Subgroups — C₂×C₃⋊D₄₂₉ #19104243

Order 5148.

120 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	—	3	4	no	maximal
4	C₃²×C₁₁×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₁×C₁₃	D₃	1	4	yes	complemented
6	D₄₂₉	—	3	8	no	—
7	C₂×D₁₄₃	—	9	1	no	Hall
8	C₂×C₃⋊D₃₉	—	11	1	no	maximal, Hall
9	C₃×C₁₁×C₁₃	C₂×D₃	1	4	yes	complemented
10	C₂×C₃⋊D₃₃	—	13	1	no	maximal, Hall
11	C₂×C₁₁×C₁₃	C₃⋊D₃	1	1	yes	characteristic, complemented
12	D₁₄₃	—	9	2	no	—
13	C₂×C₃²×C₁₃	D₁₁	1	1	yes	characteristic, complemented
14	C₃⋊D₃₉	—	11	2	no	—
15	C₂×C₃²×C₁₁	D₁₃	1	1	yes	characteristic, complemented
16	C₃⋊D₃₃	—	13	2	no	—
17	C₂×D₃₉	—	33	4	no	—
18	C₁₁×C₁₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
19	C₂×D₃₃	—	39	4	no	—
20	C₃²×C₁₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
21	C₃²×C₁₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₁₃	D₃₃	1	4	yes	complemented
23	D₃₉	—	33	8	no	—
24	C₂×C₃×C₁₁	D₃₉	1	4	yes	complemented
25	D₃₃	—	39	8	no	—
26	C₂×D₁₃	—	99	1	no	Hall
27	C₂×D₁₁	—	117	1	no	Hall
28	C₃×C₁₃	C₂×D₃₃	1	4	yes	complemented
29	C₂×C₃⋊D₃	—	143	1	no	Hall
30	C₃×C₁₁	C₂×D₃₉	1	4	yes	complemented
31	C₂×C₁₃	C₃⋊D₃₃	1	1	yes	characteristic, complemented
32	D₁₃	—	99	2	no	—
33	C₂×C₁₁	C₃⋊D₃₉	1	1	yes	characteristic, complemented
34	D₁₁	—	117	2	no	—
35	C₂×C₃²	D₁₄₃	1	1	yes	characteristic, complemented
36	C₃⋊D₃	—	143	2	no	—
37	C₁₃	C₂×C₃⋊D₃₃	1	1	yes	characteristic, complemented, Sylow
38	C₂×D₃	—	429	4	no	—
39	C₁₁	C₂×C₃⋊D₃₉	1	1	yes	characteristic, complemented, Sylow
40	C₃²	C₂×D₁₄₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	D₄₂₉	1	4	yes	complemented
42	D₃	—	429	8	no	—
43	C₂²	—	1287	1	no	Sylow
44	C₃	C₂×D₄₂₉	1	4	yes	complemented
45	C₂	—	1287	2	no	—
46	C₂	C₃⋊D₄₂₉	1	1	yes	characteristic, direct product factor

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

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
4. C₃²×C₁₁×C₁₃	C₂²	semidirect
5. C₂×C₃×C₁₁×C₁₃	D₃	semidirect
9. C₃×C₁₁×C₁₃	C₂×D₃	semidirect
11. C₂×C₁₁×C₁₃	C₃⋊D₃	semidirect
13. C₂×C₃²×C₁₃	D₁₁	semidirect
15. C₂×C₃²×C₁₁	D₁₃	semidirect
18. C₁₁×C₁₃	C₂×C₃⋊D₃	semidirect
20. C₃²×C₁₃	C₂×D₁₁	semidirect
21. C₃²×C₁₁	C₂×D₁₃	semidirect
22. C₂×C₃×C₁₃	D₃₃	semidirect
24. C₂×C₃×C₁₁	D₃₉	semidirect
28. C₃×C₁₃	C₂×D₃₃	semidirect
30. C₃×C₁₁	C₂×D₃₉	semidirect
31. C₂×C₁₃	C₃⋊D₃₃	semidirect
33. C₂×C₁₁	C₃⋊D₃₉	semidirect
35. C₂×C₃²	D₁₄₃	semidirect
37. C₁₃	C₂×C₃⋊D₃₃	semidirect
39. C₁₁	C₂×C₃⋊D₃₉	semidirect
40. C₃²	C₂×D₁₄₃	semidirect
41. C₂×C₃	D₄₂₉	semidirect
44. C₃	C₂×D₄₂₉	semidirect
46. C₂	C₃⋊D₄₂₉	direct (N × H)

Subgroups — C2×C3⋊D429 #19104243

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃⋊D₄₂₉ #19104243