Subgroups — C₅×C₁₇×D₁₃⋊C₉ #34091034

Order 19890.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₇×C₁₃⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅×C₁₇×D₁₃	C₃	1	1	yes	maximal, characteristic
3	C₁₇×D₁₃⋊C₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₃×C₁₇	C₂×C₃	1	1	yes	characteristic
5	C₅×C₁₇×D₁₃	C₉	1	1	yes	characteristic, complemented, Hall
6	C₁₇×C₁₃⋊C₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₅×C₉×C₁₇	—	13	1	no	maximal, Hall
8	C₃×C₁₇×D₁₃	C₃×C₅	1	1	yes	characteristic
9	C₅×D₁₃⋊C₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₅×C₁₃×C₁₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
11	C₅×C₉×C₁₇	—	13	1	no	Hall
12	C₃×C₁₃×C₁₇	C₂×C₃×C₅	1	1	yes	characteristic
13	C₅×C₁₃⋊C₉	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₅×C₁₇	—	13	1	no	—
15	C₁₇×D₁₃	C₅×C₉	1	1	yes	characteristic, complemented, Hall
16	C₃×C₅×D₁₃	C₃×C₁₇	1	1	yes	characteristic
17	C₂×C₉×C₁₇	—	13	1	no	Hall
18	C₃×C₅×C₁₇	D₁₃⋊C₃	1	1	yes	characteristic
19	D₁₃⋊C₉	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
20	C₁₃×C₁₇	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Hall
21	C₃×C₅×C₁₃	C₂×C₃×C₁₇	1	1	yes	characteristic
22	C₂×C₅×C₁₇	—	13	1	no	Hall
23	C₉×C₁₇	—	13	1	no	Hall
24	C₅×D₁₃	C₉×C₁₇	1	1	yes	characteristic, complemented, Hall
25	C₁₃⋊C₉	C₂×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×C₁₇	—	13	1	no	—
27	C₂×C₅×C₉	—	13	1	no	Hall
28	C₅×C₁₇	D₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Hall
29	C₃×D₁₃	C₃×C₅×C₁₇	1	1	yes	characteristic
30	C₅×C₁₃	C₂×C₉×C₁₇	1	1	yes	characteristic, complemented, Hall
31	C₃×C₁₇	C₅×D₁₃⋊C₃	1	1	yes	characteristic
32	C₅×C₉	—	13	1	no	Hall
33	C₃×C₁₃	C₂×C₃×C₅×C₁₇	1	1	yes	characteristic
34	C₂×C₁₇	—	13	1	no	Hall
35	C₂×C₃×C₅	—	13	1	no	—
36	D₁₃	C₅×C₉×C₁₇	1	1	yes	characteristic, complemented, Hall
37	C₂×C₉	—	13	1	no	Hall
38	C₁₇	C₅×D₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
39	C₃×C₅	C₁₇×D₁₃⋊C₃	1	1	yes	characteristic
40	C₁₃	C₂×C₅×C₉×C₁₇	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	—	13	1	no	Hall
42	C₉	—	13	1	no	Sylow
43	C₂×C₃	—	13	1	no	—
44	C₅	C₁₇×D₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₅×C₁₇×D₁₃⋊C₃	1	1	yes	characteristic
46	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₇	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₂×C₅×C₉×C₁₇
Frattini	C₃	C₅×C₁₇×D₁₃⋊C₃
Fitting, socle	C₃×C₅×C₁₃×C₁₇	C₂×C₃
prime radical	C₃×C₅×C₁₇×D₁₃	C₃
cosocle	C₃×C₁₃	C₂×C₃×C₅×C₁₇
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. C₅×C₁₇×C₁₃⋊C₉	C₂	semidirect
3. C₁₇×D₁₃⋊C₉	C₅	direct (N × H)
5. C₅×C₁₇×D₁₃	C₉	semidirect
6. C₁₇×C₁₃⋊C₉	C₂×C₅	semidirect
9. C₅×D₁₃⋊C₉	C₁₇	direct (N × H)
10. C₅×C₁₃×C₁₇	C₂×C₉	semidirect
13. C₅×C₁₃⋊C₉	C₂×C₁₇	semidirect
15. C₁₇×D₁₃	C₅×C₉	semidirect
19. D₁₃⋊C₉	C₅×C₁₇	direct (N × H)
20. C₁₃×C₁₇	C₂×C₅×C₉	semidirect
24. C₅×D₁₃	C₉×C₁₇	semidirect
25. C₁₃⋊C₉	C₂×C₅×C₁₇	semidirect
28. C₅×C₁₇	D₁₃⋊C₉	direct (N × H)
30. C₅×C₁₃	C₂×C₉×C₁₇	semidirect
36. D₁₃	C₅×C₉×C₁₇	semidirect
38. C₁₇	C₅×D₁₃⋊C₉	direct (N × H)
40. C₁₃	C₂×C₅×C₉×C₁₇	semidirect
44. C₅	C₁₇×D₁₃⋊C₉	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×C₁₇×C₁₃⋊C₉	2
C₃×C₅×C₁₇×D₁₃	3
C₁₇×D₁₃⋊C₉	5
C₂×C₅×C₉×C₁₇	13
C₅×D₁₃⋊C₉	17

Subgroups — C5×C17×D13⋊C9 #34091034

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₇×D₁₃⋊C₉ #34091034