Subgroups — C₂×C₅×D₇×C₁₃⋊C₃ #19129795

Order 5460.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₇×C₁₃⋊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×C₁₃×D₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×C₇×C₁₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₇×C₁₃⋊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×C₁₃×D₇	C₂×C₃	1	2	yes	complemented
8	C₂²×C₅×C₁₃⋊C₃	—	7	1	no	maximal, Hall
9	C₂×C₇×C₁₃⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented
10	D₇×C₁₃⋊C₃	C₂×C₅	1	2	yes	direct product factor
11	C₅×C₇×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₅×D₇	—	13	1	no	maximal, Hall
13	C₂×C₅×C₁₃⋊C₃	—	7	2	no	—
14	C₂×C₅×C₁₃⋊C₃	D₇	1	1	yes	characteristic, direct product factor
15	C₂×C₁₃×D₇	C₃×C₅	1	1	yes	characteristic, complemented, Hall
16	C₇×C₁₃⋊C₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
17	C₂²×C₅×C₁₃	—	7	1	no	Hall
18	C₂×C₃×C₅×C₇	—	13	1	no	—
19	C₃×C₅×D₇	—	13	2	no	—
20	C₅×C₁₃⋊C₃	C₂×D₇	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₇×C₁₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
22	C₁₃×D₇	C₂×C₃×C₅	1	2	yes	complemented
23	C₂²×C₁₃⋊C₃	—	7	1	no	Hall
24	C₂×C₅×D₇	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₅×C₁₃	—	7	2	no	—
26	C₂×C₅×C₁₃	C₃×D₇	1	1	yes	characteristic, complemented
27	C₃×C₅×C₇	—	13	1	no	Hall
28	C₇×C₁₃	C₂²×C₃×C₅	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×D₇	—	13	1	no	Hall
30	C₂×C₁₃⋊C₃	—	7	2	no	—
31	C₂×C₁₃⋊C₃	C₅×D₇	1	1	yes	characteristic, direct product factor
32	C₂×C₅×C₇	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
33	C₅×D₇	C₂×C₁₃⋊C₃	1	2	yes	direct product factor
34	C₅×C₁₃	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Hall
35	C₂²×C₃×C₅	—	91	1	no	Hall
36	C₂²×C₁₃	—	7	1	no	Hall
37	C₂×C₃×C₇	—	13	1	no	—
38	C₃×D₇	—	13	2	no	—
39	C₁₃⋊C₃	C₂×C₅×D₇	1	1	yes	characteristic, direct product factor, Hall
40	C₅×C₇	C₂²×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
41	C₂×C₃×C₅	—	13	1	no	—
42	C₂×C₃×C₅	—	91	2	no	—
43	C₂×D₇	C₅×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
44	C₂×C₁₃	—	7	2	no	—
45	C₂×C₁₃	C₃×C₅×D₇	1	1	yes	characteristic, complemented
46	C₃×C₇	—	13	1	no	Hall
47	C₂²×C₅	—	7	1	no	Hall
48	C₃×C₅	—	13	1	no	Hall
49	C₂×C₇	C₂×C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented
50	D₇	C₂×C₅×C₁₃⋊C₃	1	2	yes	direct product factor
51	C₁₃	C₂×C₃×C₅×D₇	1	1	yes	characteristic, complemented, Sylow
52	C₂²×C₃	—	91	1	no	Hall
53	C₂×C₅	—	7	2	no	—
54	C₂×C₅	D₇×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
55	C₇	C₂²×C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₃	—	13	1	no	—
57	C₂×C₃	—	91	2	no	—
58	C₅	C₂×D₇×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²	—	7	1	no	Sylow
60	C₃	—	13	1	no	Sylow
61	C₂	—	7	2	no	—
62	C₂	C₅×D₇×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₇×C₁₃⋊C₃
commutator, hypocenter	C₇×C₁₃	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₁₃	C₂×C₃
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₇×C₁₃⋊C₃	C₂	direct (N × H)
2. C₂×C₅×C₇×C₁₃⋊C₃	C₂	semidirect
3. C₂×C₅×C₁₃×D₇	C₃	semidirect
4. C₅×C₇×C₁₃⋊C₃	C₂²	semidirect
5. C₂×D₇×C₁₃⋊C₃	C₅	direct (N × H)
6. C₂×C₅×C₇×C₁₃	C₂×C₃	semidirect
7. C₅×C₁₃×D₇	C₂×C₃	semidirect
9. C₂×C₇×C₁₃⋊C₃	C₂×C₅	semidirect
10. D₇×C₁₃⋊C₃	C₂×C₅	direct (N × H)
11. C₅×C₇×C₁₃	C₂²×C₃	semidirect
14. C₂×C₅×C₁₃⋊C₃	D₇	direct (N × H)
15. C₂×C₁₃×D₇	C₃×C₅	semidirect
16. C₇×C₁₃⋊C₃	C₂²×C₅	semidirect
20. C₅×C₁₃⋊C₃	C₂×D₇	direct (N × H)
21. C₂×C₇×C₁₃	C₂×C₃×C₅	semidirect
22. C₁₃×D₇	C₂×C₃×C₅	semidirect
24. C₂×C₅×D₇	C₁₃⋊C₃	direct (N × H)
26. C₂×C₅×C₁₃	C₃×D₇	semidirect
28. C₇×C₁₃	C₂²×C₃×C₅	semidirect
31. C₂×C₁₃⋊C₃	C₅×D₇	direct (N × H)
32. C₂×C₅×C₇	C₂×C₁₃⋊C₃	semidirect
33. C₅×D₇	C₂×C₁₃⋊C₃	direct (N × H)
34. C₅×C₁₃	C₂×C₃×D₇	semidirect
39. C₁₃⋊C₃	C₂×C₅×D₇	direct (N × H)
40. C₅×C₇	C₂²×C₁₃⋊C₃	semidirect
43. C₂×D₇	C₅×C₁₃⋊C₃	direct (N × H)
45. C₂×C₁₃	C₃×C₅×D₇	semidirect
49. C₂×C₇	C₂×C₅×C₁₃⋊C₃	semidirect
50. D₇	C₂×C₅×C₁₃⋊C₃	direct (N × H)
51. C₁₃	C₂×C₃×C₅×D₇	semidirect
54. C₂×C₅	D₇×C₁₃⋊C₃	direct (N × H)
55. C₇	C₂²×C₅×C₁₃⋊C₃	semidirect
58. C₅	C₂×D₇×C₁₃⋊C₃	direct (N × H)
62. C₂	C₅×D₇×C₁₃⋊C₃	direct (N × H)

Subgroups — C2×C5×D7×C13⋊C3 #19129795

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅×D₇×C₁₃⋊C₃ #19129795