Subgroups — C₁₇×C₉⋊#1043 #29505801

Order 15300.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₇×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₁₇×C₃⋊#1043	—	3	1	no	maximal
3	C₅²×C₉×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₇×C₉⋊AGL(1,𝔽₅)	—	5	6	no	maximal
5	C₃×C₁₇×C₅⋊D₅	D₃	1	1	yes	characteristic
6	C₁₇×#1043	—	9	1	no	Hall
7	C₉×D₅×C₁₇	—	5	6	no	—
8	C₃×C₅²×C₁₇	Dic₃	1	1	yes	characteristic
9	C₁₇×ΓL(1,𝔽₁₆)	—	15	6	no	—
10	C₉⋊#1043	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₁₇×C₅⋊D₅	D₉	1	1	yes	characteristic
12	C₅×C₉×C₁₇	AGL(1,𝔽₅)	1	6	yes	complemented
13	C₁₇×Dic₉	—	25	1	no	Hall
14	C₃×D₅×C₁₇	—	5	6	no	—
15	C₉×C₅⋊D₅	C₂×C₁₇	1	1	yes	characteristic
16	C₅²×C₁₇	Dic₉	1	1	yes	characteristic, complemented, Hall
17	C₁₇×AGL(1,𝔽₅)	—	45	6	no	—
18	C₂×C₉×C₁₇	—	25	1	no	—
19	C₃⋊#1043	—	3	1	no	—
20	C₃×C₅×C₁₇	ΓL(1,𝔽₁₆)	1	6	yes	—
21	C₅²×C₉	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
22	Dic₃×C₁₇	—	75	1	no	—
23	C₉⋊AGL(1,𝔽₅)	—	5	6	no	—
24	D₅×C₁₇	—	5	6	no	—
25	C₉×C₁₇	#1043	1	1	yes	characteristic, complemented, Hall
26	C₃×C₅⋊D₅	D₃×C₁₇	1	1	yes	characteristic
27	C₂×C₃×C₁₇	—	25	1	no	—
28	#1043	—	9	1	no	Hall
29	C₉×D₅	—	5	6	no	—
30	C₅×C₁₇	C₉⋊AGL(1,𝔽₅)	1	6	yes	complemented
31	C₃×C₅²	Dic₃×C₁₇	1	1	yes	characteristic
32	C₄×C₁₇	—	225	1	no	Hall
33	ΓL(1,𝔽₁₆)	—	15	6	no	—
34	C₃×C₁₇	C₃⋊#1043	1	1	yes	characteristic
35	C₅⋊D₅	C₁₇×D₉	1	1	yes	characteristic
36	C₅×C₉	C₁₇×AGL(1,𝔽₅)	1	6	yes	complemented
37	Dic₉	—	25	1	no	Hall
38	C₂×C₁₇	—	25	1	no	—
39	C₃×D₅	—	5	6	no	—
40	C₅²	C₁₇×Dic₉	1	1	yes	characteristic, complemented, Sylow
41	AGL(1,𝔽₅)	—	45	6	no	—
42	C₂×C₉	—	25	1	no	—
43	C₁₇	C₉⋊#1043	1	1	yes	characteristic, direct product factor, Sylow
44	C₃×C₅	C₁₇×ΓL(1,𝔽₁₆)	1	6	yes	—
45	Dic₃	—	75	1	no	—
46	D₅	—	5	6	no	—
47	C₉	C₁₇×#1043	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃	—	25	1	no	—
49	C₅	C₁₇×C₉⋊AGL(1,𝔽₅)	1	6	yes	complemented
50	C₄	—	225	1	no	Sylow
51	C₃	C₁₇×C₃⋊#1043	1	1	yes	characteristic
52	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₁₇	C₉⋊#1043
commutator, hypocenter	C₅²×C₉	C₄×C₁₇
Frattini	C₃	C₁₇×C₃⋊#1043
Fitting	C₅²×C₉×C₁₇	C₄
socle	C₃×C₅²×C₁₇	Dic₃
prime radical	C₃×C₁₇×C₅⋊D₅	D₃
cosocle	C₉×C₅⋊D₅	C₂×C₁₇
LCS	G ▷ C₅²×C₉
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
3. C₅²×C₉×C₁₇	C₄	semidirect
10. C₉⋊#1043	C₁₇	direct (N × H)
12. C₅×C₉×C₁₇	AGL(1,𝔽₅)	semidirect
16. C₅²×C₁₇	Dic₉	semidirect
21. C₅²×C₉	C₄×C₁₇	semidirect
25. C₉×C₁₇	#1043	semidirect
30. C₅×C₁₇	C₉⋊AGL(1,𝔽₅)	semidirect
36. C₅×C₉	C₁₇×AGL(1,𝔽₅)	semidirect
40. C₅²	C₁₇×Dic₉	semidirect
43. C₁₇	C₉⋊#1043	direct (N × H)
47. C₉	C₁₇×#1043	semidirect
49. C₅	C₁₇×C₉⋊AGL(1,𝔽₅)	semidirect

Maximal subgroups

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

subgroup	index
C₉×C₁₇×C₅⋊D₅	2
C₁₇×C₃⋊#1043	3
C₁₇×C₉⋊AGL(1,𝔽₅)	5
C₉⋊#1043	17

Subgroups — C17×C9⋊#1043 #29505801

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×C₉⋊#1043 #29505801