Subgroups — C₂⁴×C₅×C₉×C₄₃ #72207698

Order 30960.

804 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×C₉×C₄₃	C₂	1	15	yes	maximal, direct product factor
2	C₂⁴×C₃×C₅×C₄₃	C₃	1	1	yes	maximal, characteristic
3	C₂⁴×C₉×C₄₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂³×C₃×C₅×C₄₃	C₂×C₃	1	15	yes	—
5	C₂⁴×C₅×C₄₃	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₂³×C₉×C₄₃	C₂×C₅	1	15	yes	direct product factor
7	C₂⁴×C₃×C₄₃	C₃×C₅	1	1	yes	characteristic
8	C₂²×C₅×C₉×C₄₃	C₂²	1	35	yes	direct product factor
9	C₂×C₅×C₉×C₄₃	C₂³	1	15	yes	direct product factor
10	C₂²×C₃×C₅×C₄₃	C₂²×C₃	1	35	yes	—
11	C₅×C₉×C₄₃	C₂⁴	1	1	yes	characteristic, direct product factor, Hall
12	C₂³×C₅×C₄₃	C₂×C₉	1	15	yes	direct product factor
13	C₂²×C₉×C₄₃	C₂²×C₅	1	35	yes	direct product factor
14	C₂×C₃×C₅×C₄₃	C₂³×C₃	1	15	yes	—
15	C₂³×C₃×C₄₃	C₂×C₃×C₅	1	15	yes	—
16	C₂²×C₅×C₄₃	C₂²×C₉	1	35	yes	direct product factor
17	C₂×C₉×C₄₃	C₂³×C₅	1	15	yes	direct product factor
18	C₂⁴×C₅×C₉	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂⁴×C₄₃	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
20	C₃×C₅×C₄₃	C₂⁴×C₃	1	1	yes	characteristic
21	C₂²×C₃×C₄₃	C₂²×C₃×C₅	1	35	yes	—
22	C₂×C₅×C₄₃	C₂³×C₉	1	15	yes	direct product factor
23	C₉×C₄₃	C₂⁴×C₅	1	1	yes	characteristic, direct product factor, Hall
24	C₂³×C₅×C₉	C₂×C₄₃	1	15	yes	direct product factor
25	C₂³×C₄₃	C₂×C₅×C₉	1	15	yes	direct product factor
26	C₂×C₃×C₄₃	C₂³×C₃×C₅	1	15	yes	—
27	C₂⁴×C₃×C₅	C₃×C₄₃	1	1	yes	characteristic
28	C₅×C₄₃	C₂⁴×C₉	1	1	yes	characteristic, direct product factor, Hall
29	C₂²×C₅×C₉	C₂²×C₄₃	1	35	yes	direct product factor
30	C₂²×C₄₃	C₂²×C₅×C₉	1	35	yes	direct product factor
31	C₂⁴×C₉	C₅×C₄₃	1	1	yes	characteristic, direct product factor, Hall
32	C₃×C₄₃	C₂⁴×C₃×C₅	1	1	yes	characteristic
33	C₂³×C₃×C₅	C₂×C₃×C₄₃	1	15	yes	—
34	C₂×C₅×C₉	C₂³×C₄₃	1	15	yes	direct product factor
35	C₂×C₄₃	C₂³×C₅×C₉	1	15	yes	direct product factor
36	C₂⁴×C₅	C₉×C₄₃	1	1	yes	characteristic, direct product factor, Hall
37	C₂³×C₉	C₂×C₅×C₄₃	1	15	yes	direct product factor
38	C₂²×C₃×C₅	C₂²×C₃×C₄₃	1	35	yes	—
39	C₂⁴×C₃	C₃×C₅×C₄₃	1	1	yes	characteristic
40	C₅×C₉	C₂⁴×C₄₃	1	1	yes	characteristic, direct product factor, Hall
41	C₄₃	C₂⁴×C₅×C₉	1	1	yes	characteristic, direct product factor, Sylow
42	C₂³×C₅	C₂×C₉×C₄₃	1	15	yes	direct product factor
43	C₂²×C₉	C₂²×C₅×C₄₃	1	35	yes	direct product factor
44	C₂×C₃×C₅	C₂³×C₃×C₄₃	1	15	yes	—
