Subgroups — C₃×C₅×C₁₇×D₁₃⋊C₃ #34091041

Order 19890.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₇×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₇×D₁₃⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₅×C₁₇×D₁₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₇×D₁₃⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₁₇×C₁₃⋊C₃	C₂×C₃	1	3	yes	complemented
6	C₃×C₅×C₁₃×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅×C₁₇×D₁₃	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₇×C₁₃⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃²×C₅×C₁₇	—	13	1	no	maximal, Hall
10	C₃×C₁₇×D₁₃	C₃×C₅	1	1	yes	characteristic, complemented
11	C₁₇×D₁₃⋊C₃	C₃×C₅	1	3	yes	direct product factor
12	C₃×C₅×D₁₃⋊C₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₅×C₁₃×C₁₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
14	C₃²×C₅×C₁₇	—	13	1	no	Hall
15	C₃×C₁₃×C₁₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented
16	C₁₇×C₁₃⋊C₃	C₂×C₃×C₅	1	3	yes	complemented
17	C₃×C₅×C₁₃⋊C₃	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₅×C₁₇	—	13	3	no	—
19	C₂×C₃×C₅×C₁₇	—	13	1	no	—
20	C₁₇×D₁₃	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
21	C₃×C₅×D₁₃	C₃×C₁₇	1	1	yes	characteristic, complemented
22	C₅×D₁₃⋊C₃	C₃×C₁₇	1	3	yes	direct product factor
23	C₂×C₃²×C₁₇	—	13	1	no	Hall
24	C₃×C₅×C₁₇	—	13	3	no	—
25	C₃×C₅×C₁₇	D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
26	C₃×D₁₃⋊C₃	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
27	C₁₃×C₁₇	C₂×C₃²×C₅	1	1	yes	characteristic, complemented, Hall
28	C₃×C₅×C₁₃	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
29	C₅×C₁₃⋊C₃	C₂×C₃×C₁₇	1	3	yes	complemented
30	C₂×C₅×C₁₇	—	13	1	no	Hall
31	C₃²×C₁₇	—	13	1	no	Hall
32	C₅×D₁₃	C₃²×C₁₇	1	1	yes	characteristic, complemented, Hall
33	C₃×C₁₃⋊C₃	C₂×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃×C₁₇	—	13	3	no	—
35	C₂×C₃×C₁₇	—	13	1	no	—
36	C₂×C₃²×C₅	—	13	1	no	Hall
37	C₅×C₁₇	C₃×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
38	C₃×D₁₃	C₃×C₅×C₁₇	1	1	yes	characteristic, complemented
39	D₁₃⋊C₃	C₃×C₅×C₁₇	1	3	yes	direct product factor
40	C₅×C₁₃	C₂×C₃²×C₁₇	1	1	yes	characteristic, complemented, Hall
41	C₃×C₁₇	—	13	3	no	—
42	C₃×C₁₇	C₅×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
43	C₃²×C₅	—	13	1	no	Hall
44	C₃×C₁₃	C₂×C₃×C₅×C₁₇	1	1	yes	characteristic, complemented
45	C₁₃⋊C₃	C₂×C₃×C₅×C₁₇	1	3	yes	complemented
46	C₂×C₁₇	—	13	1	no	Hall
47	C₂×C₃×C₅	—	13	3	no	—
48	C₂×C₃×C₅	—	13	1	no	—
49	D₁₃	C₃²×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
50	C₂×C₃²	—	13	1	no	Hall
51	C₁₇	C₃×C₅×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
52	C₃×C₅	—	13	3	no	—
53	C₃×C₅	C₁₇×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
54	C₁₃	C₂×C₃²×C₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₅	—	13	1	no	Hall
56	C₃²	—	13	1	no	Sylow
57	C₂×C₃	—	13	3	no	—
58	C₂×C₃	—	13	1	no	—
59	C₅	C₃×C₁₇×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
60	C₃	—	13	3	no	—
61	C₃	C₅×C₁₇×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
62	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₇	D₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₃²×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₁₇	C₂×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₅×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₇×C₁₃⋊C₃	C₂	semidirect
2. C₅×C₁₇×D₁₃⋊C₃	C₃	direct (N × H)
3. C₃×C₅×C₁₇×D₁₃	C₃	semidirect
4. C₃×C₁₇×D₁₃⋊C₃	C₅	direct (N × H)
5. C₅×C₁₇×C₁₃⋊C₃	C₂×C₃	semidirect
6. C₃×C₅×C₁₃×C₁₇	C₂×C₃	semidirect
7. C₅×C₁₇×D₁₃	C₃²	semidirect
8. C₃×C₁₇×C₁₃⋊C₃	C₂×C₅	semidirect
10. C₃×C₁₇×D₁₃	C₃×C₅	semidirect
11. C₁₇×D₁₃⋊C₃	C₃×C₅	direct (N × H)
12. C₃×C₅×D₁₃⋊C₃	C₁₇	direct (N × H)
13. C₅×C₁₃×C₁₇	C₂×C₃²	semidirect
15. C₃×C₁₃×C₁₇	C₂×C₃×C₅	semidirect
16. C₁₇×C₁₃⋊C₃	C₂×C₃×C₅	semidirect
17. C₃×C₅×C₁₃⋊C₃	C₂×C₁₇	semidirect
20. C₁₇×D₁₃	C₃²×C₅	semidirect
21. C₃×C₅×D₁₃	C₃×C₁₇	semidirect
22. C₅×D₁₃⋊C₃	C₃×C₁₇	direct (N × H)
25. C₃×C₅×C₁₇	D₁₃⋊C₃	direct (N × H)
26. C₃×D₁₃⋊C₃	C₅×C₁₇	direct (N × H)
27. C₁₃×C₁₇	C₂×C₃²×C₅	semidirect
28. C₃×C₅×C₁₃	C₂×C₃×C₁₇	semidirect
29. C₅×C₁₃⋊C₃	C₂×C₃×C₁₇	semidirect
32. C₅×D₁₃	C₃²×C₁₇	semidirect
33. C₃×C₁₃⋊C₃	C₂×C₅×C₁₇	semidirect
37. C₅×C₁₇	C₃×D₁₃⋊C₃	direct (N × H)
38. C₃×D₁₃	C₃×C₅×C₁₇	semidirect
39. D₁₃⋊C₃	C₃×C₅×C₁₇	direct (N × H)
40. C₅×C₁₃	C₂×C₃²×C₁₇	semidirect
42. C₃×C₁₇	C₅×D₁₃⋊C₃	direct (N × H)
44. C₃×C₁₃	C₂×C₃×C₅×C₁₇	semidirect
45. C₁₃⋊C₃	C₂×C₃×C₅×C₁₇	semidirect
49. D₁₃	C₃²×C₅×C₁₇	semidirect
51. C₁₇	C₃×C₅×D₁₃⋊C₃	direct (N × H)
53. C₃×C₅	C₁₇×D₁₃⋊C₃	direct (N × H)
54. C₁₃	C₂×C₃²×C₅×C₁₇	semidirect
59. C₅	C₃×C₁₇×D₁₃⋊C₃	direct (N × H)
61. C₃	C₅×C₁₇×D₁₃⋊C₃	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×C₁₃⋊C₃	2
C₅×C₁₇×D₁₃⋊C₃	3
C₃×C₅×C₁₇×D₁₃	3
C₃×C₁₇×D₁₃⋊C₃	5
C₂×C₃²×C₅×C₁₇	13
C₃×C₅×D₁₃⋊C₃	17

Subgroups — C3×C5×C17×D13⋊C3 #34091041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₁₇×D₁₃⋊C₃ #34091041