Subgroups — C₂×C₁₇×C₃⋊(C₅⋊D₅) #19099844

Order 5100.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₃⋊(C₅⋊D₅)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×C₅⋊D₅	—	3	1	no	maximal, Hall
4	C₃×C₅²×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₇×D₁₅	—	5	6	no	maximal
6	C₂×C₅²×C₁₇	D₃	1	1	yes	characteristic, complemented
7	C₁₇×C₅⋊D₅	—	3	2	no	—
8	C₂×C₃×C₅×C₁₇	D₅	1	6	yes	complemented
9	C₁₇×D₁₅	—	5	12	no	—
10	C₅²×C₁₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂×D₅×C₁₇	—	15	6	no	—
12	C₂×C₃⋊(C₅⋊D₅)	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₅×C₁₇	C₂×D₅	1	6	yes	complemented
14	C₂×D₃×C₁₇	—	25	1	no	Hall
15	C₂×C₅×C₁₇	D₁₅	1	6	yes	complemented
16	D₅×C₁₇	—	15	12	no	—
17	C₂×C₃×C₅²	C₂×C₁₇	1	1	yes	characteristic, complemented
18	C₃⋊(C₅⋊D₅)	C₂×C₁₇	1	2	yes	direct product factor
19	C₂×C₃×C₁₇	C₅⋊D₅	1	1	yes	characteristic, complemented
20	D₃×C₁₇	—	25	2	no	—
21	C₂×C₅⋊D₅	—	3	1	no	Hall
22	C₅×C₁₇	C₂×D₁₅	1	6	yes	complemented
23	C₃×C₅²	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
24	C₂²×C₁₇	—	75	1	no	Hall
25	C₂×D₁₅	—	5	6	no	—
26	C₃×C₁₇	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
27	C₂×C₅²	D₃×C₁₇	1	1	yes	characteristic, complemented
28	C₅⋊D₅	—	3	2	no	—
29	C₂×C₁₇	—	75	2	no	—
30	C₂×C₁₇	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic, direct product factor
31	C₂×C₃×C₅	D₅×C₁₇	1	6	yes	complemented
32	D₁₅	—	5	12	no	—
33	C₅²	C₂×D₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
34	C₂×D₅	—	15	6	no	—
35	C₁₇	C₂×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic, direct product factor, Sylow
36	C₃×C₅	C₂×D₅×C₁₇	1	6	yes	complemented
37	C₂×D₃	—	25	1	no	Hall
38	C₂×C₅	C₁₇×D₁₅	1	6	yes	complemented
39	D₅	—	15	12	no	—
40	C₂×C₃	C₁₇×C₅⋊D₅	1	1	yes	characteristic, complemented
41	D₃	—	25	2	no	—
42	C₅	C₂×C₁₇×D₁₅	1	6	yes	complemented
43	C₂²	—	75	1	no	Sylow
44	C₃	C₂×C₁₇×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	75	2	no	—
46	C₂	C₁₇×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₇	C₃⋊(C₅⋊D₅)
commutator, hypocenter	C₃×C₅²	C₂²×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₁₇	C₂
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₂×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₃⋊(C₅⋊D₅)	C₂	direct (N × H)
2. C₂×C₃×C₅²×C₁₇	C₂	semidirect
4. C₃×C₅²×C₁₇	C₂²	semidirect
6. C₂×C₅²×C₁₇	D₃	semidirect
8. C₂×C₃×C₅×C₁₇	D₅	semidirect
10. C₅²×C₁₇	C₂×D₃	semidirect
12. C₂×C₃⋊(C₅⋊D₅)	C₁₇	direct (N × H)
13. C₃×C₅×C₁₇	C₂×D₅	semidirect
15. C₂×C₅×C₁₇	D₁₅	semidirect
17. C₂×C₃×C₅²	C₂×C₁₇	semidirect
18. C₃⋊(C₅⋊D₅)	C₂×C₁₇	direct (N × H)
19. C₂×C₃×C₁₇	C₅⋊D₅	semidirect
22. C₅×C₁₇	C₂×D₁₅	semidirect
23. C₃×C₅²	C₂²×C₁₇	semidirect
26. C₃×C₁₇	C₂×C₅⋊D₅	semidirect
27. C₂×C₅²	D₃×C₁₇	semidirect
30. C₂×C₁₇	C₃⋊(C₅⋊D₅)	direct (N × H)
31. C₂×C₃×C₅	D₅×C₁₇	semidirect
33. C₅²	C₂×D₃×C₁₇	semidirect
35. C₁₇	C₂×C₃⋊(C₅⋊D₅)	direct (N × H)
36. C₃×C₅	C₂×D₅×C₁₇	semidirect
38. C₂×C₅	C₁₇×D₁₅	semidirect
40. C₂×C₃	C₁₇×C₅⋊D₅	semidirect
42. C₅	C₂×C₁₇×D₁₅	semidirect
44. C₃	C₂×C₁₇×C₅⋊D₅	semidirect
46. C₂	C₁₇×C₃⋊(C₅⋊D₅)	direct (N × H)

Subgroups — C2×C17×C3⋊(C5⋊D5) #19099844

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₁₇×C₃⋊(C₅⋊D₅) #19099844