Subgroups — C₂×C₅×C₁₇×D₈₇ #44443906

Order 29580.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₇×D₈₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₁₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₁₇×D₂₉	—	3	1	no	maximal, Hall
4	C₃×C₅×C₁₇×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₇×D₈₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₁₇×D₂₉	—	3	2	no	—
7	C₂×C₅×C₁₇×C₂₉	D₃	1	1	yes	characteristic, complemented
8	C₁₇×D₈₇	C₂×C₅	1	2	yes	direct product factor
9	C₂×C₃×C₁₇×C₂₉	C₂×C₅	1	1	yes	characteristic, complemented
10	C₅×C₁₇×C₂₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₇×D₂₉	—	3	1	no	Hall
12	C₂×C₅×D₈₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₁₇×C₂₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅×D₃×C₁₇	—	29	1	no	maximal, Hall
15	C₂×C₁₇×C₂₉	C₅×D₃	1	1	yes	characteristic, complemented
16	C₁₇×D₂₉	—	3	2	no	—
17	C₂×C₃×C₅×C₂₉	C₂×C₁₇	1	1	yes	characteristic, complemented
18	C₅×D₈₇	C₂×C₁₇	1	2	yes	direct product factor
19	C₂×C₅×D₂₉	—	3	1	no	Hall
20	C₂×C₃×C₅×C₁₇	D₂₉	1	1	yes	characteristic, complemented
21	C₅×D₃×C₁₇	—	29	2	no	—
22	C₁₇×C₂₉	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₂₉	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
24	C₂×D₈₇	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
25	C₂²×C₅×C₁₇	—	87	1	no	Hall
26	C₂×C₅×C₂₉	D₃×C₁₇	1	1	yes	characteristic, complemented
27	C₅×D₂₉	—	3	2	no	—
28	C₃×C₅×C₁₇	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
29	C₂×D₃×C₁₇	—	29	1	no	Hall
30	C₂×C₃×C₂₉	C₂×C₅×C₁₇	1	1	yes	characteristic, complemented
31	D₈₇	C₂×C₅×C₁₇	1	2	yes	direct product factor
32	C₂×C₅×C₁₇	—	87	2	no	—
33	C₂×C₅×C₁₇	D₈₇	1	1	yes	characteristic, direct product factor
34	C₅×C₂₉	C₂×D₃×C₁₇	1	1	yes	characteristic, complemented, Hall
35	C₂×D₂₉	—	3	1	no	Hall
36	C₂×C₃×C₁₇	C₅×D₂₉	1	1	yes	characteristic, complemented
37	D₃×C₁₇	—	29	2	no	—
38	C₃×C₂₉	C₂²×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
39	C₅×C₁₇	C₂×D₈₇	1	1	yes	characteristic, direct product factor, Hall
40	C₂²×C₁₇	—	87	1	no	Hall
41	C₂×C₅×D₃	—	29	1	no	Hall
42	C₂×C₂₉	C₅×D₃×C₁₇	1	1	yes	characteristic, complemented
43	D₂₉	—	3	2	no	—
44	C₃×C₁₇	C₂×C₅×D₂₉	1	1	yes	characteristic, complemented, Hall
45	C₂×C₁₇	—	87	2	no	—
46	C₂×C₁₇	C₅×D₈₇	1	1	yes	characteristic, direct product factor
47	C₂×C₃×C₅	C₁₇×D₂₉	1	1	yes	characteristic, complemented
48	C₅×D₃	—	29	2	no	—
