Subgroups — D₃×D₅×C₁₃×C₄₁ #44544467

Order 31980.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₁₅×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₃×C₁₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₅×C₁₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₅×C₁₃×C₄₁	—	3	1	no	maximal, Hall
5	C₃×C₅×C₁₃×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×D₃×C₁₃×C₄₁	—	5	1	no	maximal, Hall
7	D₅×C₁₃×C₄₁	—	3	1	no	—
8	D₅×C₁₃×C₄₁	D₃	1	1	yes	characteristic, direct product factor
9	C₂×C₅×C₁₃×C₄₁	—	3	1	no	—
10	D₃×C₁₃×C₄₁	—	5	1	no	—
11	D₃×C₁₃×C₄₁	D₅	1	1	yes	characteristic, direct product factor
12	C₂×C₃×C₁₃×C₄₁	—	5	1	no	—
13	C₅×C₁₃×C₄₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	D₃×D₅×C₄₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂²×C₁₃×C₄₁	—	15	1	no	Hall
16	C₃×C₁₃×C₄₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	D₁₅×C₄₁	C₂×C₁₃	1	1	yes	characteristic, complemented
18	C₅×D₃×C₄₁	C₂×C₁₃	1	1	yes	characteristic, complemented
19	C₃×D₅×C₄₁	C₂×C₁₃	1	1	yes	characteristic, complemented
20	C₂×C₁₃×C₄₁	—	3	1	no	—
21	C₂×C₁₃×C₄₁	—	5	1	no	—
22	C₂×C₁₃×C₄₁	—	15	1	no	—
23	C₂×D₅×C₄₁	—	3	1	no	Hall
24	D₃×D₅×C₁₃	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₃×C₅×C₄₁	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
26	C₁₃×C₄₁	D₃×D₅	1	1	yes	characteristic, direct product factor, Hall
27	C₂×D₃×C₄₁	—	5	1	no	Hall
28	C₂×C₅×C₄₁	—	3	1	no	—
29	D₅×C₄₁	—	3	1	no	—
30	D₅×C₄₁	D₃×C₁₃	1	1	yes	characteristic, direct product factor
31	C₁₃×D₁₅	C₂×C₄₁	1	1	yes	characteristic, complemented
32	C₅×D₃×C₁₃	C₂×C₄₁	1	1	yes	characteristic, complemented
33	C₃×D₅×C₁₃	C₂×C₄₁	1	1	yes	characteristic, complemented
34	C₂×D₅×C₁₃	—	3	1	no	Hall
35	C₂×C₃×C₄₁	—	5	1	no	—
36	D₃×C₄₁	—	5	1	no	—
37	D₃×C₄₁	D₅×C₁₃	1	1	yes	characteristic, direct product factor
38	C₅×C₄₁	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
39	C₃×C₅×C₁₃	C₂²×C₄₁	1	1	yes	characteristic, complemented, Hall
40	C₂²×C₄₁	—	15	1	no	Hall
41	C₂×D₃×C₁₃	—	5	1	no	Hall
42	C₂×C₅×C₁₃	—	3	1	no	—
43	D₅×C₁₃	—	3	1	no	—
44	D₅×C₁₃	D₃×C₄₁	1	1	yes	characteristic, direct product factor
45	C₃×C₄₁	C₂×D₅×C₁₃	1	1	yes	characteristic, complemented, Hall
46	C₂×C₄₁	—	3	1	no	—
47	C₂×C₄₁	—	5	1	no	—
48	C₂×C₄₁	—	15	1	no	—
49	C₂×C₃×C₁₃	—	5	1	no	—
50	D₃×C₁₃	—	5	1	no	—
51	D₃×C₁₃	D₅×C₄₁	1	1	yes	characteristic, direct product factor
52	C₅×C₁₃	C₂×D₃×C₄₁	1	1	yes	characteristic, complemented, Hall
53	D₃×D₅	C₁₃×C₄₁	1	1	yes	characteristic, direct product factor, Hall
54	C₂²×C₁₃	—	15	1	no	Hall
55	C₄₁	D₃×D₅×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
56	C₃×C₁₃	C₂×D₅×C₄₁	1	1	yes	characteristic, complemented, Hall
57	D₁₅	C₂×C₁₃×C₄₁	1	1	yes	characteristic, complemented
58	C₃×D₅	C₂×C₁₃×C₄₁	1	1	yes	characteristic, complemented
59	C₅×D₃	C₂×C₁₃×C₄₁	1	1	yes	characteristic, complemented
60	C₂×C₁₃	—	3	1	no	—
61	C₂×C₁₃	—	5	1	no	—
62	C₂×C₁₃	—	15	1	no	—
63	C₂×D₅	—	3	1	no	Hall
64	C₃×C₅	C₂²×C₁₃×C₄₁	1	1	yes	characteristic, complemented, Hall
65	C₁₃	D₃×D₅×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
66	C₂×D₃	—	5	1	no	Hall
67	C₂×C₅	—	3	1	no	—
68	D₅	—	3	1	no	—
69	D₅	D₃×C₁₃×C₄₁	1	1	yes	characteristic, direct product factor
70	C₂×C₃	—	5	1	no	—
71	D₃	—	5	1	no	—
72	D₃	D₅×C₁₃×C₄₁	1	1	yes	characteristic, direct product factor
73	C₅	C₂×D₃×C₁₃×C₄₁	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	15	1	no	Sylow
75	C₃	C₂×D₅×C₁₃×C₄₁	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	3	1	no	—
77	C₂	—	5	1	no	—
78	C₂	—	15	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃×C₄₁	D₃×D₅
commutator, cosocle, hypocenter	C₃×C₅	C₂²×C₁₃×C₄₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₄₁	C₂²
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₁₃×C₄₁

