Subgroups — C₃×C₅×D₅×C₁₁×C₁₇ #43242532

Order 28050.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₁₁×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₅×C₁₁×C₁₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₅×C₁₁×C₁₇	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₃×C₅×C₁₁×C₁₇	—	5	1	no	maximal
5	C₅²×C₁₁×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅×C₁₁×C₁₇	—	2	2	no	—
7	C₃×C₅×C₁₁×C₁₇	D₅	1	1	yes	characteristic, direct product factor
8	C₃×C₅×C₁₁×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented
9	C₃×C₅×D₅×C₁₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₅×C₁₁×C₁₇	—	5	1	no	—
11	D₅×C₁₁×C₁₇	C₃×C₅	1	1	yes	characteristic, direct product factor
12	C₃×C₅×D₅×C₁₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₅²×C₁₇	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₁₁×C₁₇	—	5	1	no	Hall
15	C₅×C₁₁×C₁₇	—	2	2	no	—
16	C₅×C₁₁×C₁₇	C₃×D₅	1	1	yes	characteristic, direct product factor
17	C₅×C₁₁×C₁₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented
18	C₅×D₅×C₁₇	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₅²×C₁₁	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
20	C₃×C₁₁×C₁₇	C₅×D₅	1	1	yes	characteristic, direct product factor, Hall
21	C₅×D₅×C₁₁	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₃×C₅×C₁₇	—	5	1	no	—
23	C₃×D₅×C₁₇	C₅×C₁₁	1	1	yes	characteristic, direct product factor
24	C₅²×C₁₇	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
25	C₂×C₁₁×C₁₇	—	5	1	no	Hall
26	C₂×C₃×C₅×C₁₁	—	5	1	no	—
27	C₃×D₅×C₁₁	C₅×C₁₇	1	1	yes	characteristic, direct product factor
28	C₅²×C₁₁	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
29	C₃×C₅×C₁₇	—	2	2	no	—
30	C₃×C₅×C₁₇	D₅×C₁₁	1	1	yes	characteristic, direct product factor
31	C₃×C₅×C₁₇	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented
32	C₁₁×C₁₇	C₃×C₅×D₅	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₅×C₁₇	—	5	1	no	—
34	D₅×C₁₇	C₃×C₅×C₁₁	1	1	yes	characteristic, direct product factor
35	C₃×C₅×C₁₁	—	2	2	no	—
36	C₃×C₅×C₁₁	D₅×C₁₇	1	1	yes	characteristic, direct product factor
37	C₃×C₅×C₁₁	C₂×C₅×C₁₇	1	1	yes	characteristic, complemented
38	C₃×C₅×D₅	C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Hall
39	C₂×C₅×C₁₁	—	5	1	no	—
40	D₅×C₁₁	C₃×C₅×C₁₇	1	1	yes	characteristic, direct product factor
41	C₂×C₃×C₁₇	—	5	1	no	Hall
42	C₅×C₁₇	—	2	2	no	—
43	C₅×C₁₇	C₃×D₅×C₁₁	1	1	yes	characteristic, direct product factor
44	C₅×C₁₇	C₂×C₃×C₅×C₁₁	1	1	yes	characteristic, complemented
45	C₃×C₅²	C₂×C₁₁×C₁₇	1	1	yes	characteristic, complemented, Hall
46	C₂×C₃×C₁₁	—	5	1	no	Hall
47	C₅×C₁₁	—	2	2	no	—
48	C₅×C₁₁	C₃×D₅×C₁₇	1	1	yes	characteristic, direct product factor
49	C₅×C₁₁	C₂×C₃×C₅×C₁₇	1	1	yes	characteristic, complemented
50	C₃×C₁₇	C₅×D₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
51	C₅×D₅	C₃×C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Hall
52	C₂×C₁₇	—	5	1	no	Hall
53	C₃×C₁₁	C₅×D₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
54	C₂×C₃×C₅	—	5	1	no	—
