Subgroups — C₃×AGL(1,𝔽₁₀₃) #44538552

Order 31518.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×(C₁₀₃⋊C₃)⋊C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	AGL(1,𝔽₁₀₃)	C₃	1	3	yes	maximal, direct product factor
3	C₃×D₁₀₃⋊C₁₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₀₃⋊C₁₇	C₂×C₃	1	1	yes	characteristic, complemented
5	(C₁₀₃⋊C₃)⋊C₁₇	C₂×C₃	1	3	yes	complemented
6	D₁₀₃⋊C₁₇	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×D₁₀₃⋊C₃	C₁₇	1	1	yes	maximal, characteristic, complemented, Hall
8	C₁₀₃⋊C₁₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₁₀₃⋊C₃	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
10	C₃×D₁₀₃	C₃×C₁₇	1	1	yes	characteristic, complemented
11	D₁₀₃⋊C₃	C₃×C₁₇	1	3	yes	complemented
12	C₃×C₁₀₃	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
13	C₁₀₃⋊C₃	C₂×C₃×C₁₇	1	3	yes	complemented
14	C₂×C₃²×C₁₇	—	103	1	no	maximal, Hall
15	D₁₀₃	C₃²×C₁₇	1	1	yes	characteristic, complemented, Hall
16	C₃²×C₁₇	—	103	1	no	Hall
17	C₁₀₃	C₂×C₃²×C₁₇	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃×C₁₇	—	103	1	no	—
19	C₂×C₃×C₁₇	—	103	3	no	—
20	C₃×C₁₇	—	103	3	no	—
21	C₃×C₁₇	—	103	1	no	—
22	C₂×C₁₇	—	103	1	no	Hall
23	C₂×C₃²	—	103	1	no	Hall
24	C₁₇	—	103	1	no	Sylow
25	C₃²	—	103	1	no	Sylow
26	C₂×C₃	—	103	3	no	—
27	C₂×C₃	—	103	1	no	—
28	C₃	—	103	3	no	—
29	C₃	AGL(1,𝔽₁₀₃)	1	1	yes	characteristic, direct product factor
30	C₂	—	103	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	AGL(1,𝔽₁₀₃)
commutator, cosocle, hypocenter	C₁₀₃	C₂×C₃²×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₀₃	C₂×C₃×C₁₇
LCS	G ▷ C₁₀₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×(C₁₀₃⋊C₃)⋊C₁₇	C₂	semidirect
2. AGL(1,𝔽₁₀₃)	C₃	direct (N × H)
3. C₃×D₁₀₃⋊C₁₇	C₃	semidirect
4. C₃×C₁₀₃⋊C₁₇	C₂×C₃	semidirect
5. (C₁₀₃⋊C₃)⋊C₁₇	C₂×C₃	semidirect
6. D₁₀₃⋊C₁₇	C₃²	semidirect
7. C₃×D₁₀₃⋊C₃	C₁₇	semidirect
8. C₁₀₃⋊C₁₇	C₂×C₃²	semidirect
9. C₃×C₁₀₃⋊C₃	C₂×C₁₇	semidirect
10. C₃×D₁₀₃	C₃×C₁₇	semidirect
11. D₁₀₃⋊C₃	C₃×C₁₇	semidirect
12. C₃×C₁₀₃	C₂×C₃×C₁₇	semidirect
13. C₁₀₃⋊C₃	C₂×C₃×C₁₇	semidirect
15. D₁₀₃	C₃²×C₁₇	semidirect
17. C₁₀₃	C₂×C₃²×C₁₇	semidirect
29. C₃	AGL(1,𝔽₁₀₃)	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×(C₁₀₃⋊C₃)⋊C₁₇	2
AGL(1,𝔽₁₀₃)	3
C₃×D₁₀₃⋊C₁₇	3
C₃×D₁₀₃⋊C₃	17
C₂×C₃²×C₁₇	103

Subgroups — C3×AGL(1,𝔽103) #44538552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×AGL(1,𝔽₁₀₃) #44538552