Subgroups — C₁₇×C₃⋊(C₃⋊#1044) #29506000

Order 15300.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₇×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₁₇×C₃⋊#1044	—	3	4	no	maximal
3	C₃²×C₅²×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₇×C₃⋊ΓL(1,𝔽₁₆)	—	5	2	no	maximal
5	C₃×C₁₇×C₅⋊D₅	D₃	1	4	yes	—
6	C₁₇×#1044	—	9	1	no	Hall
7	C₃²×D₅×C₁₇	—	5	2	no	—
8	C₃²×D₅×C₁₇	—	10	2	no	—
9	C₃×C₅²×C₁₇	Dic₃	1	4	yes	complemented
10	C₁₇×ΓL(1,𝔽₁₆)	—	15	8	no	—
11	C₃⋊(C₃⋊#1044)	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₇×C₅⋊D₅	C₃⋊D₃	1	1	yes	characteristic
13	C₃²×C₅×C₁₇	—	2	2	no	—
14	C₃²×C₅×C₁₇	AGL(1,𝔽₅)	1	2	yes	complemented
15	C₁₇×C₃⋊Dic₃	—	25	1	no	Hall
16	C₃×D₅×C₁₇	—	5	8	no	—
17	C₃×D₅×C₁₇	—	10	8	no	—
18	C₃²×C₅⋊D₅	C₂×C₁₇	1	1	yes	characteristic
19	C₅²×C₁₇	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
20	C₁₇×AGL(1,𝔽₅)	—	45	2	no	—
21	C₂×C₃²×C₁₇	—	25	1	no	—
22	C₃⋊#1044	—	3	4	no	—
23	C₃×C₅×C₁₇	—	2	8	no	—
24	C₃×C₅×C₁₇	ΓL(1,𝔽₁₆)	1	8	yes	complemented
25	C₃²×C₅²	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
26	Dic₃×C₁₇	—	75	4	no	—
27	C₃⋊ΓL(1,𝔽₁₆)	—	5	2	no	—
28	D₅×C₁₇	—	5	2	no	—
29	D₅×C₁₇	—	10	2	no	—
30	C₃²×C₁₇	#1044	1	1	yes	characteristic, complemented, Hall
31	C₃×C₅⋊D₅	D₃×C₁₇	1	4	yes	—
32	C₂×C₃×C₁₇	—	25	4	no	—
33	#1044	—	9	1	no	Hall
34	C₃²×D₅	—	5	2	no	—
35	C₃²×D₅	—	10	2	no	—
36	C₅×C₁₇	—	2	2	no	—
37	C₅×C₁₇	C₃⋊ΓL(1,𝔽₁₆)	1	2	yes	complemented
38	C₃×C₅²	Dic₃×C₁₇	1	4	yes	complemented
39	C₄×C₁₇	—	225	1	no	Hall
40	ΓL(1,𝔽₁₆)	—	15	8	no	—
41	C₃×C₁₇	C₃⋊#1044	1	4	yes	complemented
42	C₅⋊D₅	C₁₇×C₃⋊D₃	1	1	yes	characteristic
43	C₃²×C₅	—	2	2	no	—
44	C₃²×C₅	C₁₇×AGL(1,𝔽₅)	1	2	yes	complemented
45	C₃⋊Dic₃	—	25	1	no	Hall
46	C₂×C₁₇	—	25	1	no	—
47	C₃×D₅	—	5	8	no	—
48	C₃×D₅	—	10	8	no	—
49	C₅²	C₁₇×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
50	AGL(1,𝔽₅)	—	45	2	no	—
51	C₂×C₃²	—	25	1	no	—
52	C₁₇	C₃⋊(C₃⋊#1044)	1	1	yes	characteristic, direct product factor, Sylow
53	C₃×C₅	—	2	8	no	—
54	C₃×C₅	C₁₇×ΓL(1,𝔽₁₆)	1	8	yes	complemented
55	Dic₃	—	75	4	no	—
56	D₅	—	5	2	no	—
57	D₅	—	10	2	no	—
58	C₃²	C₁₇×#1044	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₃	—	25	4	no	—
60	C₅	—	2	2	no	—
61	C₅	C₁₇×C₃⋊ΓL(1,𝔽₁₆)	1	2	yes	complemented
62	C₄	—	225	1	no	Sylow
63	C₃	C₁₇×C₃⋊#1044	1	4	yes	complemented
64	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₁₇	C₃⋊(C₃⋊#1044)
commutator, hypocenter	C₃²×C₅²	C₄×C₁₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₁₇	C₄
prime radical	C₃²×C₁₇×C₅⋊D₅	C₂
cosocle	C₃²×C₅⋊D₅	C₂×C₁₇
LCS	G ▷ C₃²×C₅²
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
3. C₃²×C₅²×C₁₇	C₄	semidirect
9. C₃×C₅²×C₁₇	Dic₃	semidirect
11. C₃⋊(C₃⋊#1044)	C₁₇	direct (N × H)
14. C₃²×C₅×C₁₇	AGL(1,𝔽₅)	semidirect
19. C₅²×C₁₇	C₃⋊Dic₃	semidirect
24. C₃×C₅×C₁₇	ΓL(1,𝔽₁₆)	semidirect
25. C₃²×C₅²	C₄×C₁₇	semidirect
30. C₃²×C₁₇	#1044	semidirect
37. C₅×C₁₇	C₃⋊ΓL(1,𝔽₁₆)	semidirect
38. C₃×C₅²	Dic₃×C₁₇	semidirect
41. C₃×C₁₇	C₃⋊#1044	semidirect
44. C₃²×C₅	C₁₇×AGL(1,𝔽₅)	semidirect
49. C₅²	C₁₇×C₃⋊Dic₃	semidirect
52. C₁₇	C₃⋊(C₃⋊#1044)	direct (N × H)
54. C₃×C₅	C₁₇×ΓL(1,𝔽₁₆)	semidirect
58. C₃²	C₁₇×#1044	semidirect
61. C₅	C₁₇×C₃⋊ΓL(1,𝔽₁₆)	semidirect
63. C₃	C₁₇×C₃⋊#1044	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₁₇×C₅⋊D₅	2
C₁₇×C₃⋊#1044	3
C₁₇×C₃⋊ΓL(1,𝔽₁₆)	5
C₃⋊(C₃⋊#1044)	17

Subgroups — C17×C3⋊(C3⋊#1044) #29506000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×C₃⋊(C₃⋊#1044) #29506000