Subgroups — C₃×C₄²×C₉×C₂₉ #72190872

Order 12528.

300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₉×C₂₉	C₂	1	3	yes	maximal
2	C₃²×C₄²×C₂₉	C₃	1	1	yes	maximal, characteristic
3	C₄²×C₉×C₂₉	C₃	1	3	yes	maximal, direct product factor
4	C₂²×C₃×C₉×C₂₉	C₂²	1	1	yes	characteristic
5	C₃×C₄×C₉×C₂₉	C₄	1	6	yes	direct product factor
6	C₂×C₃²×C₄×C₂₉	C₂×C₃	1	3	yes	—
7	C₂×C₄×C₉×C₂₉	C₂×C₃	1	9	yes	—
8	C₂×C₃×C₉×C₂₉	C₂×C₄	1	3	yes	—
9	C₃×C₄²×C₂₉	C₉	1	3	yes	direct product factor
10	C₃×C₄²×C₂₉	C₃²	1	1	yes	characteristic
11	C₂²×C₃²×C₂₉	C₂²×C₃	1	1	yes	characteristic
12	C₃²×C₄×C₂₉	C₃×C₄	1	6	yes	—
13	C₂²×C₉×C₂₉	C₂²×C₃	1	3	yes	—
14	C₄×C₉×C₂₉	C₃×C₄	1	18	yes	direct product factor
15	C₃×C₉×C₂₉	C₄²	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₃×C₄×C₂₉	C₂×C₉	1	9	yes	—
17	C₂×C₃×C₄×C₂₉	C₂×C₃²	1	3	yes	—
18	C₂×C₃²×C₂₉	C₂×C₃×C₄	1	3	yes	—
19	C₂×C₉×C₂₉	C₂×C₃×C₄	1	9	yes	—
20	C₄²×C₂₉	C₃×C₉	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₄²×C₉	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂²×C₃×C₂₉	C₂²×C₉	1	3	yes	—
23	C₂²×C₃×C₂₉	C₂²×C₃²	1	1	yes	characteristic
24	C₃×C₄×C₂₉	C₄×C₉	1	18	yes	direct product factor
25	C₃×C₄×C₂₉	C₃²×C₄	1	6	yes	—
26	C₃²×C₂₉	C₃×C₄²	1	1	yes	characteristic
27	C₉×C₂₉	C₃×C₄²	1	3	yes	direct product factor
28	C₂×C₄×C₂₉	C₂×C₃×C₉	1	3	yes	—
29	C₂×C₃×C₄×C₉	C₂×C₂₉	1	3	yes	—
30	C₂×C₃×C₂₉	C₂×C₄×C₉	1	9	yes	—
31	C₂×C₃×C₂₉	C₂×C₃²×C₄	1	3	yes	—
32	C₃²×C₄²	C₃×C₂₉	1	1	yes	characteristic
33	C₄²×C₉	C₃×C₂₉	1	3	yes	direct product factor
34	C₂²×C₂₉	C₂²×C₃×C₉	1	1	yes	characteristic
35	C₄×C₂₉	C₃×C₄×C₉	1	6	yes	direct product factor
36	C₂²×C₃×C₉	C₂²×C₂₉	1	1	yes	characteristic
37	C₃×C₄×C₉	C₄×C₂₉	1	6	yes	direct product factor
38	C₃×C₂₉	C₄²×C₉	1	3	yes	direct product factor
39	C₃×C₂₉	C₃²×C₄²	1	1	yes	characteristic
40	C₂×C₃²×C₄	C₂×C₃×C₂₉	1	3	yes	—
41	C₂×C₄×C₉	C₂×C₃×C₂₉	1	9	yes	—
42	C₂×C₂₉	C₂×C₃×C₄×C₉	1	3	yes	—
43	C₂×C₃×C₉	C₂×C₄×C₂₉	1	3	yes	—
44	C₃×C₄²	C₉×C₂₉	1	3	yes	direct product factor
45	C₃×C₄²	C₃²×C₂₉	1	1	yes	characteristic
46	C₂²×C₃²	C₂²×C₃×C₂₉	1	1	yes	characteristic
47	C₃²×C₄	C₃×C₄×C₂₉	1	6	yes	—
48	C₂²×C₉	C₂²×C₃×C₂₉	1	3	yes	—
