Subgroups — C₄²×C₅×C₉×C₄₃ #72207694

Order 30960.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×C₉×C₄₃	C₂	1	3	yes	maximal
2	C₃×C₄²×C₅×C₄₃	C₃	1	1	yes	maximal, characteristic
3	C₄²×C₉×C₄₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₄×C₅×C₄₃	C₂×C₃	1	3	yes	—
5	C₄²×C₅×C₄₃	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₄×C₉×C₄₃	C₂×C₅	1	3	yes	—
7	C₃×C₄²×C₄₃	C₃×C₅	1	1	yes	characteristic
8	C₂²×C₅×C₉×C₄₃	C₂²	1	1	yes	characteristic
9	C₄×C₅×C₉×C₄₃	C₄	1	6	yes	direct product factor
10	C₂×C₅×C₉×C₄₃	C₂×C₄	1	3	yes	—
11	C₂²×C₃×C₅×C₄₃	C₂²×C₃	1	1	yes	characteristic
12	C₃×C₄×C₅×C₄₃	C₃×C₄	1	6	yes	—
13	C₅×C₉×C₄₃	C₄²	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₄×C₅×C₄₃	C₂×C₉	1	3	yes	—
15	C₂²×C₉×C₄₃	C₂²×C₅	1	1	yes	characteristic
16	C₄×C₉×C₄₃	C₄×C₅	1	6	yes	direct product factor
17	C₂×C₃×C₅×C₄₃	C₂×C₃×C₄	1	3	yes	—
18	C₂×C₃×C₄×C₄₃	C₂×C₃×C₅	1	3	yes	—
19	C₂²×C₅×C₄₃	C₂²×C₉	1	1	yes	characteristic
20	C₄×C₅×C₄₃	C₄×C₉	1	6	yes	direct product factor
21	C₂×C₉×C₄₃	C₂×C₄×C₅	1	3	yes	—
22	C₄²×C₅×C₉	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₄²×C₄₃	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₅×C₄₃	C₃×C₄²	1	1	yes	characteristic
25	C₂²×C₃×C₄₃	C₂²×C₃×C₅	1	1	yes	characteristic
26	C₃×C₄×C₄₃	C₃×C₄×C₅	1	6	yes	—
27	C₂×C₅×C₄₃	C₂×C₄×C₉	1	3	yes	—
28	C₉×C₄₃	C₄²×C₅	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₄×C₅×C₉	C₂×C₄₃	1	3	yes	—
30	C₂×C₄×C₄₃	C₂×C₅×C₉	1	3	yes	—
31	C₂×C₃×C₄₃	C₂×C₃×C₄×C₅	1	3	yes	—
32	C₃×C₄²×C₅	C₃×C₄₃	1	1	yes	characteristic
33	C₅×C₄₃	C₄²×C₉	1	1	yes	characteristic, direct product factor, Hall
34	C₂²×C₅×C₉	C₂²×C₄₃	1	1	yes	characteristic
35	C₄×C₅×C₉	C₄×C₄₃	1	6	yes	direct product factor
36	C₂²×C₄₃	C₂²×C₅×C₉	1	1	yes	characteristic
37	C₄×C₄₃	C₄×C₅×C₉	1	6	yes	direct product factor
38	C₄²×C₉	C₅×C₄₃	1	1	yes	characteristic, direct product factor, Hall
39	C₃×C₄₃	C₃×C₄²×C₅	1	1	yes	characteristic
40	C₂×C₃×C₄×C₅	C₂×C₃×C₄₃	1	3	yes	—
41	C₂×C₅×C₉	C₂×C₄×C₄₃	1	3	yes	—
42	C₂×C₄₃	C₂×C₄×C₅×C₉	1	3	yes	—
43	C₄²×C₅	C₉×C₄₃	1	1	yes	characteristic, direct product factor, Hall
44	C₂×C₄×C₉	C₂×C₅×C₄₃	1	3	yes	—
45	C₂²×C₃×C₅	C₂²×C₃×C₄₃	1	1	yes	characteristic
46	C₃×C₄×C₅	C₃×C₄×C₄₃	1	6	yes	—
47	C₃×C₄²	C₃×C₅×C₄₃	1	1	yes	characteristic