49	C₂₉	C₂×C₅×D₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
50	C₂²×C₅	—	87	1	no	Hall
51	C₁₇	C₂×C₅×D₈₇	1	1	yes	characteristic, direct product factor, Sylow
52	C₃×C₅	C₂×C₁₇×D₂₉	1	1	yes	characteristic, complemented, Hall
53	C₂×D₃	—	29	1	no	Hall
54	C₂×C₅	—	87	2	no	—
55	C₂×C₅	C₁₇×D₈₇	1	1	yes	characteristic, direct product factor
56	C₂×C₃	C₅×C₁₇×D₂₉	1	1	yes	characteristic, complemented
57	D₃	—	29	2	no	—
58	C₅	C₂×C₁₇×D₈₇	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²	—	87	1	no	Sylow
60	C₃	C₂×C₅×C₁₇×D₂₉	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	87	2	no	—
62	C₂	C₅×C₁₇×D₈₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₇	D₈₇
commutator, cosocle, hypocenter	C₃×C₂₉	C₂²×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₇×C₂₉	C₂
LCS	G ▷ C₃×C₂₉
UCS	C₁ ◁ C₂×C₅×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₇×D₈₇	C₂	direct (N × H)
2. C₂×C₃×C₅×C₁₇×C₂₉	C₂	semidirect
4. C₃×C₅×C₁₇×C₂₉	C₂²	semidirect
5. C₂×C₁₇×D₈₇	C₅	direct (N × H)
7. C₂×C₅×C₁₇×C₂₉	D₃	semidirect
8. C₁₇×D₈₇	C₂×C₅	direct (N × H)
9. C₂×C₃×C₁₇×C₂₉	C₂×C₅	semidirect
10. C₅×C₁₇×C₂₉	C₂×D₃	semidirect
12. C₂×C₅×D₈₇	C₁₇	direct (N × H)
13. C₃×C₁₇×C₂₉	C₂²×C₅	semidirect
15. C₂×C₁₇×C₂₉	C₅×D₃	semidirect
17. C₂×C₃×C₅×C₂₉	C₂×C₁₇	semidirect
18. C₅×D₈₇	C₂×C₁₇	direct (N × H)
20. C₂×C₃×C₅×C₁₇	D₂₉	semidirect
22. C₁₇×C₂₉	C₂×C₅×D₃	semidirect
23. C₃×C₅×C₂₉	C₂²×C₁₇	semidirect
24. C₂×D₈₇	C₅×C₁₇	direct (N × H)
26. C₂×C₅×C₂₉	D₃×C₁₇	semidirect
28. C₃×C₅×C₁₇	C₂×D₂₉	semidirect
30. C₂×C₃×C₂₉	C₂×C₅×C₁₇	semidirect
31. D₈₇	C₂×C₅×C₁₇	direct (N × H)
33. C₂×C₅×C₁₇	D₈₇	direct (N × H)
34. C₅×C₂₉	C₂×D₃×C₁₇	semidirect
36. C₂×C₃×C₁₇	C₅×D₂₉	semidirect
38. C₃×C₂₉	C₂²×C₅×C₁₇	semidirect
39. C₅×C₁₇	C₂×D₈₇	direct (N × H)
42. C₂×C₂₉	C₅×D₃×C₁₇	semidirect
44. C₃×C₁₇	C₂×C₅×D₂₉	semidirect
46. C₂×C₁₇	C₅×D₈₇	direct (N × H)
47. C₂×C₃×C₅	C₁₇×D₂₉	semidirect
49. C₂₉	C₂×C₅×D₃×C₁₇	semidirect
51. C₁₇	C₂×C₅×D₈₇	direct (N × H)
52. C₃×C₅	C₂×C₁₇×D₂₉	semidirect
55. C₂×C₅	C₁₇×D₈₇	direct (N × H)
56. C₂×C₃	C₅×C₁₇×D₂₉	semidirect
58. C₅	C₂×C₁₇×D₈₇	direct (N × H)
60. C₃	C₂×C₅×C₁₇×D₂₉	semidirect
62. C₂	C₅×C₁₇×D₈₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₁₇×D₈₇	2
C₂×C₃×C₅×C₁₇×C₂₉	2
C₂×C₅×C₁₇×D₂₉	3
C₂×C₁₇×D₈₇	5
C₂×C₅×D₈₇	17
C₂×C₅×D₃×C₁₇	29

Subgroups — C2×C5×C17×D87 #44443906

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₁₇×D₈₇ #44443906