Subgroups — C₂×C₅²×C₉×D₁₇ #29505828

Order 15300.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₉×D₁₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅²×C₉×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅²×D₁₇	C₃	1	1	yes	maximal, characteristic
4	C₅²×C₉×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅×C₉×D₁₇	C₅	1	6	yes	maximal, direct product factor
6	C₃×C₅²×D₁₇	C₂×C₃	1	2	yes	—
7	C₂×C₃×C₅²×C₁₇	C₂×C₃	1	1	yes	characteristic
8	C₂×C₅²×D₁₇	C₉	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₅×C₉×C₁₇	C₂×C₅	1	6	yes	complemented
10	C₅×C₉×D₁₇	C₂×C₅	1	12	yes	direct product factor
11	C₃×C₅²×C₁₇	C₂²×C₃	1	1	yes	characteristic
12	C₂×C₃×C₅×D₁₇	C₃×C₅	1	6	yes	—
13	C₂²×C₅²×C₉	—	17	1	no	maximal, Hall
14	C₂×C₅²×C₁₇	C₂×C₉	1	1	yes	characteristic, complemented
15	C₅²×D₁₇	C₂×C₉	1	2	yes	direct product factor
16	C₅×C₉×C₁₇	C₂²×C₅	1	6	yes	complemented
17	C₂×C₉×D₁₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₃×C₅×C₁₇	C₂×C₃×C₅	1	6	yes	—
19	C₃×C₅×D₁₇	C₂×C₃×C₅	1	12	yes	—
20	C₂×C₅²×C₉	—	17	2	no	—
21	C₂×C₅²×C₉	D₁₇	1	1	yes	characteristic, direct product factor
22	C₅²×C₁₇	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
23	C₂×C₅×D₁₇	C₅×C₉	1	6	yes	direct product factor
24	C₂×C₉×C₁₇	C₂×C₅²	1	1	yes	characteristic, complemented
25	C₉×D₁₇	C₂×C₅²	1	2	yes	direct product factor
26	C₂²×C₃×C₅²	—	17	1	no	—
27	C₃×C₅×C₁₇	C₂²×C₃×C₅	1	6	yes	—
28	C₅²×C₉	C₂×D₁₇	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₃×D₁₇	C₃×C₅²	1	1	yes	characteristic
30	C₂²×C₅×C₉	—	17	6	no	—
31	C₂×C₅×C₁₇	C₂×C₅×C₉	1	6	yes	complemented
32	C₅×D₁₇	C₂×C₅×C₉	1	12	yes	direct product factor
33	C₉×C₁₇	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃×C₅²	—	17	2	no	—
35	C₂×C₃×C₅²	C₃×D₁₇	1	1	yes	characteristic
36	C₂×C₃×C₁₇	C₂×C₃×C₅²	1	1	yes	characteristic
37	C₃×D₁₇	C₂×C₃×C₅²	1	2	yes	—
38	C₂²×C₅²	—	17	1	no	Hall
39	C₂×C₅×C₉	—	17	12	no	—
40	C₂×C₅×C₉	C₅×D₁₇	1	6	yes	direct product factor
41	C₅×C₁₇	C₂²×C₅×C₉	1	6	yes	complemented
42	C₃×C₅²	C₂×C₃×D₁₇	1	1	yes	characteristic
43	C₂×D₁₇	C₅²×C₉	1	1	yes	characteristic, direct product factor, Hall
44	C₂²×C₃×C₅	—	17	6	no	—
45	C₃×C₁₇	C₂²×C₃×C₅²	1	1	yes	characteristic
46	C₂×C₅²	—	17	2	no	—
47	C₂×C₅²	C₉×D₁₇	1	1	yes	characteristic, direct product factor
48	C₅×C₉	C₂×C₅×D₁₇	1	6	yes	direct product factor
49	C₂²×C₉	—	17	1	no	Hall
50	C₂×C₁₇	C₂×C₅²×C₉	1	1	yes	characteristic, complemented
51	D₁₇	C₂×C₅²×C₉	1	2	yes	direct product factor
52	C₂×C₃×C₅	—	17	12	no	—
53	C₂×C₃×C₅	C₃×C₅×D₁₇	1	6	yes	—
54	C₅²	C₂×C₉×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
55	C₂²×C₅	—	17	6	no	—
56	C₂×C₉	—	17	2	no	—
57	C₂×C₉	C₅²×D₁₇	1	1	yes	characteristic, direct product factor
58	C₁₇	C₂²×C₅²×C₉	1	1	yes	characteristic, complemented, Sylow
59	C₃×C₅	C₂×C₃×C₅×D₁₇	1	6	yes	—
60	C₂²×C₃	—	17	1	no	—
61	C₂×C₅	—	17	12	no	—
62	C₂×C₅	C₅×C₉×D₁₇	1	6	yes	direct product factor
63	C₉	C₂×C₅²×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
64	C₂×C₃	—	17	2	no	—
65	C₂×C₃	C₃×C₅²×D₁₇	1	1	yes	characteristic
66	C₅	C₂×C₅×C₉×D₁₇	1	6	yes	direct product factor
67	C₂²	—	17	1	no	Sylow
68	C₃	C₂×C₃×C₅²×D₁₇	1	1	yes	characteristic
69	C₂	—	17	2	no	—
70	C₂	C₅²×C₉×D₁₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅²×C₉	D₁₇
commutator, hypocenter	C₁₇	C₂²×C₅²×C₉
Frattini	C₃	C₂×C₃×C₅²×D₁₇
Fitting	C₂×C₅²×C₉×C₁₇	C₂
socle	C₂×C₃×C₅²×C₁₇	C₂×C₃
prime radical	C₂×C₃×C₅²×D₁₇	C₃
cosocle	C₃×C₁₇	C₂²×C₃×C₅²
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂×C₅²×C₉

