Subgroups — C₃×D₅×C₁₃×D₄₁ #44544416

Order 31980.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×D₂₀₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₅×C₁₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₁₃×D₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×C₁₃×D₄₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₁₃×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₁₃×D₄₁	—	5	1	no	maximal, Hall
7	C₁₃×D₂₀₅	C₂×C₃	1	1	yes	characteristic, complemented
8	D₅×C₁₃×C₄₁	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×C₁₃×D₄₁	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×C₁₃×D₄₁	—	5	1	no	—
11	C₃×C₁₃×D₄₁	D₅	1	1	yes	characteristic, direct product factor
12	C₂×C₃×C₁₃×C₄₁	—	5	1	no	—
13	C₅×C₁₃×C₄₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
14	C₃×D₅×D₄₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₁₃×D₄₁	—	5	1	no	Hall
16	C₃×C₁₃×C₄₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	C₃×D₂₀₅	C₂×C₁₃	1	1	yes	characteristic, complemented
18	C₃×D₅×C₄₁	C₂×C₁₃	1	1	yes	characteristic, complemented
19	C₃×C₅×D₄₁	C₂×C₁₃	1	1	yes	characteristic, complemented
20	C₂×C₁₃×C₄₁	—	5	1	no	—
21	C₁₃×D₄₁	—	5	1	no	—
22	C₁₃×D₄₁	C₃×D₅	1	1	yes	characteristic, direct product factor
23	D₅×D₄₁	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₃×D₅×C₁₃	—	41	1	no	maximal, Hall
25	C₃×C₅×C₄₁	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
26	C₁₃×C₄₁	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×D₄₁	—	5	1	no	Hall
28	D₂₀₅	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
29	C₅×D₄₁	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
30	D₅×C₄₁	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
31	C₂×C₃×C₅×C₁₃	—	41	1	no	—
32	C₃×D₅×C₁₃	—	41	1	no	—
33	C₃×D₅×C₁₃	D₄₁	1	1	yes	characteristic, direct product factor
34	C₂×D₅×C₁₃	—	41	1	no	Hall
35	C₂×C₃×C₄₁	—	5	1	no	—
36	C₃×D₄₁	—	5	1	no	—
37	C₃×D₄₁	D₅×C₁₃	1	1	yes	characteristic, direct product factor
38	C₅×C₄₁	C₂²×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
39	C₃×C₅×C₁₃	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
40	C₂×D₄₁	—	5	1	no	Hall
41	C₂²×C₃×C₁₃	—	205	1	no	Hall
42	C₂×C₅×C₁₃	—	41	1	no	—
43	D₅×C₁₃	—	41	1	no	—
44	D₅×C₁₃	C₃×D₄₁	1	1	yes	characteristic, direct product factor
45	C₃×C₄₁	C₂×D₅×C₁₃	1	1	yes	characteristic, complemented, Hall
46	C₂×C₄₁	—	5	1	no	—
47	D₄₁	—	5	1	no	—
48	D₄₁	C₃×D₅×C₁₃	1	1	yes	characteristic, direct product factor
49	C₂×C₃×C₁₃	—	5	1	no	—
50	C₂×C₃×C₁₃	—	41	1	no	—
51	C₂×C₃×C₁₃	—	205	1	no	—
52	C₅×C₁₃	C₂×C₃×D₄₁	1	1	yes	characteristic, complemented, Hall
53	C₂×C₃×D₅	—	41	1	no	Hall
54	C₂²×C₁₃	—	205	1	no	Hall
