Subgroups — C₃×C₇×D₅×C₁₃⋊C₃ #22551237

Order 8190.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₅×C₁₃⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₇×D₅×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₇×C₁₃⋊C₃	—	5	1	no	maximal, Hall
5	C₃×C₅×C₇×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
6	C₅×C₇×C₁₃⋊C₃	C₂×C₃	1	3	yes	complemented
7	C₃×D₅×C₁₃⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×D₅×C₁₃	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇×C₁₃⋊C₃	D₅	1	1	yes	characteristic, direct product factor, Hall
10	C₃²×C₇×D₅	—	13	1	no	maximal, Hall
11	C₃×C₅×C₁₃⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₇×C₁₃	—	5	1	no	—
13	C₂×C₇×C₁₃⋊C₃	—	5	3	no	—
14	C₅×C₇×C₁₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
15	C₃×D₅×C₁₃	C₃×C₇	1	1	yes	characteristic, complemented
16	D₅×C₁₃⋊C₃	C₃×C₇	1	3	yes	direct product factor
17	C₃²×C₅×C₇	—	13	1	no	Hall
18	C₃×C₇×C₁₃	C₃×D₅	1	1	yes	characteristic, complemented
19	C₇×C₁₃⋊C₃	C₃×D₅	1	3	yes	direct product factor
20	C₂×C₃×C₁₃⋊C₃	—	5	1	no	Hall
21	C₃×C₇×D₅	—	13	3	no	—
22	C₃×C₇×D₅	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
23	C₃×C₅×C₁₃	C₂×C₃×C₇	1	1	yes	characteristic, complemented
24	C₅×C₁₃⋊C₃	C₂×C₃×C₇	1	3	yes	complemented
25	C₂×C₇×C₁₃	—	5	1	no	Hall
26	D₅×C₁₃	C₃²×C₇	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃²×C₇	—	65	1	no	Hall
28	C₃×C₁₃⋊C₃	C₇×D₅	1	1	yes	characteristic, direct product factor, Hall
29	C₃×C₅×C₇	—	13	3	no	—
30	C₃×C₅×C₇	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
31	C₇×C₁₃	C₃²×D₅	1	1	yes	characteristic, complemented, Hall
32	C₃²×D₅	—	13	1	no	Hall
33	C₂×C₃×C₁₃	—	5	1	no	—
34	C₂×C₁₃⋊C₃	—	5	3	no	—
35	C₇×D₅	C₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
36	C₅×C₁₃	C₂×C₃²×C₇	1	1	yes	characteristic, complemented, Hall
37	C₃²×C₇	—	13	1	no	Hall
38	C₃²×C₅	—	13	1	no	Hall
39	C₂×C₃×C₇	—	5	1	no	—
40	C₂×C₃×C₇	—	65	3	no	—
41	C₃×C₁₃	C₃×C₇×D₅	1	1	yes	characteristic, complemented
42	C₁₃⋊C₃	C₃×C₇×D₅	1	3	yes	direct product factor
43	C₅×C₇	C₂×C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
44	C₃×D₅	—	13	3	no	—
45	C₃×D₅	C₇×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
46	C₂×C₁₃	—	5	1	no	Hall
47	C₃×C₇	—	13	3	no	—
48	C₃×C₇	D₅×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
49	C₂×C₃²	—	65	1	no	Hall
50	C₃×C₅	—	13	3	no	—
51	C₃×C₅	C₂×C₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented
52	C₂×C₇	—	5	1	no	Hall
53	C₁₃	C₃²×C₇×D₅	1	1	yes	characteristic, complemented, Sylow
54	D₅	C₃×C₇×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
55	C₃²	—	13	1	no	Sylow
56	C₇	C₃×D₅×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
57	C₂×C₃	—	5	1	no	—
58	C₂×C₃	—	65	3	no	—
59	C₅	C₂×C₃×C₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
60	C₃	—	13	3	no	—
61	C₃	C₇×D₅×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
62	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇	D₅×C₁₃⋊C₃
commutator, hypocenter	C₅×C₁₃	C₂×C₃²×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₃	C₂×C₃
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₇×C₁₃⋊C₃	C₂	semidirect
2. C₇×D₅×C₁₃⋊C₃	C₃	direct (N × H)
3. C₃×C₇×D₅×C₁₃	C₃	semidirect
5. C₃×C₅×C₇×C₁₃	C₂×C₃	semidirect
6. C₅×C₇×C₁₃⋊C₃	C₂×C₃	semidirect
7. C₃×D₅×C₁₃⋊C₃	C₇	direct (N × H)
8. C₇×D₅×C₁₃	C₃²	semidirect
9. C₃×C₇×C₁₃⋊C₃	D₅	direct (N × H)
11. C₃×C₅×C₁₃⋊C₃	C₂×C₇	semidirect
14. C₅×C₇×C₁₃	C₂×C₃²	semidirect
15. C₃×D₅×C₁₃	C₃×C₇	semidirect
16. D₅×C₁₃⋊C₃	C₃×C₇	direct (N × H)
18. C₃×C₇×C₁₃	C₃×D₅	semidirect
19. C₇×C₁₃⋊C₃	C₃×D₅	direct (N × H)
22. C₃×C₇×D₅	C₁₃⋊C₃	direct (N × H)
23. C₃×C₅×C₁₃	C₂×C₃×C₇	semidirect
24. C₅×C₁₃⋊C₃	C₂×C₃×C₇	semidirect
26. D₅×C₁₃	C₃²×C₇	semidirect
28. C₃×C₁₃⋊C₃	C₇×D₅	direct (N × H)
30. C₃×C₅×C₇	C₂×C₁₃⋊C₃	semidirect
31. C₇×C₁₃	C₃²×D₅	semidirect
35. C₇×D₅	C₃×C₁₃⋊C₃	direct (N × H)
36. C₅×C₁₃	C₂×C₃²×C₇	semidirect
41. C₃×C₁₃	C₃×C₇×D₅	semidirect
42. C₁₃⋊C₃	C₃×C₇×D₅	direct (N × H)
43. C₅×C₇	C₂×C₃×C₁₃⋊C₃	semidirect
45. C₃×D₅	C₇×C₁₃⋊C₃	direct (N × H)
48. C₃×C₇	D₅×C₁₃⋊C₃	direct (N × H)
51. C₃×C₅	C₂×C₇×C₁₃⋊C₃	semidirect
53. C₁₃	C₃²×C₇×D₅	semidirect
54. D₅	C₃×C₇×C₁₃⋊C₃	direct (N × H)
56. C₇	C₃×D₅×C₁₃⋊C₃	direct (N × H)
59. C₅	C₂×C₃×C₇×C₁₃⋊C₃	semidirect
61. C₃	C₇×D₅×C₁₃⋊C₃	direct (N × H)

Subgroups — C3×C7×D5×C13⋊C3 #22551237

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₇×D₅×C₁₃⋊C₃ #22551237