Subgroups — C₂×C₃×C₅×C₁₁×D₁₇ #26014444

Order 11220.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁×D₁₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₁₁×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₁₁×D₁₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₁×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₁×D₁₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₁₁×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅×C₁₁×D₁₇	C₂×C₃	1	2	yes	direct product factor
8	C₂×C₃×C₁₁×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented
9	C₃×C₁₁×D₁₇	C₂×C₅	1	2	yes	direct product factor
10	C₂×C₃×C₅×D₁₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅×C₁₁×C₁₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₁₁×D₁₇	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×C₁₁	—	17	1	no	maximal, Hall
14	C₃×C₁₁×C₁₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₅×C₁₇	C₂×C₁₁	1	1	yes	characteristic, complemented
16	C₃×C₅×D₁₇	C₂×C₁₁	1	2	yes	direct product factor
17	C₂×C₁₁×C₁₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented
18	C₁₁×D₁₇	C₂×C₃×C₅	1	2	yes	direct product factor
19	C₂×C₅×D₁₇	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₃×C₅×C₁₁	—	17	2	no	—
21	C₂×C₃×C₅×C₁₁	D₁₇	1	1	yes	characteristic, direct product factor
22	C₃×C₅×C₁₇	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
23	C₂²×C₅×C₁₁	—	17	1	no	Hall
24	C₂×C₃×D₁₇	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
25	C₁₁×C₁₇	C₂²×C₃×C₅	1	1	yes	characteristic, complemented, Hall
26	C₂×C₅×C₁₇	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
27	C₅×D₁₇	C₂×C₃×C₁₁	1	2	yes	direct product factor
28	C₃×C₅×C₁₁	C₂×D₁₇	1	1	yes	characteristic, direct product factor, Hall
29	C₂²×C₃×C₁₁	—	17	1	no	Hall
30	C₂×C₅×C₁₁	—	17	2	no	—
31	C₂×C₅×C₁₁	C₃×D₁₇	1	1	yes	characteristic, direct product factor
32	C₂×C₃×C₁₇	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented
33	C₃×D₁₇	C₂×C₅×C₁₁	1	2	yes	direct product factor
34	C₅×C₁₇	C₂²×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
35	C₂×D₁₇	C₃×C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
36	C₂×C₃×C₁₁	—	17	2	no	—
37	C₂×C₃×C₁₁	C₅×D₁₇	1	1	yes	characteristic, direct product factor
38	C₂²×C₃×C₅	—	17	1	no	Hall
39	C₅×C₁₁	C₂×C₃×D₁₇	1	1	yes	characteristic, direct product factor, Hall
40	C₃×C₁₇	C₂²×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
41	C₂²×C₁₁	—	17	1	no	Hall
42	C₂×C₁₇	C₂×C₃×C₅×C₁₁	1	1	yes	characteristic, complemented
43	D₁₇	C₂×C₃×C₅×C₁₁	1	2	yes	direct product factor
44	C₃×C₁₁	C₂×C₅×D₁₇	1	1	yes	characteristic, direct product factor, Hall
45	C₂×C₃×C₅	—	17	2	no	—
46	C₂×C₃×C₅	C₁₁×D₁₇	1	1	yes	characteristic, direct product factor
47	C₂×C₁₁	—	17	2	no	—
48	C₂×C₁₁	C₃×C₅×D₁₇	1	1	yes	characteristic, direct product factor
49	C₂²×C₅	—	17	1	no	Hall
