Subgroups — C₂⁴×C₃×C₉×C₂₉ #72190879

Order 12528.

1340 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₉×C₂₉	C₂	1	15	yes	maximal, direct product factor
2	C₂⁴×C₃²×C₂₉	C₃	1	1	yes	maximal, characteristic
3	C₂⁴×C₉×C₂₉	C₃	1	3	yes	maximal, direct product factor
4	C₂²×C₃×C₉×C₂₉	C₂²	1	35	yes	direct product factor
5	C₂³×C₃²×C₂₉	C₂×C₃	1	15	yes	—
6	C₂³×C₉×C₂₉	C₂×C₃	1	45	yes	direct product factor
7	C₂×C₃×C₉×C₂₉	C₂³	1	15	yes	direct product factor
8	C₂⁴×C₃×C₂₉	C₉	1	3	yes	direct product factor
9	C₂⁴×C₃×C₂₉	C₃²	1	1	yes	characteristic
10	C₂²×C₃²×C₂₉	C₂²×C₃	1	35	yes	—
11	C₂²×C₉×C₂₉	C₂²×C₃	1	105	yes	direct product factor
12	C₃×C₉×C₂₉	C₂⁴	1	1	yes	characteristic, direct product factor, Hall
13	C₂³×C₃×C₂₉	C₂×C₉	1	45	yes	direct product factor
14	C₂³×C₃×C₂₉	C₂×C₃²	1	15	yes	—
15	C₂×C₃²×C₂₉	C₂³×C₃	1	15	yes	—
16	C₂×C₉×C₂₉	C₂³×C₃	1	45	yes	direct product factor
17	C₂⁴×C₂₉	C₃×C₉	1	1	yes	characteristic, direct product factor, Hall
18	C₂⁴×C₃×C₉	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂²×C₃×C₂₉	C₂²×C₉	1	105	yes	direct product factor
20	C₂²×C₃×C₂₉	C₂²×C₃²	1	35	yes	—
21	C₃²×C₂₉	C₂⁴×C₃	1	1	yes	characteristic
22	C₉×C₂₉	C₂⁴×C₃	1	3	yes	direct product factor
23	C₂³×C₂₉	C₂×C₃×C₉	1	15	yes	direct product factor
24	C₂³×C₃×C₉	C₂×C₂₉	1	15	yes	direct product factor
25	C₂×C₃×C₂₉	C₂³×C₉	1	45	yes	direct product factor
26	C₂×C₃×C₂₉	C₂³×C₃²	1	15	yes	—
27	C₂⁴×C₃²	C₃×C₂₉	1	1	yes	characteristic
28	C₂⁴×C₉	C₃×C₂₉	1	3	yes	direct product factor
29	C₂²×C₂₉	C₂²×C₃×C₉	1	35	yes	direct product factor
30	C₂²×C₃×C₉	C₂²×C₂₉	1	35	yes	direct product factor
31	C₃×C₂₉	C₂⁴×C₉	1	3	yes	direct product factor
32	C₃×C₂₉	C₂⁴×C₃²	1	1	yes	characteristic
33	C₂³×C₃²	C₂×C₃×C₂₉	1	15	yes	—
34	C₂³×C₉	C₂×C₃×C₂₉	1	45	yes	direct product factor
35	C₂×C₂₉	C₂³×C₃×C₉	1	15	yes	direct product factor
36	C₂×C₃×C₉	C₂³×C₂₉	1	15	yes	direct product factor
37	C₂⁴×C₃	C₉×C₂₉	1	3	yes	direct product factor
38	C₂⁴×C₃	C₃²×C₂₉	1	1	yes	characteristic
39	C₂²×C₃²	C₂²×C₃×C₂₉	1	35	yes	—
40	C₂²×C₉	C₂²×C₃×C₂₉	1	105	yes	direct product factor
41	C₂₉	C₂⁴×C₃×C₉	1	1	yes	characteristic, direct product factor, Sylow
42	C₃×C₉	C₂⁴×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
43	C₂³×C₃	C₂×C₉×C₂₉	1	45	yes	direct product factor
44	C₂³×C₃	C₂×C₃²×C₂₉	1	15	yes	—
45	C₂×C₃²	C₂³×C₃×C₂₉	1	15	yes	—
