Subgroups — C₄₃×D₁₅⋊D₁₃ #46776589

Order 33540.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₁₅×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₄₃×D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄₃×D₆₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₁₃×C₄₃	—	3	1	no	maximal, Hall
5	C₃×C₅×C₁₃×C₄₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×D₁₃×C₄₃	—	5	1	no	maximal, Hall
7	C₄₃×D₆₅	D₃	1	1	yes	characteristic, complemented
8	D₅×C₁₃×C₄₃	—	3	1	no	—
9	C₅×D₁₃×C₄₃	—	3	1	no	—
10	C₄₃×D₃₉	D₅	1	1	yes	characteristic, complemented
11	D₃×C₁₃×C₄₃	—	5	1	no	—
12	C₃×D₁₃×C₄₃	—	5	1	no	—
13	C₅×C₁₃×C₄₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	D₃×D₅×C₄₃	—	13	1	no	maximal, Hall
15	C₂×D₁₃×C₄₃	—	15	1	no	Hall
16	C₃×C₁₃×C₄₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	D₁₅×C₄₃	D₁₃	1	1	yes	characteristic, complemented
18	C₅×D₃×C₄₃	—	13	1	no	—
19	C₃×D₅×C₄₃	—	13	1	no	—
20	C₂×C₁₃×C₄₃	—	15	1	no	—
21	D₁₃×C₄₃	—	3	1	no	—
22	D₁₃×C₄₃	—	5	1	no	—
23	C₂×D₅×C₄₃	—	39	1	no	Hall
24	D₁₅⋊D₁₃	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₃×C₅×C₄₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
26	C₁₃×C₄₃	D₃×D₅	1	1	yes	characteristic, complemented, Hall
27	C₂×D₃×C₄₃	—	65	1	no	Hall
28	C₂×C₅×C₄₃	—	39	1	no	—
29	D₅×C₄₃	—	3	1	no	—
30	D₅×C₄₃	—	13	1	no	—
31	C₁₃×D₁₅	C₂×C₄₃	1	1	yes	characteristic, complemented
32	C₅×D₃₉	C₂×C₄₃	1	1	yes	characteristic, complemented
33	C₃×D₆₅	C₂×C₄₃	1	1	yes	characteristic, complemented
34	D₅×D₁₃	—	3	1	no	Hall
35	C₂×C₃×C₄₃	—	65	1	no	—
36	D₃×C₄₃	—	5	1	no	—
37	D₃×C₄₃	—	13	1	no	—
38	C₅×C₄₃	D₃×D₁₃	1	1	yes	characteristic, complemented, Hall
39	C₃×C₅×C₁₃	C₂²×C₄₃	1	1	yes	characteristic, complemented, Hall
40	C₂²×C₄₃	—	195	1	no	Hall
41	D₃×D₁₃	—	5	1	no	Hall
42	D₆₅	D₃×C₄₃	1	1	yes	characteristic, complemented
43	C₅×D₁₃	—	3	1	no	—
44	D₅×C₁₃	—	3	1	no	—
45	C₃×C₄₃	D₅×D₁₃	1	1	yes	characteristic, complemented, Hall
46	C₂×C₄₃	—	15	1	no	—
47	C₂×C₄₃	—	39	1	no	—
48	C₂×C₄₃	—	65	1	no	—
49	D₃₉	D₅×C₄₃	1	1	yes	characteristic, complemented
50	C₃×D₁₃	—	5	1	no	—
51	D₃×C₁₃	—	5	1	no	—
52	C₅×C₁₃	C₂×D₃×C₄₃	1	1	yes	characteristic, complemented, Hall
53	D₃×D₅	—	13	1	no	Hall
54	C₂×D₁₃	—	15	1	no	Hall
55	C₄₃	D₁₅⋊D₁₃	1	1	yes	characteristic, direct product factor, Sylow
56	C₃×C₁₃	C₂×D₅×C₄₃	1	1	yes	characteristic, complemented, Hall
57	D₁₅	D₁₃×C₄₃	1	1	yes	characteristic, complemented
58	C₃×D₅	—	13	1	no	—
59	C₅×D₃	—	13	1	no	—
60	C₂×C₁₃	—	15	1	no	—
61	D₁₃	—	3	1	no	—
62	D₁₃	—	5	1	no	—
63	C₂×D₅	—	39	1	no	Hall
64	C₃×C₅	C₂×D₁₃×C₄₃	1	1	yes	characteristic, complemented, Hall
65	C₁₃	D₃×D₅×C₄₃	1	1	yes	characteristic, complemented, Sylow
66	C₂×D₃	—	65	1	no	Hall
67	C₂×C₅	—	39	1	no	—
68	D₅	—	3	1	no	—
69	D₅	—	13	1	no	—
70	C₂×C₃	—	65	1	no	—
71	D₃	—	5	1	no	—
72	D₃	—	13	1	no	—
73	C₅	D₃×D₁₃×C₄₃	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	195	1	no	Sylow
75	C₃	D₅×D₁₃×C₄₃	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	15	1	no	—
77	C₂	—	39	1	no	—
78	C₂	—	65	1	no	—