50	C₁₇	C₂²×C₃×C₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
51	C₃×C₅	C₂×C₁₁×D₁₇	1	1	yes	characteristic, direct product factor, Hall
52	C₂²×C₃	—	17	1	no	Hall
53	C₁₁	C₂×C₃×C₅×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
54	C₂×C₅	—	17	2	no	—
55	C₂×C₅	C₃×C₁₁×D₁₇	1	1	yes	characteristic, direct product factor
56	C₂×C₃	—	17	2	no	—
57	C₂×C₃	C₅×C₁₁×D₁₇	1	1	yes	characteristic, direct product factor
58	C₅	C₂×C₃×C₁₁×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²	—	17	1	no	Sylow
60	C₃	C₂×C₅×C₁₁×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	17	2	no	—
62	C₂	C₃×C₅×C₁₁×D₁₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅×C₁₁	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂²×C₃×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₁×C₁₇	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂×C₃×C₅×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₁×D₁₇	C₂	direct (N × H)
2. C₂×C₃×C₅×C₁₁×C₁₇	C₂	semidirect
3. C₂×C₅×C₁₁×D₁₇	C₃	direct (N × H)
4. C₃×C₅×C₁₁×C₁₇	C₂²	semidirect
5. C₂×C₃×C₁₁×D₁₇	C₅	direct (N × H)
6. C₂×C₅×C₁₁×C₁₇	C₂×C₃	semidirect
7. C₅×C₁₁×D₁₇	C₂×C₃	direct (N × H)
8. C₂×C₃×C₁₁×C₁₇	C₂×C₅	semidirect
9. C₃×C₁₁×D₁₇	C₂×C₅	direct (N × H)
10. C₂×C₃×C₅×D₁₇	C₁₁	direct (N × H)
11. C₅×C₁₁×C₁₇	C₂²×C₃	semidirect
12. C₂×C₁₁×D₁₇	C₃×C₅	direct (N × H)
14. C₃×C₁₁×C₁₇	C₂²×C₅	semidirect
15. C₂×C₃×C₅×C₁₇	C₂×C₁₁	semidirect
16. C₃×C₅×D₁₇	C₂×C₁₁	direct (N × H)
17. C₂×C₁₁×C₁₇	C₂×C₃×C₅	semidirect
18. C₁₁×D₁₇	C₂×C₃×C₅	direct (N × H)
19. C₂×C₅×D₁₇	C₃×C₁₁	direct (N × H)
21. C₂×C₃×C₅×C₁₁	D₁₇	direct (N × H)
22. C₃×C₅×C₁₇	C₂²×C₁₁	semidirect
24. C₂×C₃×D₁₇	C₅×C₁₁	direct (N × H)
25. C₁₁×C₁₇	C₂²×C₃×C₅	semidirect
26. C₂×C₅×C₁₇	C₂×C₃×C₁₁	semidirect
27. C₅×D₁₇	C₂×C₃×C₁₁	direct (N × H)
28. C₃×C₅×C₁₁	C₂×D₁₇	direct (N × H)
31. C₂×C₅×C₁₁	C₃×D₁₇	direct (N × H)
32. C₂×C₃×C₁₇	C₂×C₅×C₁₁	semidirect
33. C₃×D₁₇	C₂×C₅×C₁₁	direct (N × H)
34. C₅×C₁₇	C₂²×C₃×C₁₁	semidirect
35. C₂×D₁₇	C₃×C₅×C₁₁	direct (N × H)
37. C₂×C₃×C₁₁	C₅×D₁₇	direct (N × H)
39. C₅×C₁₁	C₂×C₃×D₁₇	direct (N × H)
40. C₃×C₁₇	C₂²×C₅×C₁₁	semidirect
42. C₂×C₁₇	C₂×C₃×C₅×C₁₁	semidirect
43. D₁₇	C₂×C₃×C₅×C₁₁	direct (N × H)
44. C₃×C₁₁	C₂×C₅×D₁₇	direct (N × H)
46. C₂×C₃×C₅	C₁₁×D₁₇	direct (N × H)
48. C₂×C₁₁	C₃×C₅×D₁₇	direct (N × H)
50. C₁₇	C₂²×C₃×C₅×C₁₁	semidirect
51. C₃×C₅	C₂×C₁₁×D₁₇	direct (N × H)
53. C₁₁	C₂×C₃×C₅×D₁₇	direct (N × H)
55. C₂×C₅	C₃×C₁₁×D₁₇	direct (N × H)
57. C₂×C₃	C₅×C₁₁×D₁₇	direct (N × H)
58. C₅	C₂×C₃×C₁₁×D₁₇	direct (N × H)
60. C₃	C₂×C₅×C₁₁×D₁₇	direct (N × H)
62. C₂	C₃×C₅×C₁₁×D₁₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₁₁×D₁₇	2
C₂×C₃×C₅×C₁₁×C₁₇	2
C₂×C₅×C₁₁×D₁₇	3
C₂×C₃×C₁₁×D₁₇	5
C₂×C₃×C₅×D₁₇	11
C₂²×C₃×C₅×C₁₁	17

Subgroups — C2×C3×C5×C11×D17 #26014444

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×C₁₁×D₁₇ #26014444