Subgroups — C₂³×C₃×C₁₇×C₅₉ #72201377

Order 24072.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₇×C₅₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂²×C₃×C₁₇×C₅₉	C₂	1	7	yes	maximal, direct product factor
3	C₂×C₃×C₁₇×C₅₉	C₂²	1	7	yes	direct product factor
4	C₂²×C₁₇×C₅₉	C₂×C₃	1	7	yes	direct product factor
5	C₃×C₁₇×C₅₉	C₂³	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₁₇×C₅₉	C₂²×C₃	1	7	yes	direct product factor
7	C₂³×C₃×C₅₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₇×C₅₉	C₂³×C₃	1	1	yes	characteristic, direct product factor, Hall
9	C₂²×C₃×C₅₉	C₂×C₁₇	1	7	yes	direct product factor
10	C₂³×C₅₉	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
11	C₂³×C₃×C₁₇	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₃×C₅₉	C₂²×C₁₇	1	7	yes	direct product factor
13	C₂²×C₅₉	C₂×C₃×C₁₇	1	7	yes	direct product factor
14	C₂²×C₃×C₁₇	C₂×C₅₉	1	7	yes	direct product factor
15	C₃×C₅₉	C₂³×C₁₇	1	1	yes	characteristic, direct product factor, Hall
16	C₂³×C₁₇	C₃×C₅₉	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₅₉	C₂²×C₃×C₁₇	1	7	yes	direct product factor
18	C₂×C₃×C₁₇	C₂²×C₅₉	1	7	yes	direct product factor
19	C₂²×C₁₇	C₂×C₃×C₅₉	1	7	yes	direct product factor
20	C₅₉	C₂³×C₃×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₃×C₁₇	C₂³×C₅₉	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₁₇	C₂²×C₃×C₅₉	1	7	yes	direct product factor
23	C₂³×C₃	C₁₇×C₅₉	1	1	yes	characteristic, direct product factor, Hall
24	C₁₇	C₂³×C₃×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
25	C₂²×C₃	C₂×C₁₇×C₅₉	1	7	yes	direct product factor
26	C₂³	C₃×C₁₇×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	C₂²×C₁₇×C₅₉	1	7	yes	direct product factor
28	C₂²	C₂×C₃×C₁₇×C₅₉	1	7	yes	direct product factor
29	C₃	C₂³×C₁₇×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	C₂²×C₃×C₁₇×C₅₉	1	7	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×C₁₇×C₅₉	C₃	direct (N × H)
2. C₂²×C₃×C₁₇×C₅₉	C₂	direct (N × H)
3. C₂×C₃×C₁₇×C₅₉	C₂²	direct (N × H)
4. C₂²×C₁₇×C₅₉	C₂×C₃	direct (N × H)
5. C₃×C₁₇×C₅₉	C₂³	direct (N × H)
6. C₂×C₁₇×C₅₉	C₂²×C₃	direct (N × H)
7. C₂³×C₃×C₅₉	C₁₇	direct (N × H)
8. C₁₇×C₅₉	C₂³×C₃	direct (N × H)
9. C₂²×C₃×C₅₉	C₂×C₁₇	direct (N × H)
10. C₂³×C₅₉	C₃×C₁₇	direct (N × H)
11. C₂³×C₃×C₁₇	C₅₉	direct (N × H)
12. C₂×C₃×C₅₉	C₂²×C₁₇	direct (N × H)
13. C₂²×C₅₉	C₂×C₃×C₁₇	direct (N × H)
14. C₂²×C₃×C₁₇	C₂×C₅₉	direct (N × H)
15. C₃×C₅₉	C₂³×C₁₇	direct (N × H)
16. C₂³×C₁₇	C₃×C₅₉	direct (N × H)
17. C₂×C₅₉	C₂²×C₃×C₁₇	direct (N × H)
18. C₂×C₃×C₁₇	C₂²×C₅₉	direct (N × H)
19. C₂²×C₁₇	C₂×C₃×C₅₉	direct (N × H)
20. C₅₉	C₂³×C₃×C₁₇	direct (N × H)
21. C₃×C₁₇	C₂³×C₅₉	direct (N × H)
22. C₂×C₁₇	C₂²×C₃×C₅₉	direct (N × H)
23. C₂³×C₃	C₁₇×C₅₉	direct (N × H)
24. C₁₇	C₂³×C₃×C₅₉	direct (N × H)
25. C₂²×C₃	C₂×C₁₇×C₅₉	direct (N × H)
26. C₂³	C₃×C₁₇×C₅₉	direct (N × H)
27. C₂×C₃	C₂²×C₁₇×C₅₉	direct (N × H)
28. C₂²	C₂×C₃×C₁₇×C₅₉	direct (N × H)
29. C₃	C₂³×C₁₇×C₅₉	direct (N × H)
30. C₂	C₂²×C₃×C₁₇×C₅₉	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×C₁₇×C₅₉	3
C₂²×C₃×C₁₇×C₅₉	2
C₂³×C₃×C₅₉	17
C₂³×C₃×C₁₇	59

Subgroups — C23×C3×C17×C59 #72201377

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₃×C₁₇×C₅₉ #72201377