55	C₃×D₅	C₅×C₁₁×C₁₇	1	1	yes	characteristic, direct product factor
56	C₅²	C₂×C₃×C₁₁×C₁₇	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₁₁	—	5	1	no	Hall
58	C₁₇	C₃×C₅×D₅×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
59	C₃×C₅	—	2	2	no	—
60	C₃×C₅	D₅×C₁₁×C₁₇	1	1	yes	characteristic, direct product factor
61	C₃×C₅	C₂×C₅×C₁₁×C₁₇	1	1	yes	characteristic, complemented
62	C₁₁	C₃×C₅×D₅×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
63	C₂×C₅	—	5	1	no	—
64	D₅	C₃×C₅×C₁₁×C₁₇	1	1	yes	characteristic, direct product factor
65	C₂×C₃	—	5	1	no	Hall
66	C₅	—	2	2	no	—
67	C₅	C₂×C₃×C₅×C₁₁×C₁₇	1	1	yes	characteristic, complemented
68	C₅	C₃×D₅×C₁₁×C₁₇	1	1	yes	characteristic, direct product factor
69	C₃	C₅×D₅×C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
70	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₁×C₁₇	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₃×C₅×C₁₁×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₁×C₁₇	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₃×C₅×C₁₁×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₁₁×C₁₇	C₂	semidirect
2. C₅×D₅×C₁₁×C₁₇	C₃	direct (N × H)
3. C₃×D₅×C₁₁×C₁₇	C₅	direct (N × H)
5. C₅²×C₁₁×C₁₇	C₂×C₃	semidirect
7. C₃×C₅×C₁₁×C₁₇	D₅	direct (N × H)
8. C₃×C₅×C₁₁×C₁₇	C₂×C₅	semidirect
9. C₃×C₅×D₅×C₁₇	C₁₁	direct (N × H)
11. D₅×C₁₁×C₁₇	C₃×C₅	direct (N × H)
12. C₃×C₅×D₅×C₁₁	C₁₇	direct (N × H)
13. C₃×C₅²×C₁₇	C₂×C₁₁	semidirect
16. C₅×C₁₁×C₁₇	C₃×D₅	direct (N × H)
17. C₅×C₁₁×C₁₇	C₂×C₃×C₅	semidirect
18. C₅×D₅×C₁₇	C₃×C₁₁	direct (N × H)
19. C₃×C₅²×C₁₁	C₂×C₁₇	semidirect
20. C₃×C₁₁×C₁₇	C₅×D₅	direct (N × H)
21. C₅×D₅×C₁₁	C₃×C₁₇	direct (N × H)
23. C₃×D₅×C₁₇	C₅×C₁₁	direct (N × H)
24. C₅²×C₁₇	C₂×C₃×C₁₁	semidirect
27. C₃×D₅×C₁₁	C₅×C₁₇	direct (N × H)
28. C₅²×C₁₁	C₂×C₃×C₁₇	semidirect
30. C₃×C₅×C₁₇	D₅×C₁₁	direct (N × H)
31. C₃×C₅×C₁₇	C₂×C₅×C₁₁	semidirect
32. C₁₁×C₁₇	C₃×C₅×D₅	direct (N × H)
34. D₅×C₁₇	C₃×C₅×C₁₁	direct (N × H)
36. C₃×C₅×C₁₁	D₅×C₁₇	direct (N × H)
37. C₃×C₅×C₁₁	C₂×C₅×C₁₇	semidirect
38. C₃×C₅×D₅	C₁₁×C₁₇	direct (N × H)
40. D₅×C₁₁	C₃×C₅×C₁₇	direct (N × H)
43. C₅×C₁₇	C₃×D₅×C₁₁	direct (N × H)
44. C₅×C₁₇	C₂×C₃×C₅×C₁₁	semidirect
45. C₃×C₅²	C₂×C₁₁×C₁₇	semidirect
48. C₅×C₁₁	C₃×D₅×C₁₇	direct (N × H)
49. C₅×C₁₁	C₂×C₃×C₅×C₁₇	semidirect
50. C₃×C₁₇	C₅×D₅×C₁₁	direct (N × H)
51. C₅×D₅	C₃×C₁₁×C₁₇	direct (N × H)
53. C₃×C₁₁	C₅×D₅×C₁₇	direct (N × H)
55. C₃×D₅	C₅×C₁₁×C₁₇	direct (N × H)
56. C₅²	C₂×C₃×C₁₁×C₁₇	semidirect
58. C₁₇	C₃×C₅×D₅×C₁₁	direct (N × H)
60. C₃×C₅	D₅×C₁₁×C₁₇	direct (N × H)
61. C₃×C₅	C₂×C₅×C₁₁×C₁₇	semidirect
62. C₁₁	C₃×C₅×D₅×C₁₇	direct (N × H)
64. D₅	C₃×C₅×C₁₁×C₁₇	direct (N × H)
67. C₅	C₂×C₃×C₅×C₁₁×C₁₇	semidirect
68. C₅	C₃×D₅×C₁₁×C₁₇	direct (N × H)
69. C₃	C₅×D₅×C₁₁×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
C₃×C₅²×C₁₁×C₁₇	2
C₅×D₅×C₁₁×C₁₇	3
C₃×D₅×C₁₁×C₁₇	5
C₂×C₃×C₅×C₁₁×C₁₇	5
C₃×C₅×D₅×C₁₇	11
C₃×C₅×D₅×C₁₁	17

Subgroups — C3×C5×D5×C11×C17 #43242532

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×D₅×C₁₁×C₁₇ #43242532