C₅	C₂²×C₃×C₅×C₁₀₇	1	6	yes	direct product factor
32	C₂²	C₃×C₅²×C₁₀₇	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₂²×C₅²×C₁₀₇	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₂×C₃×C₅²×C₁₀₇	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×C₅²×C₁₀₇	C₂	direct (N × H)
2. C₂²×C₅²×C₁₀₇	C₃	direct (N × H)
3. C₃×C₅²×C₁₀₇	C₂²	direct (N × H)
4. C₂²×C₃×C₅×C₁₀₇	C₅	direct (N × H)
5. C₂×C₅²×C₁₀₇	C₂×C₃	direct (N × H)
6. C₂×C₃×C₅×C₁₀₇	C₂×C₅	direct (N × H)
7. C₅²×C₁₀₇	C₂²×C₃	direct (N × H)
8. C₂²×C₅×C₁₀₇	C₃×C₅	direct (N × H)
9. C₃×C₅×C₁₀₇	C₂²×C₅	direct (N × H)
10. C₂²×C₃×C₁₀₇	C₅²	direct (N × H)
11. C₂×C₅×C₁₀₇	C₂×C₃×C₅	direct (N × H)
12. C₂×C₃×C₁₀₇	C₂×C₅²	direct (N × H)
13. C₅×C₁₀₇	C₂²×C₃×C₅	direct (N × H)
14. C₂²×C₁₀₇	C₃×C₅²	direct (N × H)
15. C₃×C₁₀₇	C₂²×C₅²	direct (N × H)
16. C₂²×C₃×C₅²	C₁₀₇	direct (N × H)
17. C₂×C₁₀₇	C₂×C₃×C₅²	direct (N × H)
18. C₂×C₃×C₅²	C₂×C₁₀₇	direct (N × H)
19. C₁₀₇	C₂²×C₃×C₅²	direct (N × H)
20. C₂²×C₅²	C₃×C₁₀₇	direct (N × H)
21. C₃×C₅²	C₂²×C₁₀₇	direct (N × H)
22. C₂²×C₃×C₅	C₅×C₁₀₇	direct (N × H)
23. C₂×C₅²	C₂×C₃×C₁₀₇	direct (N × H)
24. C₂×C₃×C₅	C₂×C₅×C₁₀₇	direct (N × H)
25. C₅²	C₂²×C₃×C₁₀₇	direct (N × H)
26. C₂²×C₅	C₃×C₅×C₁₀₇	direct (N × H)
27. C₃×C₅	C₂²×C₅×C₁₀₇	direct (N × H)
28. C₂²×C₃	C₅²×C₁₀₇	direct (N × H)
29. C₂×C₅	C₂×C₃×C₅×C₁₀₇	direct (N × H)
30. C₂×C₃	C₂×C₅²×C₁₀₇	direct (N × H)
31. C₅	C₂²×C₃×C₅×C₁₀₇	direct (N × H)
32. C₂²	C₃×C₅²×C₁₀₇	direct (N × H)
33. C₃	C₂²×C₅²×C₁₀₇	direct (N × H)
34. C₂	C₂×C₃×C₅²×C₁₀₇	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×C₅²×C₁₀₇	2
C₂²×C₅²×C₁₀₇	3
C₂²×C₃×C₅×C₁₀₇	5
C₂²×C₃×C₅²	107

Subgroups — C22×C3×C52×C107 #44545649

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×C₅²×C₁₀₇ #44545649