Subgroups — C₂⁴×C₃²×C₁₃₉ #72197693

Order 20016.

804 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃²×C₁₃₉	C₂	1	15	yes	maximal, direct product factor
2	C₂⁴×C₃×C₁₃₉	C₃	1	4	yes	maximal, direct product factor
3	C₂³×C₃×C₁₃₉	C₂×C₃	1	60	yes	direct product factor
4	C₂²×C₃²×C₁₃₉	C₂²	1	35	yes	direct product factor
5	C₂×C₃²×C₁₃₉	C₂³	1	15	yes	direct product factor
6	C₂⁴×C₁₃₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₂²×C₃×C₁₃₉	C₂²×C₃	1	140	yes	direct product factor
8	C₃²×C₁₃₉	C₂⁴	1	1	yes	characteristic, direct product factor, Hall
9	C₂³×C₁₃₉	C₂×C₃²	1	15	yes	direct product factor
10	C₂×C₃×C₁₃₉	C₂³×C₃	1	60	yes	direct product factor
11	C₂²×C₁₃₉	C₂²×C₃²	1	35	yes	direct product factor
12	C₃×C₁₃₉	C₂⁴×C₃	1	4	yes	direct product factor
13	C₂×C₁₃₉	C₂³×C₃²	1	15	yes	direct product factor
14	C₂⁴×C₃²	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₁₃₉	C₂⁴×C₃²	1	1	yes	characteristic, direct product factor, Sylow
16	C₂³×C₃²	C₂×C₁₃₉	1	15	yes	direct product factor
17	C₂⁴×C₃	C₃×C₁₃₉	1	4	yes	direct product factor
18	C₂²×C₃²	C₂²×C₁₃₉	1	35	yes	direct product factor
19	C₂³×C₃	C₂×C₃×C₁₃₉	1	60	yes	direct product factor
20	C₂×C₃²	C₂³×C₁₃₉	1	15	yes	direct product factor
21	C₂⁴	C₃²×C₁₃₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₂²×C₃	C₂²×C₃×C₁₃₉	1	140	yes	direct product factor
23	C₃²	C₂⁴×C₁₃₉	1	1	yes	characteristic, direct product factor, Sylow
24	C₂³	C₂×C₃²×C₁₃₉	1	15	yes	direct product factor
25	C₂×C₃	C₂³×C₃×C₁₃₉	1	60	yes	direct product factor
26	C₂²	C₂²×C₃²×C₁₃₉	1	35	yes	direct product factor
27	C₃	C₂⁴×C₃×C₁₃₉	1	4	yes	direct product factor
28	C₂	C₂³×C₃²×C₁₃₉	1	15	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. C₂³×C₃²×C₁₃₉	C₂	direct (N × H)
2. C₂⁴×C₃×C₁₃₉	C₃	direct (N × H)
3. C₂³×C₃×C₁₃₉	C₂×C₃	direct (N × H)
4. C₂²×C₃²×C₁₃₉	C₂²	direct (N × H)
5. C₂×C₃²×C₁₃₉	C₂³	direct (N × H)
6. C₂⁴×C₁₃₉	C₃²	direct (N × H)
7. C₂²×C₃×C₁₃₉	C₂²×C₃	direct (N × H)
8. C₃²×C₁₃₉	C₂⁴	direct (N × H)
9. C₂³×C₁₃₉	C₂×C₃²	direct (N × H)
10. C₂×C₃×C₁₃₉	C₂³×C₃	direct (N × H)
11. C₂²×C₁₃₉	C₂²×C₃²	direct (N × H)
12. C₃×C₁₃₉	C₂⁴×C₃	direct (N × H)
13. C₂×C₁₃₉	C₂³×C₃²	direct (N × H)
14. C₂⁴×C₃²	C₁₃₉	direct (N × H)
15. C₁₃₉	C₂⁴×C₃²	direct (N × H)
16. C₂³×C₃²	C₂×C₁₃₉	direct (N × H)
17. C₂⁴×C₃	C₃×C₁₃₉	direct (N × H)
18. C₂²×C₃²	C₂²×C₁₃₉	direct (N × H)
19. C₂³×C₃	C₂×C₃×C₁₃₉	direct (N × H)
20. C₂×C₃²	C₂³×C₁₃₉	direct (N × H)
21. C₂⁴	C₃²×C₁₃₉	direct (N × H)
22. C₂²×C₃	C₂²×C₃×C₁₃₉	direct (N × H)
23. C₃²	C₂⁴×C₁₃₉	direct (N × H)
24. C₂³	C₂×C₃²×C₁₃₉	direct (N × H)
25. C₂×C₃	C₂³×C₃×C₁₃₉	direct (N × H)
26. C₂²	C₂²×C₃²×C₁₃₉	direct (N × H)
27. C₃	C₂⁴×C₃×C₁₃₉	direct (N × H)
28. C₂	C₂³×C₃²×C₁₃₉	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₃²×C₁₃₉	2
C₂⁴×C₃×C₁₃₉	3
C₂⁴×C₃²	139

Subgroups — C24×C32×C139 #72197693

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₃²×C₁₃₉ #72197693