Subgroups — C₂×C₃×C₅×C₁₃×D₄₁ #44544486

Order 31980.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅×C₁₃	D₄₁
commutator, cosocle, hypocenter	C₄₁	C₂²×C₃×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₃×C₄₁	C₂
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₂×C₃×C₅×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₃×D₄₁	C₂	direct (N × H)
2. C₂×C₃×C₅×C₁₃×C₄₁	C₂	semidirect
3. C₂×C₅×C₁₃×D₄₁	C₃	direct (N × H)
4. C₃×C₅×C₁₃×C₄₁	C₂²	semidirect
5. C₂×C₃×C₁₃×D₄₁	C₅	direct (N × H)
6. C₅×C₁₃×D₄₁	C₂×C₃	direct (N × H)
7. C₂×C₅×C₁₃×C₄₁	C₂×C₃	semidirect
8. C₃×C₁₃×D₄₁	C₂×C₅	direct (N × H)
9. C₂×C₃×C₁₃×C₄₁	C₂×C₅	semidirect
10. C₅×C₁₃×C₄₁	C₂²×C₃	semidirect
11. C₂×C₃×C₅×D₄₁	C₁₃	direct (N × H)
12. C₂×C₁₃×D₄₁	C₃×C₅	direct (N × H)
13. C₃×C₁₃×C₄₁	C₂²×C₅	semidirect
14. C₂×C₃×C₅×C₄₁	C₂×C₁₃	semidirect
15. C₃×C₅×D₄₁	C₂×C₁₃	direct (N × H)
16. C₂×C₁₃×C₄₁	C₂×C₃×C₅	semidirect
17. C₁₃×D₄₁	C₂×C₃×C₅	direct (N × H)
18. C₂×C₅×D₄₁	C₃×C₁₃	direct (N × H)
20. C₃×C₅×C₄₁	C₂²×C₁₃	semidirect
21. C₁₃×C₄₁	C₂²×C₃×C₅	semidirect
22. C₂×C₃×D₄₁	C₅×C₁₃	direct (N × H)
23. C₂×C₅×C₄₁	C₂×C₃×C₁₃	semidirect
24. C₅×D₄₁	C₂×C₃×C₁₃	direct (N × H)
26. C₂×C₃×C₅×C₁₃	D₄₁	direct (N × H)
28. C₂×C₃×C₄₁	C₂×C₅×C₁₃	semidirect
29. C₃×D₄₁	C₂×C₅×C₁₃	direct (N × H)
30. C₅×C₄₁	C₂²×C₃×C₁₃	semidirect
31. C₃×C₅×C₁₃	C₂×D₄₁	direct (N × H)
32. C₂×D₄₁	C₃×C₅×C₁₃	direct (N × H)
35. C₂×C₅×C₁₃	C₃×D₄₁	direct (N × H)
36. C₃×C₄₁	C₂²×C₅×C₁₃	semidirect
37. C₂×C₄₁	C₂×C₃×C₅×C₁₃	semidirect
38. D₄₁	C₂×C₃×C₅×C₁₃	direct (N × H)
40. C₂×C₃×C₁₃	C₅×D₄₁	direct (N × H)
41. C₅×C₁₃	C₂×C₃×D₄₁	direct (N × H)
44. C₄₁	C₂²×C₃×C₅×C₁₃	semidirect
45. C₃×C₁₃	C₂×C₅×D₄₁	direct (N × H)
47. C₂×C₃×C₅	C₁₃×D₄₁	direct (N × H)
49. C₂×C₁₃	C₃×C₅×D₄₁	direct (N × H)
51. C₃×C₅	C₂×C₁₃×D₄₁	direct (N × H)
52. C₁₃	C₂×C₃×C₅×D₄₁	direct (N × H)
55. C₂×C₅	C₃×C₁₃×D₄₁	direct (N × H)
57. C₂×C₃	C₅×C₁₃×D₄₁	direct (N × H)
58. C₅	C₂×C₃×C₁₃×D₄₁	direct (N × H)
60. C₃	C₂×C₅×C₁₃×D₄₁	direct (N × H)
62. C₂	C₃×C₅×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×C₅×C₁₃×D₄₁	2
C₂×C₃×C₅×C₁₃×C₄₁	2
C₂×C₅×C₁₃×D₄₁	3
C₂×C₃×C₁₃×D₄₁	5
C₂×C₃×C₅×D₄₁	13
C₂²×C₃×C₅×C₁₃	41

Subgroups — C2×C3×C5×C13×D41 #44544486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×C₁₃×D₄₁ #44544486