Subgroups — C₂×D₃×C₁₉×C₁₂₁ #42119939

Order 27588.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₁₉×C₁₂₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₉×C₁₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₉×C₁₂₁	—	3	1	no	maximal, Hall
4	C₃×C₁₉×C₁₂₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₉×C₁₂₁	—	3	2	no	—
6	C₂×C₁₉×C₁₂₁	D₃	1	1	yes	characteristic, direct product factor
7	C₂×D₃×C₁₁×C₁₉	C₁₁	1	1	yes	maximal, characteristic
8	C₁₉×C₁₂₁	C₂×D₃	1	1	yes	characteristic, direct product factor, Hall
9	C₂×D₃×C₁₂₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₁₁×C₁₉	C₂×C₁₁	1	1	yes	characteristic
11	D₃×C₁₁×C₁₉	C₂×C₁₁	1	2	yes	—
12	C₂²×C₁₁×C₁₉	—	3	1	no	—
13	C₂×C₃×C₁₂₁	C₂×C₁₉	1	1	yes	characteristic, complemented
14	D₃×C₁₂₁	C₂×C₁₉	1	2	yes	direct product factor
15	C₃×C₁₁×C₁₉	C₂²×C₁₁	1	1	yes	characteristic
16	C₂²×C₁₂₁	—	3	1	no	Hall
17	C₂×C₁₁×C₁₉	—	3	2	no	—
18	C₂×C₁₁×C₁₉	D₃×C₁₁	1	1	yes	characteristic
19	C₃×C₁₂₁	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
20	C₂×C₁₂₁	—	3	2	no	—
21	C₂×C₁₂₁	D₃×C₁₉	1	1	yes	characteristic, direct product factor
22	C₂×D₃×C₁₉	C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
23	C₁₁×C₁₉	C₂×D₃×C₁₁	1	1	yes	characteristic
24	C₂×D₃×C₁₁	C₁₁×C₁₉	1	1	yes	characteristic
25	C₁₂₁	C₂×D₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₃×C₁₉	C₂×C₁₂₁	1	1	yes	characteristic, complemented
27	D₃×C₁₉	C₂×C₁₂₁	1	2	yes	direct product factor
28	C₂²×C₁₉	—	3	1	no	Hall
29	C₂×C₃×C₁₁	C₂×C₁₁×C₁₉	1	1	yes	characteristic
30	D₃×C₁₁	C₂×C₁₁×C₁₉	1	2	yes	—
31	C₃×C₁₉	C₂²×C₁₂₁	1	1	yes	characteristic, complemented, Hall
32	C₂²×C₁₁	—	3	1	no	—
33	C₂×C₁₉	—	3	2	no	—
34	C₂×C₁₉	D₃×C₁₂₁	1	1	yes	characteristic, direct product factor
35	C₃×C₁₁	C₂²×C₁₁×C₁₉	1	1	yes	characteristic
36	C₂×C₁₁	—	3	2	no	—
37	C₂×C₁₁	D₃×C₁₁×C₁₉	1	1	yes	characteristic
38	C₁₉	C₂×D₃×C₁₂₁	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×D₃	C₁₉×C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
40	C₁₁	C₂×D₃×C₁₁×C₁₉	1	1	yes	characteristic
41	C₂×C₃	C₂×C₁₉×C₁₂₁	1	1	yes	characteristic, complemented
42	D₃	C₂×C₁₉×C₁₂₁	1	2	yes	direct product factor
43	C₂²	—	3	1	no	Sylow
44	C₃	C₂²×C₁₉×C₁₂₁	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	3	2	no	—
46	C₂	D₃×C₁₉×C₁₂₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₁₂₁	D₃
commutator, hypocenter	C₃	C₂²×C₁₉×C₁₂₁
Frattini	C₁₁	C₂×D₃×C₁₁×C₁₉
Fitting	C₂×C₃×C₁₉×C₁₂₁	C₂
socle	C₂×C₃×C₁₁×C₁₉	C₂×C₁₁
prime radical	C₂×D₃×C₁₁×C₁₉	C₁₁
cosocle	C₃×C₁₁	C₂²×C₁₁×C₁₉
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₁₉×C₁₂₁

Complements

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

N	H ≅ G/N	type
1. D₃×C₁₉×C₁₂₁	C₂	direct (N × H)
2. C₂×C₃×C₁₉×C₁₂₁	C₂	semidirect
4. C₃×C₁₉×C₁₂₁	C₂²	semidirect
6. C₂×C₁₉×C₁₂₁	D₃	direct (N × H)
8. C₁₉×C₁₂₁	C₂×D₃	direct (N × H)
9. C₂×D₃×C₁₂₁	C₁₉	direct (N × H)
13. C₂×C₃×C₁₂₁	C₂×C₁₉	semidirect
14. D₃×C₁₂₁	C₂×C₁₉	direct (N × H)
19. C₃×C₁₂₁	C₂²×C₁₉	semidirect
21. C₂×C₁₂₁	D₃×C₁₉	direct (N × H)
22. C₂×D₃×C₁₉	C₁₂₁	direct (N × H)
25. C₁₂₁	C₂×D₃×C₁₉	direct (N × H)
26. C₂×C₃×C₁₉	C₂×C₁₂₁	semidirect
27. D₃×C₁₉	C₂×C₁₂₁	direct (N × H)
31. C₃×C₁₉	C₂²×C₁₂₁	semidirect
34. C₂×C₁₉	D₃×C₁₂₁	direct (N × H)
38. C₁₉	C₂×D₃×C₁₂₁	direct (N × H)
39. C₂×D₃	C₁₉×C₁₂₁	direct (N × H)
41. C₂×C₃	C₂×C₁₉×C₁₂₁	semidirect
42. D₃	C₂×C₁₉×C₁₂₁	direct (N × H)
44. C₃	C₂²×C₁₉×C₁₂₁	semidirect
46. C₂	D₃×C₁₉×C₁₂₁	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₃×C₁₉×C₁₂₁	2
C₂×C₃×C₁₉×C₁₂₁	2
C₂²×C₁₉×C₁₂₁	3
C₂×D₃×C₁₁×C₁₉	11
C₂×D₃×C₁₂₁	19

Subgroups — C2×D3×C19×C121 #42119939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×C₁₉×C₁₂₁ #42119939