Subgroups — C₂×C₃×C₉²×C₅₉ #72205656

Order 28674.

504 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₉×C₅₉	C₃	1	4	yes	maximal
2	C₂×C₉²×C₅₉	C₃	1	9	yes	maximal, direct product factor
3	C₂×C₃³×C₅₉	C₃²	1	1	yes	characteristic
4	C₂×C₃×C₉×C₅₉	C₉	1	36	yes	direct product factor
5	C₂×C₃×C₉×C₅₉	C₃²	1	12	yes	—
6	C₃×C₉²×C₅₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃²×C₉×C₅₉	C₂×C₃	1	4	yes	—
8	C₉²×C₅₉	C₂×C₃	1	9	yes	direct product factor
9	C₃³×C₅₉	C₂×C₃²	1	1	yes	characteristic
10	C₃×C₉×C₅₉	C₂×C₉	1	36	yes	direct product factor
11	C₃×C₉×C₅₉	C₂×C₃²	1	12	yes	—
12	C₂×C₃²×C₅₉	C₃×C₉	1	12	yes	—
13	C₂×C₃²×C₅₉	C₃³	1	1	yes	characteristic
14	C₂×C₉×C₅₉	C₃×C₉	1	36	yes	direct product factor
15	C₃²×C₅₉	C₂×C₃×C₉	1	12	yes	—
16	C₃²×C₅₉	C₂×C₃³	1	1	yes	characteristic
17	C₉×C₅₉	C₂×C₃×C₉	1	36	yes	direct product factor
18	C₂×C₃×C₉²	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₃×C₅₉	C₉²	1	9	yes	direct product factor
20	C₂×C₃×C₅₉	C₃²×C₉	1	4	yes	—
21	C₃×C₉²	C₂×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₃×C₅₉	C₂×C₉²	1	9	yes	direct product factor
23	C₃×C₅₉	C₂×C₃²×C₉	1	4	yes	—
24	C₂×C₃²×C₉	C₃×C₅₉	1	4	yes	—
25	C₂×C₉²	C₃×C₅₉	1	9	yes	direct product factor
26	C₂×C₅₉	C₃×C₉²	1	1	yes	characteristic, direct product factor, Hall
27	C₃²×C₉	C₂×C₃×C₅₉	1	4	yes	—
28	C₉²	C₂×C₃×C₅₉	1	9	yes	direct product factor
29	C₅₉	C₂×C₃×C₉²	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₃³	C₃²×C₅₉	1	1	yes	characteristic
31	C₂×C₃×C₉	C₉×C₅₉	1	36	yes	direct product factor
32	C₂×C₃×C₉	C₃²×C₅₉	1	12	yes	—
33	C₃³	C₂×C₃²×C₅₉	1	1	yes	characteristic
34	C₃×C₉	C₂×C₉×C₅₉	1	36	yes	direct product factor
35	C₃×C₉	C₂×C₃²×C₅₉	1	12	yes	—
36	C₂×C₃²	C₃×C₉×C₅₉	1	12	yes	—
37	C₂×C₃²	C₃³×C₅₉	1	1	yes	characteristic
38	C₂×C₉	C₃×C₉×C₅₉	1	36	yes	direct product factor
39	C₃²	C₂×C₃×C₉×C₅₉	1	12	yes	—
40	C₃²	C₂×C₃³×C₅₉	1	1	yes	characteristic
41	C₉	C₂×C₃×C₉×C₅₉	1	36	yes	direct product factor
42	C₂×C₃	C₉²×C₅₉	1	9	yes	direct product factor
43	C₂×C₃	C₃²×C₉×C₅₉	1	4	yes	—
44	C₃	C₂×C₉²×C₅₉	1	9	yes	direct product factor
45	C₃	C₂×C₃²×C₉×C₅₉	1	4	yes	—
46	C₂	C₃×C₉²×C₅₉	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃²	C₂×C₃³×C₅₉
socle, prime radical	C₂×C₃³×C₅₉	C₃²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₉²×C₅₉	C₃	direct (N × H)
4. C₂×C₃×C₉×C₅₉	C₉	direct (N × H)
6. C₃×C₉²×C₅₉	C₂	direct (N × H)
8. C₉²×C₅₉	C₂×C₃	direct (N × H)
10. C₃×C₉×C₅₉	C₂×C₉	direct (N × H)
14. C₂×C₉×C₅₉	C₃×C₉	direct (N × H)
17. C₉×C₅₉	C₂×C₃×C₉	direct (N × H)
18. C₂×C₃×C₉²	C₅₉	direct (N × H)
19. C₂×C₃×C₅₉	C₉²	direct (N × H)
21. C₃×C₉²	C₂×C₅₉	direct (N × H)
22. C₃×C₅₉	C₂×C₉²	direct (N × H)
25. C₂×C₉²	C₃×C₅₉	direct (N × H)
26. C₂×C₅₉	C₃×C₉²	direct (N × H)
28. C₉²	C₂×C₃×C₅₉	direct (N × H)
29. C₅₉	C₂×C₃×C₉²	direct (N × H)
31. C₂×C₃×C₉	C₉×C₅₉	direct (N × H)
34. C₃×C₉	C₂×C₉×C₅₉	direct (N × H)
38. C₂×C₉	C₃×C₉×C₅₉	direct (N × H)
41. C₉	C₂×C₃×C₉×C₅₉	direct (N × H)
42. C₂×C₃	C₉²×C₅₉	direct (N × H)
44. C₃	C₂×C₉²×C₅₉	direct (N × H)
46. C₂	C₃×C₉²×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
C₂×C₃²×C₉×C₅₉	3
C₂×C₉²×C₅₉	3
C₃×C₉²×C₅₉	2
C₂×C₃×C₉²	59

Subgroups — C2×C3×C92×C59 #72205656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₉²×C₅₉ #72205656