48	C₅×C₉	C₄²×C₄₃	1	1	yes	characteristic, direct product factor, Hall
49	C₄₃	C₄²×C₅×C₉	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×C₄×C₅	C₂×C₉×C₄₃	1	3	yes	—
51	C₂²×C₉	C₂²×C₅×C₄₃	1	1	yes	characteristic
52	C₄×C₉	C₄×C₅×C₄₃	1	6	yes	direct product factor
53	C₂×C₃×C₅	C₂×C₃×C₄×C₄₃	1	3	yes	—
54	C₂×C₃×C₄	C₂×C₃×C₅×C₄₃	1	3	yes	—
55	C₂²×C₅	C₂²×C₉×C₄₃	1	1	yes	characteristic
56	C₄×C₅	C₄×C₉×C₄₃	1	6	yes	direct product factor
57	C₂×C₉	C₂×C₄×C₅×C₄₃	1	3	yes	—
58	C₄²	C₅×C₉×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
59	C₃×C₅	C₃×C₄²×C₄₃	1	1	yes	characteristic
60	C₂²×C₃	C₂²×C₃×C₅×C₄₃	1	1	yes	characteristic
61	C₃×C₄	C₃×C₄×C₅×C₄₃	1	6	yes	—
62	C₂×C₅	C₂×C₄×C₉×C₄₃	1	3	yes	—
63	C₉	C₄²×C₅×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
64	C₂×C₄	C₂×C₅×C₉×C₄₃	1	3	yes	—
65	C₂×C₃	C₂×C₃×C₄×C₅×C₄₃	1	3	yes	—
66	C₅	C₄²×C₉×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
67	C₂²	C₂²×C₅×C₉×C₄₃	1	1	yes	characteristic
68	C₄	C₄×C₅×C₉×C₄₃	1	6	yes	direct product factor
69	C₃	C₃×C₄²×C₅×C₄₃	1	1	yes	characteristic
70	C₂	C₂×C₄×C₅×C₉×C₄₃	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃	C₂²×C₃×C₅×C₄₃
socle, prime radical	C₂²×C₃×C₅×C₄₃	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×C₄₃	C₅	direct (N × H)
5. C₄²×C₅×C₄₃	C₉	direct (N × H)
9. C₄×C₅×C₉×C₄₃	C₄	direct (N × H)
13. C₅×C₉×C₄₃	C₄²	direct (N × H)
16. C₄×C₉×C₄₃	C₄×C₅	direct (N × H)
20. C₄×C₅×C₄₃	C₄×C₉	direct (N × H)
22. C₄²×C₅×C₉	C₄₃	direct (N × H)
23. C₄²×C₄₃	C₅×C₉	direct (N × H)
28. C₉×C₄₃	C₄²×C₅	direct (N × H)
33. C₅×C₄₃	C₄²×C₉	direct (N × H)
35. C₄×C₅×C₉	C₄×C₄₃	direct (N × H)
37. C₄×C₄₃	C₄×C₅×C₉	direct (N × H)
38. C₄²×C₉	C₅×C₄₃	direct (N × H)
43. C₄²×C₅	C₉×C₄₃	direct (N × H)
48. C₅×C₉	C₄²×C₄₃	direct (N × H)
49. C₄₃	C₄²×C₅×C₉	direct (N × H)
52. C₄×C₉	C₄×C₅×C₄₃	direct (N × H)
56. C₄×C₅	C₄×C₉×C₄₃	direct (N × H)
58. C₄²	C₅×C₉×C₄₃	direct (N × H)
63. C₉	C₄²×C₅×C₄₃	direct (N × H)
66. C₅	C₄²×C₉×C₄₃	direct (N × H)
68. C₄	C₄×C₅×C₉×C₄₃	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×C₄×C₅×C₉×C₄₃	2
C₃×C₄²×C₅×C₄₃	3
C₄²×C₉×C₄₃	5
C₄²×C₅×C₉	43

Subgroups — C42×C5×C9×C43 #72207694

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×C₅×C₉×C₄₃ #72207694