Subgroups — C₁₇×C₃⋊ΓL(1,𝔽₁₆) #15690366

Order 3060.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₅×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₁₇×ΓL(1,𝔽₁₆)	—	3	4	no	maximal
3	C₃²×C₅×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₇×C₃⋊Dic₃	—	5	1	no	maximal, Hall
5	C₃×D₅×C₁₇	D₃	1	4	yes	—
6	C₁₇×AGL(1,𝔽₅)	—	9	1	no	Hall
7	C₂×C₃²×C₁₇	—	5	1	no	—
8	C₃×C₅×C₁₇	Dic₃	1	4	yes	complemented
9	Dic₃×C₁₇	—	15	4	no	—
10	C₃⋊ΓL(1,𝔽₁₆)	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	D₅×C₁₇	C₃⋊D₃	1	1	yes	characteristic
12	C₃²×C₁₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₁₇	—	5	4	no	—
14	C₃²×D₅	C₂×C₁₇	1	1	yes	characteristic
15	C₅×C₁₇	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
16	C₄×C₁₇	—	45	1	no	Hall
17	ΓL(1,𝔽₁₆)	—	3	4	no	—
18	C₃×C₁₇	ΓL(1,𝔽₁₆)	1	4	yes	complemented
19	C₃²×C₅	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
20	C₃⋊Dic₃	—	5	1	no	Hall
21	C₂×C₁₇	—	5	1	no	—
22	C₃×D₅	D₃×C₁₇	1	4	yes	—
23	AGL(1,𝔽₅)	—	9	1	no	Hall
24	C₂×C₃²	—	5	1	no	—
25	C₁₇	C₃⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic, direct product factor, Sylow
26	C₃×C₅	Dic₃×C₁₇	1	4	yes	complemented
27	Dic₃	—	15	4	no	—
28	D₅	C₁₇×C₃⋊D₃	1	1	yes	characteristic
29	C₃²	C₁₇×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃	—	5	4	no	—
31	C₅	C₁₇×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	45	1	no	Sylow
33	C₃	C₁₇×ΓL(1,𝔽₁₆)	1	4	yes	complemented
34	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₁₇	C₃⋊ΓL(1,𝔽₁₆)
commutator, hypocenter	C₃²×C₅	C₄×C₁₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₇	C₄
prime radical	C₃²×D₅×C₁₇	C₂
cosocle	C₃²×D₅	C₂×C₁₇
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
3. C₃²×C₅×C₁₇	C₄	semidirect
8. C₃×C₅×C₁₇	Dic₃	semidirect
10. C₃⋊ΓL(1,𝔽₁₆)	C₁₇	direct (N × H)
12. C₃²×C₁₇	AGL(1,𝔽₅)	semidirect
15. C₅×C₁₇	C₃⋊Dic₃	semidirect
18. C₃×C₁₇	ΓL(1,𝔽₁₆)	semidirect
19. C₃²×C₅	C₄×C₁₇	semidirect
25. C₁₇	C₃⋊ΓL(1,𝔽₁₆)	direct (N × H)
26. C₃×C₅	Dic₃×C₁₇	semidirect
29. C₃²	C₁₇×AGL(1,𝔽₅)	semidirect
31. C₅	C₁₇×C₃⋊Dic₃	semidirect
33. C₃	C₁₇×ΓL(1,𝔽₁₆)	semidirect

Maximal subgroups

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

subgroup	index
C₃²×D₅×C₁₇	2
C₁₇×ΓL(1,𝔽₁₆)	3
C₁₇×C₃⋊Dic₃	5
C₃⋊ΓL(1,𝔽₁₆)	17

Subgroups — C17×C3⋊ΓL(1,𝔽16) #15690366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×C₃⋊ΓL(1,𝔽₁₆) #15690366