Subgroups — C₂×C₃×D₄₂₉ #19104247

Order 5148.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₄₂₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄₂₉	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₃×D₁₄₃	—	3	1	no	maximal
5	C₃²×C₁₁×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₁₁×C₁₃	—	2	1	no	—
7	C₂×C₃×C₁₁×C₁₃	D₃	1	1	yes	characteristic, complemented
8	C₂×C₃×C₁₁×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
9	D₄₂₉	C₂×C₃	1	2	yes	direct product factor
10	C₃×D₁₄₃	—	3	2	no	—
11	C₂×D₁₄₃	—	3	1	no	Hall
12	C₂×C₃×D₃₉	—	11	1	no	maximal, Hall
13	C₃×C₁₁×C₁₃	—	2	1	no	—
14	C₃×C₁₁×C₁₃	C₂×D₃	1	1	yes	characteristic, complemented
15	C₃×C₁₁×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₂×C₃×D₃₃	—	13	1	no	maximal, Hall
17	C₂×C₁₁×C₁₃	C₃×D₃	1	1	yes	characteristic, complemented
18	D₁₄₃	—	3	2	no	—
19	C₂×C₃²×C₁₃	D₁₁	1	1	yes	characteristic, complemented
20	C₃×D₃₉	—	11	2	no	—
21	C₂×C₃²×C₁₁	D₁₃	1	1	yes	characteristic, complemented
22	C₃×D₃₃	—	13	2	no	—
23	C₂×D₃₉	—	11	1	no	—
24	C₂×C₃×D₁₃	—	33	1	no	—
25	C₁₁×C₁₃	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
26	C₂×D₃₃	—	13	1	no	—
27	C₂×C₃×D₁₁	—	39	1	no	—
28	C₃²×C₁₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
29	C₃²×C₁₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₁₃	—	2	1	no	—
31	C₂×C₃×C₁₃	C₃×D₁₁	1	1	yes	characteristic, complemented
32	C₂×C₃×C₁₃	D₃₃	1	1	yes	characteristic, complemented
33	D₃₉	—	11	2	no	—
34	C₃×D₁₃	—	33	2	no	—
35	C₂×C₃×C₁₁	—	2	1	no	—
36	C₂×C₃×C₁₁	C₃×D₁₃	1	1	yes	characteristic, complemented
37	C₂×C₃×C₁₁	D₃₉	1	1	yes	characteristic, complemented
38	D₃₃	—	13	2	no	—
39	C₃×D₁₁	—	39	2	no	—
40	C₂×D₁₃	—	33	1	no	Hall
41	C₂×D₁₁	—	39	1	no	Hall
42	C₃×C₁₃	—	2	1	no	—
43	C₃×C₁₃	C₂×C₃×D₁₁	1	1	yes	characteristic, complemented
44	C₃×C₁₃	C₂×D₃₃	1	1	yes	characteristic, complemented
45	C₂×C₃×D₃	—	143	1	no	Hall
46	C₃×C₁₁	—	2	1	no	—
47	C₃×C₁₁	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented
48	C₃×C₁₁	C₂×D₃₉	1	1	yes	characteristic, complemented
49	C₂×C₁₃	C₃×D₃₃	1	1	yes	characteristic, complemented
50	D₁₃	—	33	2	no	—
51	C₂×C₁₁	C₃×D₃₉	1	1	yes	characteristic, complemented
52	D₁₁	—	39	2	no	—
53	C₂×C₃²	D₁₄₃	1	1	yes	characteristic, complemented
54	C₃×D₃	—	143	2	no	—
55	C₁₃	C₂×C₃×D₃₃	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₃	—	429	1	no	—
57	C₂×D₃	—	143	1	no	—
58	C₁₁	C₂×C₃×D₃₉	1	1	yes	characteristic, complemented, Sylow
59	C₃²	C₂×D₁₄₃	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₃	—	2	1	no	—
61	C₂×C₃	—	429	2	no	—
62	C₂×C₃	C₃×D₁₄₃	1	1	yes	characteristic, complemented
63	C₂×C₃	D₄₂₉	1	1	yes	characteristic, direct product factor
64	D₃	—	143	2	no	—
65	C₂²	—	429	1	no	Sylow
66	C₃	—	2	1	no	—
67	C₃	C₂×C₃×D₁₄₃	1	1	yes	characteristic, complemented
68	C₃	C₂×D₄₂₉	1	1	yes	characteristic, direct product factor
69	C₂	—	429	2	no	—
70	C₂	C₃×D₄₂₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₄₂₉
commutator, hypocenter	C₃×C₁₁×C₁₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₁×C₁₃	C₂
LCS	G ▷ C₃×C₁₁×C₁₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₄₂₉	C₂	direct (N × H)
2. C₂×C₃²×C₁₁×C₁₃	C₂	semidirect
3. C₂×D₄₂₉	C₃	direct (N × H)
5. C₃²×C₁₁×C₁₃	C₂²	semidirect
7. C₂×C₃×C₁₁×C₁₃	D₃	semidirect
8. C₂×C₃×C₁₁×C₁₃	C₂×C₃	semidirect
9. D₄₂₉	C₂×C₃	direct (N × H)
14. C₃×C₁₁×C₁₃	C₂×D₃	semidirect
15. C₃×C₁₁×C₁₃	C₂²×C₃	semidirect
17. C₂×C₁₁×C₁₃	C₃×D₃	semidirect
19. C₂×C₃²×C₁₃	D₁₁	semidirect
21. C₂×C₃²×C₁₁	D₁₃	semidirect
25. C₁₁×C₁₃	C₂×C₃×D₃	semidirect
28. C₃²×C₁₃	C₂×D₁₁	semidirect
29. C₃²×C₁₁	C₂×D₁₃	semidirect
31. C₂×C₃×C₁₃	C₃×D₁₁	semidirect
32. C₂×C₃×C₁₃	D₃₃	semidirect
36. C₂×C₃×C₁₁	C₃×D₁₃	semidirect
37. C₂×C₃×C₁₁	D₃₉	semidirect
43. C₃×C₁₃	C₂×C₃×D₁₁	semidirect
44. C₃×C₁₃	C₂×D₃₃	semidirect
47. C₃×C₁₁	C₂×C₃×D₁₃	semidirect
48. C₃×C₁₁	C₂×D₃₉	semidirect
49. C₂×C₁₃	C₃×D₃₃	semidirect
51. C₂×C₁₁	C₃×D₃₉	semidirect
53. C₂×C₃²	D₁₄₃	semidirect
55. C₁₃	C₂×C₃×D₃₃	semidirect
58. C₁₁	C₂×C₃×D₃₉	semidirect
59. C₃²	C₂×D₁₄₃	semidirect
62. C₂×C₃	C₃×D₁₄₃	semidirect
63. C₂×C₃	D₄₂₉	direct (N × H)
67. C₃	C₂×C₃×D₁₄₃	semidirect
68. C₃	C₂×D₄₂₉	direct (N × H)
70. C₂	C₃×D₄₂₉	direct (N × H)

Subgroups — C2×C3×D429 #19104247

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×D₄₂₉ #19104247