Subgroups — C₂×C₃²×C₁₉×D₅₃ #49136332

Order 36252.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₉×D₅₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₉×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₁₉×D₅₃	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₁₉×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₉×D₅₃	C₂×C₃	1	8	yes	direct product factor
6	C₂×C₃×C₁₉×C₅₃	C₂×C₃	1	4	yes	complemented
7	C₂×C₁₉×D₅₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₁₉×C₅₃	C₂²×C₃	1	4	yes	complemented
9	C₂×C₁₉×C₅₃	C₂×C₃²	1	1	yes	characteristic, complemented
10	C₁₉×D₅₃	C₂×C₃²	1	2	yes	direct product factor
11	C₂×C₃²×D₅₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₉×C₅₃	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃²×C₅₃	C₂×C₁₉	1	1	yes	characteristic, complemented
14	C₃²×D₅₃	C₂×C₁₉	1	2	yes	direct product factor
15	C₂²×C₃²×C₁₉	—	53	1	no	maximal, Hall
16	C₂×C₃×D₅₃	C₃×C₁₉	1	4	yes	direct product factor
17	C₃²×C₅₃	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃²×C₁₉	—	53	2	no	—
19	C₂×C₃²×C₁₉	D₅₃	1	1	yes	characteristic, direct product factor
20	C₂×C₃×C₅₃	C₂×C₃×C₁₉	1	4	yes	complemented
21	C₃×D₅₃	C₂×C₃×C₁₉	1	8	yes	direct product factor
22	C₂²×C₃×C₁₉	—	53	4	no	—
23	C₂×D₅₃	C₃²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
24	C₃²×C₁₉	C₂×D₅₃	1	1	yes	characteristic, direct product factor, Hall
25	C₃×C₅₃	C₂²×C₃×C₁₉	1	4	yes	complemented
26	C₂×C₃×C₁₉	—	53	8	no	—
27	C₂×C₃×C₁₉	C₃×D₅₃	1	4	yes	direct product factor
28	C₂×C₅₃	C₂×C₃²×C₁₉	1	1	yes	characteristic, complemented
29	D₅₃	C₂×C₃²×C₁₉	1	2	yes	direct product factor
30	C₂²×C₁₉	—	53	1	no	Hall
31	C₃×C₁₉	C₂×C₃×D₅₃	1	4	yes	direct product factor
32	C₅₃	C₂²×C₃²×C₁₉	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₁₉	—	53	2	no	—
34	C₂×C₁₉	C₃²×D₅₃	1	1	yes	characteristic, direct product factor
35	C₂²×C₃²	—	53	1	no	Hall
36	C₁₉	C₂×C₃²×D₅₃	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₃²	—	53	2	no	—
38	C₂×C₃²	C₁₉×D₅₃	1	1	yes	characteristic, direct product factor
39	C₂²×C₃	—	53	4	no	—
40	C₃²	C₂×C₁₉×D₅₃	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₃	—	53	8	no	—
42	C₂×C₃	C₃×C₁₉×D₅₃	1	4	yes	direct product factor
43	C₂²	—	53	1	no	Sylow
44	C₃	C₂×C₃×C₁₉×D₅₃	1	4	yes	direct product factor
45	C₂	—	53	2	no	—
46	C₂	C₃²×C₁₉×D₅₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₁₉	D₅₃
commutator, cosocle, hypocenter	C₅₃	C₂²×C₃²×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₉×C₅₃	C₂
LCS	G ▷ C₅₃
UCS	C₁ ◁ C₂×C₃²×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₉×D₅₃	C₂	direct (N × H)
2. C₂×C₃²×C₁₉×C₅₃	C₂	semidirect
3. C₂×C₃×C₁₉×D₅₃	C₃	direct (N × H)
4. C₃²×C₁₉×C₅₃	C₂²	semidirect
5. C₃×C₁₉×D₅₃	C₂×C₃	direct (N × H)
6. C₂×C₃×C₁₉×C₅₃	C₂×C₃	semidirect
7. C₂×C₁₉×D₅₃	C₃²	direct (N × H)
8. C₃×C₁₉×C₅₃	C₂²×C₃	semidirect
9. C₂×C₁₉×C₅₃	C₂×C₃²	semidirect
10. C₁₉×D₅₃	C₂×C₃²	direct (N × H)
11. C₂×C₃²×D₅₃	C₁₉	direct (N × H)
12. C₁₉×C₅₃	C₂²×C₃²	semidirect
13. C₂×C₃²×C₅₃	C₂×C₁₉	semidirect
14. C₃²×D₅₃	C₂×C₁₉	direct (N × H)
16. C₂×C₃×D₅₃	C₃×C₁₉	direct (N × H)
17. C₃²×C₅₃	C₂²×C₁₉	semidirect
19. C₂×C₃²×C₁₉	D₅₃	direct (N × H)
20. C₂×C₃×C₅₃	C₂×C₃×C₁₉	semidirect
21. C₃×D₅₃	C₂×C₃×C₁₉	direct (N × H)
23. C₂×D₅₃	C₃²×C₁₉	direct (N × H)
24. C₃²×C₁₉	C₂×D₅₃	direct (N × H)
25. C₃×C₅₃	C₂²×C₃×C₁₉	semidirect
27. C₂×C₃×C₁₉	C₃×D₅₃	direct (N × H)
28. C₂×C₅₃	C₂×C₃²×C₁₉	semidirect
29. D₅₃	C₂×C₃²×C₁₉	direct (N × H)
31. C₃×C₁₉	C₂×C₃×D₅₃	direct (N × H)
32. C₅₃	C₂²×C₃²×C₁₉	semidirect
34. C₂×C₁₉	C₃²×D₅₃	direct (N × H)
36. C₁₉	C₂×C₃²×D₅₃	direct (N × H)
38. C₂×C₃²	C₁₉×D₅₃	direct (N × H)
40. C₃²	C₂×C₁₉×D₅₃	direct (N × H)
42. C₂×C₃	C₃×C₁₉×D₅₃	direct (N × H)
44. C₃	C₂×C₃×C₁₉×D₅₃	direct (N × H)
46. C₂	C₃²×C₁₉×D₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₁₉×D₅₃	2
C₂×C₃²×C₁₉×C₅₃	2
C₂×C₃×C₁₉×D₅₃	3
C₂×C₃²×D₅₃	19
C₂²×C₃²×C₁₉	53

Subgroups — C2×C32×C19×D53 #49136332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₁₉×D₅₃ #49136332