Subgroups — C₂×C₅×C₇×D₅×C₁₇ #26045466

Order 11900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×D₅×C₁₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅²×C₇×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₇×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×D₅×C₁₇	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₂²×C₅×C₇×C₁₇	—	5	1	no	maximal
6	C₂×C₅×D₅×C₁₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₅×C₇×C₁₇	—	2	2	no	—
8	C₂×C₅×C₇×C₁₇	—	5	2	no	—
9	C₂×C₅×C₇×C₁₇	D₅	1	1	yes	characteristic, direct product factor
10	C₂×C₅×C₇×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented
11	C₇×D₅×C₁₇	C₂×C₅	1	2	yes	direct product factor
12	C₂×C₅²×C₁₇	C₂×C₇	1	1	yes	characteristic, complemented
13	C₅×D₅×C₁₇	C₂×C₇	1	2	yes	direct product factor
14	C₂×C₅×C₇×D₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₅×C₇×C₁₇	—	2	2	no	—
16	C₅×C₇×C₁₇	C₂×D₅	1	1	yes	characteristic, direct product factor
17	C₅×C₇×C₁₇	C₂²×C₅	1	1	yes	characteristic, complemented
18	C₂²×C₇×C₁₇	—	5	1	no	Hall
19	C₅²×C₁₇	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅²×C₇	C₂×C₁₇	1	1	yes	characteristic, complemented
21	C₅×C₇×D₅	C₂×C₁₇	1	2	yes	direct product factor
22	C₂²×C₅×C₁₇	—	5	1	no	—
23	C₂×D₅×C₁₇	C₅×C₇	1	1	yes	characteristic, direct product factor
24	C₂×C₇×C₁₇	—	5	2	no	—
25	C₂×C₇×C₁₇	C₅×D₅	1	1	yes	characteristic, direct product factor
26	C₅²×C₇	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
27	C₂×C₅×C₁₇	—	2	2	no	—
28	C₂×C₅×C₁₇	—	5	2	no	—
29	C₂×C₅×C₁₇	C₇×D₅	1	1	yes	characteristic, direct product factor
30	C₂×C₅×C₁₇	C₂×C₅×C₇	1	1	yes	characteristic, complemented
31	D₅×C₁₇	C₂×C₅×C₇	1	2	yes	direct product factor
32	C₂²×C₅×C₇	—	5	1	no	—
33	C₂×C₇×D₅	C₅×C₁₇	1	1	yes	characteristic, direct product factor
34	C₇×C₁₇	C₂×C₅×D₅	1	1	yes	characteristic, direct product factor, Hall
35	C₂×C₅×D₅	C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
36	C₅×C₁₇	—	2	2	no	—
37	C₅×C₁₇	C₂×C₇×D₅	1	1	yes	characteristic, direct product factor
38	C₅×C₁₇	C₂²×C₅×C₇	1	1	yes	characteristic, complemented
39	C₂×C₅×C₇	—	2	2	no	—
40	C₂×C₅×C₇	—	5	2	no	—
41	C₂×C₅×C₇	D₅×C₁₇	1	1	yes	characteristic, direct product factor
42	C₂×C₅×C₇	C₂×C₅×C₁₇	1	1	yes	characteristic, complemented
43	C₇×D₅	C₂×C₅×C₁₇	1	2	yes	direct product factor
44	C₂²×C₁₇	—	5	1	no	Hall
45	C₂×C₅²	C₂×C₇×C₁₇	1	1	yes	characteristic, complemented
46	C₅×D₅	C₂×C₇×C₁₇	1	2	yes	direct product factor
47	C₅×C₇	—	2	2	no	—
48	C₅×C₇	C₂×D₅×C₁₇	1	1	yes	characteristic, direct product factor
49	C₅×C₇	C₂²×C₅×C₁₇	1	1	yes	characteristic, complemented
50	C₂×C₁₇	—	5	2	no	—
51	C₂×C₁₇	C₅×C₇×D₅	1	1	yes	characteristic, direct product factor
52	C₂²×C₇	—	5	1	no	Hall
53	C₅²	C₂²×C₇×C₁₇	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₅	—	5	1	no	—
55	C₂×D₅	C₅×C₇×C₁₇	1	1	yes	characteristic, direct product factor