Complements

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

N	H ≅ G/N	type
1. C₁₃×D₁₅×C₄₁	C₂	semidirect
2. C₅×D₃×C₁₃×C₄₁	C₂	semidirect
3. C₃×D₅×C₁₃×C₄₁	C₂	semidirect
5. C₃×C₅×C₁₃×C₄₁	C₂²	semidirect
8. D₅×C₁₃×C₄₁	D₃	direct (N × H)
11. D₃×C₁₃×C₄₁	D₅	direct (N × H)
13. C₅×C₁₃×C₄₁	C₂×D₃	semidirect
14. D₃×D₅×C₄₁	C₁₃	direct (N × H)
16. C₃×C₁₃×C₄₁	C₂×D₅	semidirect
17. D₁₅×C₄₁	C₂×C₁₃	semidirect
18. C₅×D₃×C₄₁	C₂×C₁₃	semidirect
19. C₃×D₅×C₄₁	C₂×C₁₃	semidirect
24. D₃×D₅×C₁₃	C₄₁	direct (N × H)
25. C₃×C₅×C₄₁	C₂²×C₁₃	semidirect
26. C₁₃×C₄₁	D₃×D₅	direct (N × H)
30. D₅×C₄₁	D₃×C₁₃	direct (N × H)
31. C₁₃×D₁₅	C₂×C₄₁	semidirect
32. C₅×D₃×C₁₃	C₂×C₄₁	semidirect
33. C₃×D₅×C₁₃	C₂×C₄₁	semidirect
37. D₃×C₄₁	D₅×C₁₃	direct (N × H)
38. C₅×C₄₁	C₂×D₃×C₁₃	semidirect
39. C₃×C₅×C₁₃	C₂²×C₄₁	semidirect
44. D₅×C₁₃	D₃×C₄₁	direct (N × H)
45. C₃×C₄₁	C₂×D₅×C₁₃	semidirect
51. D₃×C₁₃	D₅×C₄₁	direct (N × H)
52. C₅×C₁₃	C₂×D₃×C₄₁	semidirect
53. D₃×D₅	C₁₃×C₄₁	direct (N × H)
55. C₄₁	D₃×D₅×C₁₃	direct (N × H)
56. C₃×C₁₃	C₂×D₅×C₄₁	semidirect
57. D₁₅	C₂×C₁₃×C₄₁	semidirect
58. C₃×D₅	C₂×C₁₃×C₄₁	semidirect
59. C₅×D₃	C₂×C₁₃×C₄₁	semidirect
64. C₃×C₅	C₂²×C₁₃×C₄₁	semidirect
65. C₁₃	D₃×D₅×C₄₁	direct (N × H)
69. D₅	D₃×C₁₃×C₄₁	direct (N × H)
72. D₃	D₅×C₁₃×C₄₁	direct (N × H)
73. C₅	C₂×D₃×C₁₃×C₄₁	semidirect
75. C₃	C₂×D₅×C₁₃×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×D₁₅×C₄₁	2
C₅×D₃×C₁₃×C₄₁	2
C₃×D₅×C₁₃×C₄₁	2
C₂×D₅×C₁₃×C₄₁	3
C₂×D₃×C₁₃×C₄₁	5
D₃×D₅×C₄₁	13
D₃×D₅×C₁₃	41

Subgroups — D3×D5×C13×C41 #44544467

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₅×C₁₃×C₄₁ #44544467