	subgroup	G/H
center, hypercenter	C₄₃	D₁₅⋊D₁₃
commutator, cosocle, hypocenter	C₃×C₅×C₁₃	C₂²×C₄₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₄₃	C₂²
LCS	G ▷ C₃×C₅×C₁₃
UCS	C₁ ◁ C₄₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×D₁₅×C₄₃	C₂	semidirect
2. C₅×C₄₃×D₃₉	C₂	semidirect
3. C₃×C₄₃×D₆₅	C₂	semidirect
5. C₃×C₅×C₁₃×C₄₃	C₂²	semidirect
7. C₄₃×D₆₅	D₃	semidirect
10. C₄₃×D₃₉	D₅	semidirect
13. C₅×C₁₃×C₄₃	C₂×D₃	semidirect
16. C₃×C₁₃×C₄₃	C₂×D₅	semidirect
17. D₁₅×C₄₃	D₁₃	semidirect
24. D₁₅⋊D₁₃	C₄₃	direct (N × H)
25. C₃×C₅×C₄₃	C₂×D₁₃	semidirect
26. C₁₃×C₄₃	D₃×D₅	semidirect
31. C₁₃×D₁₅	C₂×C₄₃	semidirect
32. C₅×D₃₉	C₂×C₄₃	semidirect
33. C₃×D₆₅	C₂×C₄₃	semidirect
38. C₅×C₄₃	D₃×D₁₃	semidirect
39. C₃×C₅×C₁₃	C₂²×C₄₃	semidirect
42. D₆₅	D₃×C₄₃	semidirect
45. C₃×C₄₃	D₅×D₁₃	semidirect
49. D₃₉	D₅×C₄₃	semidirect
52. C₅×C₁₃	C₂×D₃×C₄₃	semidirect
55. C₄₃	D₁₅⋊D₁₃	direct (N × H)
56. C₃×C₁₃	C₂×D₅×C₄₃	semidirect
57. D₁₅	D₁₃×C₄₃	semidirect
64. C₃×C₅	C₂×D₁₃×C₄₃	semidirect
65. C₁₃	D₃×D₅×C₄₃	semidirect
73. C₅	D₃×D₁₃×C₄₃	semidirect
75. C₃	D₅×D₁₃×C₄₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×D₁₅×C₄₃	2
C₅×C₄₃×D₃₉	2
C₃×C₄₃×D₆₅	2
D₅×D₁₃×C₄₃	3
D₃×D₁₃×C₄₃	5
D₃×D₅×C₄₃	13
D₁₅⋊D₁₃	43

Subgroups — C43×D15⋊D13 #46776589

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×D₁₅⋊D₁₃ #46776589