45	C₂³×C₃	C₂×C₃×C₅×C₄₃	1	15	yes	—
46	C₂²×C₅	C₂²×C₉×C₄₃	1	35	yes	direct product factor
47	C₂×C₉	C₂³×C₅×C₄₃	1	15	yes	direct product factor
48	C₂⁴	C₅×C₉×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
49	C₃×C₅	C₂⁴×C₃×C₄₃	1	1	yes	characteristic
50	C₂²×C₃	C₂²×C₃×C₅×C₄₃	1	35	yes	—
51	C₂×C₅	C₂³×C₉×C₄₃	1	15	yes	direct product factor
52	C₉	C₂⁴×C₅×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
53	C₂³	C₂×C₅×C₉×C₄₃	1	15	yes	direct product factor
54	C₂×C₃	C₂³×C₃×C₅×C₄₃	1	15	yes	—
55	C₅	C₂⁴×C₉×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
56	C₂²	C₂²×C₅×C₉×C₄₃	1	35	yes	direct product factor
57	C₃	C₂⁴×C₃×C₅×C₄₃	1	1	yes	characteristic
58	C₂	C₂³×C₅×C₉×C₄₃	1	15	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂⁴×C₃×C₅×C₄₃
socle, prime radical	C₂⁴×C₃×C₅×C₄₃	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×C₅×C₉×C₄₃	C₂	direct (N × H)
3. C₂⁴×C₉×C₄₃	C₅	direct (N × H)
5. C₂⁴×C₅×C₄₃	C₉	direct (N × H)
6. C₂³×C₉×C₄₃	C₂×C₅	direct (N × H)
8. C₂²×C₅×C₉×C₄₃	C₂²	direct (N × H)
9. C₂×C₅×C₉×C₄₃	C₂³	direct (N × H)
11. C₅×C₉×C₄₃	C₂⁴	direct (N × H)
12. C₂³×C₅×C₄₃	C₂×C₉	direct (N × H)
13. C₂²×C₉×C₄₃	C₂²×C₅	direct (N × H)
16. C₂²×C₅×C₄₃	C₂²×C₉	direct (N × H)
17. C₂×C₉×C₄₃	C₂³×C₅	direct (N × H)
18. C₂⁴×C₅×C₉	C₄₃	direct (N × H)
19. C₂⁴×C₄₃	C₅×C₉	direct (N × H)
22. C₂×C₅×C₄₃	C₂³×C₉	direct (N × H)
23. C₉×C₄₃	C₂⁴×C₅	direct (N × H)
24. C₂³×C₅×C₉	C₂×C₄₃	direct (N × H)
25. C₂³×C₄₃	C₂×C₅×C₉	direct (N × H)
28. C₅×C₄₃	C₂⁴×C₉	direct (N × H)
29. C₂²×C₅×C₉	C₂²×C₄₃	direct (N × H)
30. C₂²×C₄₃	C₂²×C₅×C₉	direct (N × H)
31. C₂⁴×C₉	C₅×C₄₃	direct (N × H)
34. C₂×C₅×C₉	C₂³×C₄₃	direct (N × H)
35. C₂×C₄₃	C₂³×C₅×C₉	direct (N × H)
36. C₂⁴×C₅	C₉×C₄₃	direct (N × H)
37. C₂³×C₉	C₂×C₅×C₄₃	direct (N × H)
40. C₅×C₉	C₂⁴×C₄₃	direct (N × H)
41. C₄₃	C₂⁴×C₅×C₉	direct (N × H)
42. C₂³×C₅	C₂×C₉×C₄₃	direct (N × H)
43. C₂²×C₉	C₂²×C₅×C₄₃	direct (N × H)
46. C₂²×C₅	C₂²×C₉×C₄₃	direct (N × H)
47. C₂×C₉	C₂³×C₅×C₄₃	direct (N × H)
48. C₂⁴	C₅×C₉×C₄₃	direct (N × H)
51. C₂×C₅	C₂³×C₉×C₄₃	direct (N × H)
52. C₉	C₂⁴×C₅×C₄₃	direct (N × H)
53. C₂³	C₂×C₅×C₉×C₄₃	direct (N × H)
55. C₅	C₂⁴×C₉×C₄₃	direct (N × H)
56. C₂²	C₂²×C₅×C₉×C₄₃	direct (N × H)
58. C₂	C₂³×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
C₂³×C₅×C₉×C₄₃	2
C₂⁴×C₃×C₅×C₄₃	3
C₂⁴×C₉×C₄₃	5
C₂⁴×C₅×C₉	43

Subgroups — C24×C5×C9×C43 #72207698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₅×C₉×C₄₃ #72207698