49	C₄×C₉	C₃×C₄×C₂₉	1	18	yes	direct product factor
50	C₂₉	C₃×C₄²×C₉	1	1	yes	characteristic, direct product factor, Sylow
51	C₃×C₉	C₄²×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
52	C₂×C₃×C₄	C₂×C₉×C₂₉	1	9	yes	—
53	C₂×C₃×C₄	C₂×C₃²×C₂₉	1	3	yes	—
54	C₂×C₃²	C₂×C₃×C₄×C₂₉	1	3	yes	—
55	C₂×C₉	C₂×C₃×C₄×C₂₉	1	9	yes	—
56	C₄²	C₃×C₉×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
57	C₂²×C₃	C₂²×C₉×C₂₉	1	3	yes	—
58	C₂²×C₃	C₂²×C₃²×C₂₉	1	1	yes	characteristic
59	C₃×C₄	C₄×C₉×C₂₉	1	18	yes	direct product factor
60	C₃×C₄	C₃²×C₄×C₂₉	1	6	yes	—
61	C₃²	C₃×C₄²×C₂₉	1	1	yes	characteristic
62	C₉	C₃×C₄²×C₂₉	1	3	yes	direct product factor
63	C₂×C₄	C₂×C₃×C₉×C₂₉	1	3	yes	—
64	C₂×C₃	C₂×C₄×C₉×C₂₉	1	9	yes	—
65	C₂×C₃	C₂×C₃²×C₄×C₂₉	1	3	yes	—
66	C₂²	C₂²×C₃×C₉×C₂₉	1	1	yes	characteristic
67	C₄	C₃×C₄×C₉×C₂₉	1	6	yes	direct product factor
68	C₃	C₄²×C₉×C₂₉	1	3	yes	direct product factor
69	C₃	C₃²×C₄²×C₂₉	1	1	yes	characteristic
70	C₂	C₂×C₃×C₄×C₉×C₂₉	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃	C₂²×C₃²×C₂₉
socle, prime radical	C₂²×C₃²×C₂₉	C₂²×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄²×C₉×C₂₉	C₃	direct (N × H)
5. C₃×C₄×C₉×C₂₉	C₄	direct (N × H)
9. C₃×C₄²×C₂₉	C₉	direct (N × H)
14. C₄×C₉×C₂₉	C₃×C₄	direct (N × H)
15. C₃×C₉×C₂₉	C₄²	direct (N × H)
20. C₄²×C₂₉	C₃×C₉	direct (N × H)
21. C₃×C₄²×C₉	C₂₉	direct (N × H)
24. C₃×C₄×C₂₉	C₄×C₉	direct (N × H)
27. C₉×C₂₉	C₃×C₄²	direct (N × H)
33. C₄²×C₉	C₃×C₂₉	direct (N × H)
35. C₄×C₂₉	C₃×C₄×C₉	direct (N × H)
37. C₃×C₄×C₉	C₄×C₂₉	direct (N × H)
38. C₃×C₂₉	C₄²×C₉	direct (N × H)
44. C₃×C₄²	C₉×C₂₉	direct (N × H)
49. C₄×C₉	C₃×C₄×C₂₉	direct (N × H)
50. C₂₉	C₃×C₄²×C₉	direct (N × H)
51. C₃×C₉	C₄²×C₂₉	direct (N × H)
56. C₄²	C₃×C₉×C₂₉	direct (N × H)
59. C₃×C₄	C₄×C₉×C₂₉	direct (N × H)
62. C₉	C₃×C₄²×C₂₉	direct (N × H)
67. C₄	C₃×C₄×C₉×C₂₉	direct (N × H)
68. C₃	C₄²×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
C₂×C₃×C₄×C₉×C₂₉	2
C₃²×C₄²×C₂₉	3
C₄²×C₉×C₂₉	3
C₃×C₄²×C₉	29

Subgroups — C3×C42×C9×C29 #72190872

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄²×C₉×C₂₉ #72190872