Subgroups — C₃×C₅×D₁₇×C₄₉ #38735913

Order 24990.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₇×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₁₇×C₄₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₁₇×C₄₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₇×C₄₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₇×D₁₇	C₇	1	1	yes	maximal, characteristic
6	C₃×C₁₇×C₄₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×C₇×C₁₇	C₂×C₇	1	1	yes	characteristic
8	D₁₇×C₄₉	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃×C₅×C₄₉	—	17	1	no	maximal, Hall
10	C₅×C₇×D₁₇	C₃×C₇	1	1	yes	characteristic
11	C₁₇×C₄₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
12	C₃×C₅×C₄₉	D₁₇	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₇×D₁₇	C₅×C₇	1	1	yes	characteristic
14	C₅×C₇×C₁₇	C₂×C₃×C₇	1	1	yes	characteristic
15	C₃×C₅×D₁₇	C₄₉	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₅×C₄₉	—	17	1	no	Hall
17	C₃×C₇×C₁₇	C₂×C₅×C₇	1	1	yes	characteristic
18	C₂×C₃×C₄₉	—	17	1	no	Hall
19	C₃×C₅×C₁₇	C₂×C₄₉	1	1	yes	characteristic, complemented, Hall
20	C₅×C₄₉	C₃×D₁₇	1	1	yes	characteristic, direct product factor, Hall
21	C₇×D₁₇	C₃×C₅×C₇	1	1	yes	characteristic
22	C₂×C₃×C₅×C₇	—	17	1	no	—
23	C₅×D₁₇	C₃×C₄₉	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₄₉	C₅×D₁₇	1	1	yes	characteristic, direct product factor, Hall
25	C₇×C₁₇	C₂×C₃×C₅×C₇	1	1	yes	characteristic
26	C₃×C₅×C₇	C₇×D₁₇	1	1	yes	characteristic
27	C₃×D₁₇	C₅×C₄₉	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₄₉	—	17	1	no	Hall
29	C₅×C₁₇	C₂×C₃×C₄₉	1	1	yes	characteristic, complemented, Hall
30	C₂×C₅×C₇	—	17	1	no	—
31	C₃×C₁₇	C₂×C₅×C₄₉	1	1	yes	characteristic, complemented, Hall
32	C₄₉	C₃×C₅×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
33	C₂×C₃×C₇	—	17	1	no	—
34	C₅×C₇	C₃×C₇×D₁₇	1	1	yes	characteristic
35	D₁₇	C₃×C₅×C₄₉	1	1	yes	characteristic, direct product factor, Hall
36	C₂×C₃×C₅	—	17	1	no	Hall
37	C₃×C₇	C₅×C₇×D₁₇	1	1	yes	characteristic
38	C₁₇	C₂×C₃×C₅×C₄₉	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	D₁₇×C₄₉	1	1	yes	characteristic, direct product factor, Hall
40	C₂×C₇	—	17	1	no	—
41	C₂×C₅	—	17	1	no	Hall
42	C₇	C₃×C₅×C₇×D₁₇	1	1	yes	characteristic
43	C₂×C₃	—	17	1	no	Hall
44	C₅	C₃×D₁₇×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₅×D₁₇×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	17	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅×C₄₉	D₁₇
commutator, hypocenter	C₁₇	C₂×C₃×C₅×C₄₉
Frattini	C₇	C₃×C₅×C₇×D₁₇
Fitting	C₃×C₅×C₁₇×C₄₉	C₂
socle	C₃×C₅×C₇×C₁₇	C₂×C₇
prime radical	C₃×C₅×C₇×D₁₇	C₇
cosocle	C₇×C₁₇	C₂×C₃×C₅×C₇
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₃×C₅×C₄₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₇×C₄₉	C₂	semidirect
2. C₅×D₁₇×C₄₉	C₃	direct (N × H)
3. C₃×D₁₇×C₄₉	C₅	direct (N × H)
4. C₅×C₁₇×C₄₉	C₂×C₃	semidirect
6. C₃×C₁₇×C₄₉	C₂×C₅	semidirect
8. D₁₇×C₄₉	C₃×C₅	direct (N × H)
11. C₁₇×C₄₉	C₂×C₃×C₅	semidirect
12. C₃×C₅×C₄₉	D₁₇	direct (N × H)
15. C₃×C₅×D₁₇	C₄₉	direct (N × H)
19. C₃×C₅×C₁₇	C₂×C₄₉	semidirect
20. C₅×C₄₉	C₃×D₁₇	direct (N × H)
23. C₅×D₁₇	C₃×C₄₉	direct (N × H)
24. C₃×C₄₉	C₅×D₁₇	direct (N × H)
27. C₃×D₁₇	C₅×C₄₉	direct (N × H)
29. C₅×C₁₇	C₂×C₃×C₄₉	semidirect
31. C₃×C₁₇	C₂×C₅×C₄₉	semidirect
32. C₄₉	C₃×C₅×D₁₇	direct (N × H)
35. D₁₇	C₃×C₅×C₄₉	direct (N × H)
38. C₁₇	C₂×C₃×C₅×C₄₉	semidirect
39. C₃×C₅	D₁₇×C₄₉	direct (N × H)
44. C₅	C₃×D₁₇×C₄₉	direct (N × H)
45. C₃	C₅×D₁₇×C₄₉	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×C₅×C₁₇×C₄₉	2
C₅×D₁₇×C₄₉	3
C₃×D₁₇×C₄₉	5
C₃×C₅×C₇×D₁₇	7
C₂×C₃×C₅×C₄₉	17

Subgroups — C3×C5×D17×C49 #38735913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×D₁₇×C₄₉ #38735913