46	C₂×C₉	C₂³×C₃×C₂₉	1	45	yes	direct product factor
47	C₂⁴	C₃×C₉×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
48	C₂²×C₃	C₂²×C₉×C₂₉	1	105	yes	direct product factor
49	C₂²×C₃	C₂²×C₃²×C₂₉	1	35	yes	—
50	C₃²	C₂⁴×C₃×C₂₉	1	1	yes	characteristic
51	C₉	C₂⁴×C₃×C₂₉	1	3	yes	direct product factor
52	C₂³	C₂×C₃×C₉×C₂₉	1	15	yes	direct product factor
53	C₂×C₃	C₂³×C₉×C₂₉	1	45	yes	direct product factor
54	C₂×C₃	C₂³×C₃²×C₂₉	1	15	yes	—
55	C₂²	C₂²×C₃×C₉×C₂₉	1	35	yes	direct product factor
56	C₃	C₂⁴×C₉×C₂₉	1	3	yes	direct product factor
57	C₃	C₂⁴×C₃²×C₂₉	1	1	yes	characteristic
58	C₂	C₂³×C₃×C₉×C₂₉	1	15	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂⁴×C₃²×C₂₉
socle, prime radical	C₂⁴×C₃²×C₂₉	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₉×C₂₉	C₂	direct (N × H)
3. C₂⁴×C₉×C₂₉	C₃	direct (N × H)
4. C₂²×C₃×C₉×C₂₉	C₂²	direct (N × H)
6. C₂³×C₉×C₂₉	C₂×C₃	direct (N × H)
7. C₂×C₃×C₉×C₂₉	C₂³	direct (N × H)
8. C₂⁴×C₃×C₂₉	C₉	direct (N × H)
11. C₂²×C₉×C₂₉	C₂²×C₃	direct (N × H)
12. C₃×C₉×C₂₉	C₂⁴	direct (N × H)
13. C₂³×C₃×C₂₉	C₂×C₉	direct (N × H)
16. C₂×C₉×C₂₉	C₂³×C₃	direct (N × H)
17. C₂⁴×C₂₉	C₃×C₉	direct (N × H)
18. C₂⁴×C₃×C₉	C₂₉	direct (N × H)
19. C₂²×C₃×C₂₉	C₂²×C₉	direct (N × H)
22. C₉×C₂₉	C₂⁴×C₃	direct (N × H)
23. C₂³×C₂₉	C₂×C₃×C₉	direct (N × H)
24. C₂³×C₃×C₉	C₂×C₂₉	direct (N × H)
25. C₂×C₃×C₂₉	C₂³×C₉	direct (N × H)
28. C₂⁴×C₉	C₃×C₂₉	direct (N × H)
29. C₂²×C₂₉	C₂²×C₃×C₉	direct (N × H)
30. C₂²×C₃×C₉	C₂²×C₂₉	direct (N × H)
31. C₃×C₂₉	C₂⁴×C₉	direct (N × H)
34. C₂³×C₉	C₂×C₃×C₂₉	direct (N × H)
35. C₂×C₂₉	C₂³×C₃×C₉	direct (N × H)
36. C₂×C₃×C₉	C₂³×C₂₉	direct (N × H)
37. C₂⁴×C₃	C₉×C₂₉	direct (N × H)
40. C₂²×C₉	C₂²×C₃×C₂₉	direct (N × H)
41. C₂₉	C₂⁴×C₃×C₉	direct (N × H)
42. C₃×C₉	C₂⁴×C₂₉	direct (N × H)
43. C₂³×C₃	C₂×C₉×C₂₉	direct (N × H)
46. C₂×C₉	C₂³×C₃×C₂₉	direct (N × H)
47. C₂⁴	C₃×C₉×C₂₉	direct (N × H)
48. C₂²×C₃	C₂²×C₉×C₂₉	direct (N × H)
51. C₉	C₂⁴×C₃×C₂₉	direct (N × H)
52. C₂³	C₂×C₃×C₉×C₂₉	direct (N × H)
53. C₂×C₃	C₂³×C₉×C₂₉	direct (N × H)
55. C₂²	C₂²×C₃×C₉×C₂₉	direct (N × H)
56. C₃	C₂⁴×C₉×C₂₉	direct (N × H)
58. C₂	C₂³×C₃×C₉×C₂₉	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×C₃×C₉×C₂₉	2
C₂⁴×C₃²×C₂₉	3
C₂⁴×C₉×C₂₉	3
C₂⁴×C₃×C₉	29

Subgroups — C24×C3×C9×C29 #72190879

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₃×C₉×C₂₉ #72190879