Subgroups — C₂×C₅×C₇×D₁₃⋊C₃ #19129784

Order 5460.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×D₁₃⋊C₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₇×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₇×D₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×C₇×C₁₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇×D₁₃⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₇×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅×C₇×D₁₃	C₂×C₃	1	2	yes	complemented
8	C₂×C₅×D₁₃⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₇×C₁₃⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented
10	C₇×D₁₃⋊C₃	C₂×C₅	1	2	yes	direct product factor
11	C₅×C₇×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₃×C₅×C₇	—	13	1	no	maximal, Hall
13	C₂×C₅×C₁₃⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented
14	C₅×D₁₃⋊C₃	C₂×C₇	1	2	yes	direct product factor
15	C₂×C₇×D₁₃	C₃×C₅	1	1	yes	characteristic, complemented, Hall
16	C₇×C₁₃⋊C₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅×D₁₃	C₃×C₇	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₅×C₇	—	13	2	no	—
19	C₂×C₃×C₅×C₇	—	13	1	no	—
20	C₅×C₁₃⋊C₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
21	C₂×C₇×C₁₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
22	C₇×D₁₃	C₂×C₃×C₅	1	2	yes	complemented
23	C₂×D₁₃⋊C₃	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
24	C₂²×C₅×C₇	—	13	1	no	Hall
25	C₂×C₅×C₁₃	C₂×C₃×C₇	1	1	yes	characteristic, complemented
26	C₅×D₁₃	C₂×C₃×C₇	1	2	yes	complemented
27	C₃×C₅×C₇	—	13	1	no	Hall
28	C₇×C₁₃	C₂²×C₃×C₅	1	1	yes	characteristic, complemented, Hall
29	C₂²×C₃×C₇	—	13	1	no	Hall
30	C₂×C₁₃⋊C₃	C₂×C₅×C₇	1	1	yes	characteristic, complemented
31	D₁₃⋊C₃	C₂×C₅×C₇	1	2	yes	direct product factor
32	C₂×C₅×C₇	—	13	2	no	—
33	C₂×C₅×C₇	D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
34	C₅×C₁₃	C₂²×C₃×C₇	1	1	yes	characteristic, complemented, Hall
35	C₂²×C₃×C₅	—	13	1	no	Hall
36	C₂×D₁₃	C₃×C₅×C₇	1	1	yes	characteristic, complemented, Hall
37	C₂×C₃×C₇	—	13	2	no	—
38	C₂×C₃×C₇	—	13	1	no	—
39	C₁₃⋊C₃	C₂²×C₅×C₇	1	1	yes	characteristic, complemented, Hall
40	C₅×C₇	C₂×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
41	C₂×C₃×C₅	—	13	2	no	—
42	C₂×C₃×C₅	—	13	1	no	—
43	C₂²×C₇	—	13	1	no	Hall
44	C₂×C₁₃	C₂×C₃×C₅×C₇	1	1	yes	characteristic, complemented
45	D₁₃	C₂×C₃×C₅×C₇	1	2	yes	complemented
46	C₃×C₇	—	13	1	no	Hall
47	C₂²×C₅	—	13	1	no	Hall
48	C₃×C₅	—	13	1	no	Hall
49	C₂×C₇	—	13	2	no	—
50	C₂×C₇	C₅×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
51	C₁₃	C₂²×C₃×C₅×C₇	1	1	yes	characteristic, complemented, Sylow
52	C₂²×C₃	—	13	1	no	Hall
53	C₂×C₅	—	13	2	no	—
54	C₂×C₅	C₇×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
55	C₇	C₂×C₅×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
56	C₂×C₃	—	13	2	no	—
57	C₂×C₃	—	13	1	no	—
58	C₅	C₂×C₇×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²	—	13	1	no	Sylow
60	C₃	—	13	1	no	Sylow
61	C₂	—	13	2	no	—
62	C₂	C₅×C₇×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₇	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₂²×C₃×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₁₃	C₂×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₅×C₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×D₁₃⋊C₃	C₂	direct (N × H)
2. C₂×C₅×C₇×C₁₃⋊C₃	C₂	semidirect
3. C₂×C₅×C₇×D₁₃	C₃	semidirect
4. C₅×C₇×C₁₃⋊C₃	C₂²	semidirect
5. C₂×C₇×D₁₃⋊C₃	C₅	direct (N × H)
6. C₂×C₅×C₇×C₁₃	C₂×C₃	semidirect
7. C₅×C₇×D₁₃	C₂×C₃	semidirect
8. C₂×C₅×D₁₃⋊C₃	C₇	direct (N × H)
9. C₂×C₇×C₁₃⋊C₃	C₂×C₅	semidirect
10. C₇×D₁₃⋊C₃	C₂×C₅	direct (N × H)
11. C₅×C₇×C₁₃	C₂²×C₃	semidirect
13. C₂×C₅×C₁₃⋊C₃	C₂×C₇	semidirect
14. C₅×D₁₃⋊C₃	C₂×C₇	direct (N × H)
15. C₂×C₇×D₁₃	C₃×C₅	semidirect
16. C₇×C₁₃⋊C₃	C₂²×C₅	semidirect
17. C₂×C₅×D₁₃	C₃×C₇	semidirect
20. C₅×C₁₃⋊C₃	C₂²×C₇	semidirect
21. C₂×C₇×C₁₃	C₂×C₃×C₅	semidirect
22. C₇×D₁₃	C₂×C₃×C₅	semidirect
23. C₂×D₁₃⋊C₃	C₅×C₇	direct (N × H)
25. C₂×C₅×C₁₃	C₂×C₃×C₇	semidirect
26. C₅×D₁₃	C₂×C₃×C₇	semidirect
28. C₇×C₁₃	C₂²×C₃×C₅	semidirect
30. C₂×C₁₃⋊C₃	C₂×C₅×C₇	semidirect
31. D₁₃⋊C₃	C₂×C₅×C₇	direct (N × H)
33. C₂×C₅×C₇	D₁₃⋊C₃	direct (N × H)
34. C₅×C₁₃	C₂²×C₃×C₇	semidirect
36. C₂×D₁₃	C₃×C₅×C₇	semidirect
39. C₁₃⋊C₃	C₂²×C₅×C₇	semidirect
40. C₅×C₇	C₂×D₁₃⋊C₃	direct (N × H)
44. C₂×C₁₃	C₂×C₃×C₅×C₇	semidirect
45. D₁₃	C₂×C₃×C₅×C₇	semidirect
50. C₂×C₇	C₅×D₁₃⋊C₃	direct (N × H)
51. C₁₃	C₂²×C₃×C₅×C₇	semidirect
54. C₂×C₅	C₇×D₁₃⋊C₃	direct (N × H)
55. C₇	C₂×C₅×D₁₃⋊C₃	direct (N × H)
58. C₅	C₂×C₇×D₁₃⋊C₃	direct (N × H)
62. C₂	C₅×C₇×D₁₃⋊C₃	direct (N × H)

Subgroups — C2×C5×C7×D13⋊C3 #19129784

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅×C₇×D₁₃⋊C₃ #19129784