56	C₁₇	C₂×C₅×C₇×D₅	1	1	yes	characteristic, direct product factor, Sylow
57	C₂×C₇	—	5	2	no	—
58	C₂×C₇	C₅×D₅×C₁₇	1	1	yes	characteristic, direct product factor
59	C₂×C₅	—	2	2	no	—
60	C₂×C₅	—	5	2	no	—
61	C₂×C₅	C₇×D₅×C₁₇	1	1	yes	characteristic, direct product factor
62	C₂×C₅	C₂×C₅×C₇×C₁₇	1	1	yes	characteristic, complemented
63	D₅	C₂×C₅×C₇×C₁₇	1	2	yes	direct product factor
64	C₇	C₂×C₅×D₅×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
65	C₅	—	2	2	no	—
66	C₅	C₂²×C₅×C₇×C₁₇	1	1	yes	characteristic, complemented
67	C₅	C₂×C₇×D₅×C₁₇	1	1	yes	characteristic, direct product factor
68	C₂²	—	5	1	no	Sylow
69	C₂	—	5	2	no	—
70	C₂	C₅×C₇×D₅×C₁₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₇×C₁₇	D₅
commutator, cosocle, hypocenter	C₅	C₂²×C₅×C₇×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₇×C₁₇	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₅×C₇×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×D₅×C₁₇	C₂	direct (N × H)
2. C₂×C₅²×C₇×C₁₇	C₂	semidirect
3. C₅²×C₇×C₁₇	C₂²	semidirect
4. C₂×C₇×D₅×C₁₇	C₅	direct (N × H)
6. C₂×C₅×D₅×C₁₇	C₇	direct (N × H)
9. C₂×C₅×C₇×C₁₇	D₅	direct (N × H)
10. C₂×C₅×C₇×C₁₇	C₂×C₅	semidirect
11. C₇×D₅×C₁₇	C₂×C₅	direct (N × H)
12. C₂×C₅²×C₁₇	C₂×C₇	semidirect
13. C₅×D₅×C₁₇	C₂×C₇	direct (N × H)
14. C₂×C₅×C₇×D₅	C₁₇	direct (N × H)
16. C₅×C₇×C₁₇	C₂×D₅	direct (N × H)
17. C₅×C₇×C₁₇	C₂²×C₅	semidirect
19. C₅²×C₁₇	C₂²×C₇	semidirect
20. C₂×C₅²×C₇	C₂×C₁₇	semidirect
21. C₅×C₇×D₅	C₂×C₁₇	direct (N × H)
23. C₂×D₅×C₁₇	C₅×C₇	direct (N × H)
25. C₂×C₇×C₁₇	C₅×D₅	direct (N × H)
26. C₅²×C₇	C₂²×C₁₇	semidirect
29. C₂×C₅×C₁₇	C₇×D₅	direct (N × H)
30. C₂×C₅×C₁₇	C₂×C₅×C₇	semidirect
31. D₅×C₁₇	C₂×C₅×C₇	direct (N × H)
33. C₂×C₇×D₅	C₅×C₁₇	direct (N × H)
34. C₇×C₁₇	C₂×C₅×D₅	direct (N × H)
35. C₂×C₅×D₅	C₇×C₁₇	direct (N × H)
37. C₅×C₁₇	C₂×C₇×D₅	direct (N × H)
38. C₅×C₁₇	C₂²×C₅×C₇	semidirect
41. C₂×C₅×C₇	D₅×C₁₇	direct (N × H)
42. C₂×C₅×C₇	C₂×C₅×C₁₇	semidirect
43. C₇×D₅	C₂×C₅×C₁₇	direct (N × H)
45. C₂×C₅²	C₂×C₇×C₁₇	semidirect
46. C₅×D₅	C₂×C₇×C₁₇	direct (N × H)
48. C₅×C₇	C₂×D₅×C₁₇	direct (N × H)
49. C₅×C₇	C₂²×C₅×C₁₇	semidirect
51. C₂×C₁₇	C₅×C₇×D₅	direct (N × H)
53. C₅²	C₂²×C₇×C₁₇	semidirect
55. C₂×D₅	C₅×C₇×C₁₇	direct (N × H)
56. C₁₇	C₂×C₅×C₇×D₅	direct (N × H)
58. C₂×C₇	C₅×D₅×C₁₇	direct (N × H)
61. C₂×C₅	C₇×D₅×C₁₇	direct (N × H)
62. C₂×C₅	C₂×C₅×C₇×C₁₇	semidirect
63. D₅	C₂×C₅×C₇×C₁₇	direct (N × H)
64. C₇	C₂×C₅×D₅×C₁₇	direct (N × H)
66. C₅	C₂²×C₅×C₇×C₁₇	semidirect
67. C₅	C₂×C₇×D₅×C₁₇	direct (N × H)
70. C₂	C₅×C₇×D₅×C₁₇	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×C₇×D₅×C₁₇	2
C₂×C₅²×C₇×C₁₇	2
C₂×C₇×D₅×C₁₇	5
C₂²×C₅×C₇×C₁₇	5
C₂×C₅×D₅×C₁₇	7
C₂×C₅×C₇×D₅	17

Subgroups — C2×C5×C7×D5×C17 #26045466

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₇×D₅×C₁₇ #26045466