55	C₄₁	C₂×C₃×D₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
56	C₃×C₁₃	D₅×D₄₁	1	1	yes	characteristic, direct product factor, Hall
57	C₂×C₃×C₅	—	41	1	no	—
58	C₃×D₅	—	41	1	no	—
59	C₃×D₅	C₁₃×D₄₁	1	1	yes	characteristic, direct product factor
60	C₂×C₁₃	—	5	1	no	—
61	C₂×C₁₃	—	41	1	no	—
62	C₂×C₁₃	—	205	1	no	—
63	C₂×D₅	—	41	1	no	Hall
64	C₃×C₅	C₂×C₁₃×D₄₁	1	1	yes	characteristic, complemented, Hall
65	C₁₃	C₃×D₅×D₄₁	1	1	yes	characteristic, direct product factor, Sylow
66	C₂²×C₃	—	205	1	no	Hall
67	C₂×C₅	—	41	1	no	—
68	D₅	—	41	1	no	—
69	D₅	C₃×C₁₃×D₄₁	1	1	yes	characteristic, direct product factor
70	C₂×C₃	—	5	1	no	—
71	C₂×C₃	—	41	1	no	—
72	C₂×C₃	—	205	1	no	—
73	C₅	C₂×C₃×C₁₃×D₄₁	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	205	1	no	Sylow
75	C₃	D₅×C₁₃×D₄₁	1	1	yes	characteristic, direct product factor, Sylow
76	C₂	—	5	1	no	—
77	C₂	—	41	1	no	—
78	C₂	—	205	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₃	D₅×D₄₁
commutator, cosocle, hypocenter	C₅×C₄₁	C₂²×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₄₁	C₂²
LCS	G ▷ C₅×C₄₁
UCS	C₁ ◁ C₃×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃×D₂₀₅	C₂	semidirect
2. C₃×D₅×C₁₃×C₄₁	C₂	semidirect
3. C₃×C₅×C₁₃×D₄₁	C₂	semidirect
4. D₅×C₁₃×D₄₁	C₃	direct (N × H)
5. C₃×C₅×C₁₃×C₄₁	C₂²	semidirect
7. C₁₃×D₂₀₅	C₂×C₃	semidirect
8. D₅×C₁₃×C₄₁	C₂×C₃	semidirect
9. C₅×C₁₃×D₄₁	C₂×C₃	semidirect
11. C₃×C₁₃×D₄₁	D₅	direct (N × H)
13. C₅×C₁₃×C₄₁	C₂²×C₃	semidirect
14. C₃×D₅×D₄₁	C₁₃	direct (N × H)
16. C₃×C₁₃×C₄₁	C₂×D₅	semidirect
17. C₃×D₂₀₅	C₂×C₁₃	semidirect
18. C₃×D₅×C₄₁	C₂×C₁₃	semidirect
19. C₃×C₅×D₄₁	C₂×C₁₃	semidirect
22. C₁₃×D₄₁	C₃×D₅	direct (N × H)
23. D₅×D₄₁	C₃×C₁₃	direct (N × H)
25. C₃×C₅×C₄₁	C₂²×C₁₃	semidirect
26. C₁₃×C₄₁	C₂×C₃×D₅	semidirect
28. D₂₀₅	C₂×C₃×C₁₃	semidirect
29. C₅×D₄₁	C₂×C₃×C₁₃	semidirect
30. D₅×C₄₁	C₂×C₃×C₁₃	semidirect
33. C₃×D₅×C₁₃	D₄₁	direct (N × H)
37. C₃×D₄₁	D₅×C₁₃	direct (N × H)
38. C₅×C₄₁	C₂²×C₃×C₁₃	semidirect
39. C₃×C₅×C₁₃	C₂×D₄₁	semidirect
44. D₅×C₁₃	C₃×D₄₁	direct (N × H)
45. C₃×C₄₁	C₂×D₅×C₁₃	semidirect
48. D₄₁	C₃×D₅×C₁₃	direct (N × H)
52. C₅×C₁₃	C₂×C₃×D₄₁	semidirect
55. C₄₁	C₂×C₃×D₅×C₁₃	semidirect
56. C₃×C₁₃	D₅×D₄₁	direct (N × H)
59. C₃×D₅	C₁₃×D₄₁	direct (N × H)
64. C₃×C₅	C₂×C₁₃×D₄₁	semidirect
65. C₁₃	C₃×D₅×D₄₁	direct (N × H)
69. D₅	C₃×C₁₃×D₄₁	direct (N × H)
73. C₅	C₂×C₃×C₁₃×D₄₁	semidirect
75. C₃	D₅×C₁₃×D₄₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₁₃×D₂₀₅	2
C₃×D₅×C₁₃×C₄₁	2
C₃×C₅×C₁₃×D₄₁	2
D₅×C₁₃×D₄₁	3
C₂×C₃×C₁₃×D₄₁	5
C₃×D₅×D₄₁	13
C₂×C₃×D₅×C₁₃	41

Subgroups — C3×D5×C13×D41 #44544416

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×C₁₃×D₄₁ #44544416