Subgroups — C₂×C₃×C₁₇×C₅⋊D₅ #19099838

Order 5100.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇×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	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅²×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×D₅×C₁₇	—	5	6	no	maximal
6	C₂×C₅²×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₇×C₅⋊D₅	C₂×C₃	1	2	yes	direct product factor
8	C₂×C₃×C₅×C₁₇	D₅	1	6	yes	complemented
9	C₃×D₅×C₁₇	—	5	12	no	—
10	C₅²×C₁₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×D₅×C₁₇	—	5	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	C₂²×C₃×C₁₇	—	25	1	no	Hall
15	C₂×C₅×C₁₇	C₃×D₅	1	6	yes	complemented
16	D₅×C₁₇	—	5	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	—	25	2	no	—
20	C₂×C₃×C₁₇	C₅⋊D₅	1	1	yes	characteristic, direct product factor
21	C₂×C₅⋊D₅	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
22	C₅×C₁₇	C₂×C₃×D₅	1	6	yes	complemented
23	C₃×C₅²	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
24	C₂²×C₁₇	—	25	1	no	Hall
25	C₂×C₃×D₅	—	5	6	no	—
26	C₃×C₁₇	C₂×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₅²	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
28	C₅⋊D₅	C₂×C₃×C₁₇	1	2	yes	direct product factor
29	C₂×C₁₇	—	25	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	C₃×D₅	—	5	12	no	—
33	C₅²	C₂²×C₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
34	C₂×D₅	—	5	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	C₂²×C₃	—	25	1	no	Hall
38	C₂×C₅	C₃×D₅×C₁₇	1	6	yes	complemented
39	D₅	—	5	12	no	—
40	C₂×C₃	—	25	2	no	—
41	C₂×C₃	C₁₇×C₅⋊D₅	1	1	yes	characteristic, direct product factor
42	C₅	C₂×C₃×D₅×C₁₇	1	6	yes	complemented
43	C₂²	—	25	1	no	Sylow
44	C₃	C₂×C₁₇×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	—	25	2	no	—
46	C₂	C₃×C₁₇×C₅⋊D₅	1	1	yes	characteristic, direct product factor

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

Complements

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

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

Subgroups — C2×C3×C17×C5⋊D5 #19099838

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×C₁₇×C₅⋊D₅ #19099838