Subgroups — C₂×C₃²×C₅×D₁₁ #14520484

Order 1980.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×C₅×D₁₁	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₅×D₁₁	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₅×C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃²×D₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₃×C₅×C₁₁	C₂×C₃	1	4	yes	complemented
7	C₃×C₅×D₁₁	C₂×C₃	1	8	yes	direct product factor
8	C₂×C₅×D₁₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃²×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
10	C₃²×D₁₁	C₂×C₅	1	2	yes	direct product factor
11	C₂²×C₃²×C₅	—	11	1	no	maximal, Hall
12	C₃×C₅×C₁₁	C₂²×C₃	1	4	yes	complemented
13	C₂×C₃×D₁₁	C₃×C₅	1	4	yes	direct product factor
14	C₂×C₅×C₁₁	C₂×C₃²	1	1	yes	characteristic, complemented
15	C₅×D₁₁	C₂×C₃²	1	2	yes	direct product factor
16	C₃²×C₁₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃²×C₅	—	11	2	no	—
18	C₂×C₃²×C₅	D₁₁	1	1	yes	characteristic, direct product factor
19	C₂×C₃×C₁₁	C₂×C₃×C₅	1	4	yes	complemented
20	C₃×D₁₁	C₂×C₃×C₅	1	8	yes	direct product factor
21	C₂²×C₃×C₅	—	11	4	no	—
22	C₅×C₁₁	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
23	C₃²×C₅	C₂×D₁₁	1	1	yes	characteristic, direct product factor, Hall
24	C₂×D₁₁	C₃²×C₅	1	1	yes	characteristic, direct product factor, Hall
25	C₂²×C₃²	—	11	1	no	Hall
26	C₃×C₁₁	C₂²×C₃×C₅	1	4	yes	complemented
27	C₂×C₃×C₅	—	11	8	no	—
28	C₂×C₃×C₅	C₃×D₁₁	1	4	yes	direct product factor
29	C₂×C₁₁	C₂×C₃²×C₅	1	1	yes	characteristic, complemented
30	D₁₁	C₂×C₃²×C₅	1	2	yes	direct product factor
31	C₂²×C₅	—	11	1	no	Hall
32	C₂×C₃²	—	11	2	no	—
33	C₂×C₃²	C₅×D₁₁	1	1	yes	characteristic, direct product factor
34	C₃×C₅	C₂×C₃×D₁₁	1	4	yes	direct product factor
35	C₂²×C₃	—	11	4	no	—
36	C₁₁	C₂²×C₃²×C₅	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₅	—	11	2	no	—
38	C₂×C₅	C₃²×D₁₁	1	1	yes	characteristic, direct product factor
39	C₃²	C₂×C₅×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₃	—	11	8	no	—
41	C₂×C₃	C₃×C₅×D₁₁	1	4	yes	direct product factor
42	C₅	C₂×C₃²×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
43	C₂²	—	11	1	no	Sylow
44	C₃	C₂×C₃×C₅×D₁₁	1	4	yes	direct product factor
45	C₂	—	11	2	no	—
46	C₂	C₃²×C₅×D₁₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₅	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂²×C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₁₁	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₃²×C₅

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×C₅×C₁₁	C₂	semidirect
2. C₃²×C₅×D₁₁	C₂	direct (N × H)
3. C₂×C₃×C₅×D₁₁	C₃	direct (N × H)
4. C₃²×C₅×C₁₁	C₂²	semidirect
5. C₂×C₃²×D₁₁	C₅	direct (N × H)
6. C₂×C₃×C₅×C₁₁	C₂×C₃	semidirect
7. C₃×C₅×D₁₁	C₂×C₃	direct (N × H)
8. C₂×C₅×D₁₁	C₃²	direct (N × H)
9. C₂×C₃²×C₁₁	C₂×C₅	semidirect
10. C₃²×D₁₁	C₂×C₅	direct (N × H)
12. C₃×C₅×C₁₁	C₂²×C₃	semidirect
13. C₂×C₃×D₁₁	C₃×C₅	direct (N × H)
14. C₂×C₅×C₁₁	C₂×C₃²	semidirect
15. C₅×D₁₁	C₂×C₃²	direct (N × H)
16. C₃²×C₁₁	C₂²×C₅	semidirect
18. C₂×C₃²×C₅	D₁₁	direct (N × H)
19. C₂×C₃×C₁₁	C₂×C₃×C₅	semidirect
20. C₃×D₁₁	C₂×C₃×C₅	direct (N × H)
22. C₅×C₁₁	C₂²×C₃²	semidirect
23. C₃²×C₅	C₂×D₁₁	direct (N × H)
24. C₂×D₁₁	C₃²×C₅	direct (N × H)
26. C₃×C₁₁	C₂²×C₃×C₅	semidirect
28. C₂×C₃×C₅	C₃×D₁₁	direct (N × H)
29. C₂×C₁₁	C₂×C₃²×C₅	semidirect
30. D₁₁	C₂×C₃²×C₅	direct (N × H)
33. C₂×C₃²	C₅×D₁₁	direct (N × H)
34. C₃×C₅	C₂×C₃×D₁₁	direct (N × H)
36. C₁₁	C₂²×C₃²×C₅	semidirect
38. C₂×C₅	C₃²×D₁₁	direct (N × H)
39. C₃²	C₂×C₅×D₁₁	direct (N × H)
41. C₂×C₃	C₃×C₅×D₁₁	direct (N × H)
42. C₅	C₂×C₃²×D₁₁	direct (N × H)
44. C₃	C₂×C₃×C₅×D₁₁	direct (N × H)
46. C₂	C₃²×C₅×D₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₅×C₁₁	2
C₃²×C₅×D₁₁	2
C₂×C₃×C₅×D₁₁	3
C₂×C₃²×D₁₁	5
C₂²×C₃²×C₅	11

Subgroups — C2×C32×C5×D11 #14520484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₅×D₁₁ #14520484