Complements

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

N	H ≅ G/N	type
1. C₅²×C₉×D₁₇	C₂	direct (N × H)
2. C₂×C₅²×C₉×C₁₇	C₂	semidirect
4. C₅²×C₉×C₁₇	C₂²	semidirect
5. C₂×C₅×C₉×D₁₇	C₅	direct (N × H)
8. C₂×C₅²×D₁₇	C₉	direct (N × H)
9. C₂×C₅×C₉×C₁₇	C₂×C₅	semidirect
10. C₅×C₉×D₁₇	C₂×C₅	direct (N × H)
14. C₂×C₅²×C₁₇	C₂×C₉	semidirect
15. C₅²×D₁₇	C₂×C₉	direct (N × H)
16. C₅×C₉×C₁₇	C₂²×C₅	semidirect
17. C₂×C₉×D₁₇	C₅²	direct (N × H)
21. C₂×C₅²×C₉	D₁₇	direct (N × H)
22. C₅²×C₁₇	C₂²×C₉	semidirect
23. C₂×C₅×D₁₇	C₅×C₉	direct (N × H)
24. C₂×C₉×C₁₇	C₂×C₅²	semidirect
25. C₉×D₁₇	C₂×C₅²	direct (N × H)
28. C₅²×C₉	C₂×D₁₇	direct (N × H)
31. C₂×C₅×C₁₇	C₂×C₅×C₉	semidirect
32. C₅×D₁₇	C₂×C₅×C₉	direct (N × H)
33. C₉×C₁₇	C₂²×C₅²	semidirect
40. C₂×C₅×C₉	C₅×D₁₇	direct (N × H)
41. C₅×C₁₇	C₂²×C₅×C₉	semidirect
43. C₂×D₁₇	C₅²×C₉	direct (N × H)
47. C₂×C₅²	C₉×D₁₇	direct (N × H)
48. C₅×C₉	C₂×C₅×D₁₇	direct (N × H)
50. C₂×C₁₇	C₂×C₅²×C₉	semidirect
51. D₁₇	C₂×C₅²×C₉	direct (N × H)
54. C₅²	C₂×C₉×D₁₇	direct (N × H)
57. C₂×C₉	C₅²×D₁₇	direct (N × H)
58. C₁₇	C₂²×C₅²×C₉	semidirect
62. C₂×C₅	C₅×C₉×D₁₇	direct (N × H)
63. C₉	C₂×C₅²×D₁₇	direct (N × H)
66. C₅	C₂×C₅×C₉×D₁₇	direct (N × H)
70. C₂	C₅²×C₉×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
C₅²×C₉×D₁₇	2
C₂×C₅²×C₉×C₁₇	2
C₂×C₃×C₅²×D₁₇	3
C₂×C₅×C₉×D₁₇	5
C₂²×C₅²×C₉	17

Subgroups — C2×C52×C9×D17 #29505828

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅²×C₉×D₁₇ #29505828