Subgroups — C₅×C₄₁×AGL(1,𝔽₁₃) #44544342

Order 31980.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄₁×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₄₁×#261	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₁₃⋊C₃×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₄₁×AGL(1,𝔽₁₃)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×D₁₃×C₄₁	C₂×C₃	1	1	yes	characteristic
6	C₄₁×D₁₃⋊C₃	C₂×C₅	1	1	yes	characteristic
7	C₅×C₁₃×C₄₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₃×C₄×C₅×C₄₁	—	13	1	no	maximal, Hall
9	C₄₁×#261	C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₁₃⋊C₃×C₄₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₅×C₄₁	—	13	1	no	—
12	D₁₃×C₄₁	C₂×C₃×C₅	1	1	yes	characteristic
13	C₄×C₅×C₄₁	—	13	1	no	Hall
14	C₅×AGL(1,𝔽₁₃)	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₃×C₅×C₄₁	—	13	1	no	Hall
16	C₁₃×C₄₁	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Hall
17	C₃×C₄×C₄₁	—	13	1	no	Hall
18	C₂×C₅×C₄₁	—	13	1	no	—
19	C₅×D₁₃⋊C₃	C₂×C₄₁	1	1	yes	characteristic
20	C₅×#261	C₃×C₄₁	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₄₁	—	13	1	no	—
22	C₅×C₄₁	AGL(1,𝔽₁₃)	1	1	yes	characteristic, direct product factor, Hall
23	C₅×C₁₃⋊C₃	C₄×C₄₁	1	1	yes	characteristic, complemented, Hall
24	C₄×C₄₁	—	13	1	no	Hall
25	AGL(1,𝔽₁₃)	C₅×C₄₁	1	1	yes	characteristic, direct product factor, Hall
26	C₅×D₁₃	C₂×C₃×C₄₁	1	1	yes	characteristic
27	C₃×C₄₁	—	13	1	no	Hall
28	C₂×C₄₁	—	13	1	no	—
29	D₁₃⋊C₃	C₂×C₅×C₄₁	1	1	yes	characteristic
30	C₅×C₁₃	C₃×C₄×C₄₁	1	1	yes	characteristic, complemented, Hall
31	C₃×C₄×C₅	—	13	1	no	Hall
32	#261	C₃×C₅×C₄₁	1	1	yes	characteristic, complemented, Hall
33	C₄₁	C₅×AGL(1,𝔽₁₃)	1	1	yes	characteristic, direct product factor, Sylow
34	C₁₃⋊C₃	C₄×C₅×C₄₁	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×C₅	—	13	1	no	—
36	D₁₃	C₂×C₃×C₅×C₄₁	1	1	yes	characteristic
37	C₄×C₅	—	13	1	no	Hall
38	C₃×C₅	—	13	1	no	Hall
39	C₁₃	C₃×C₄×C₅×C₄₁	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₄	—	13	1	no	Hall
41	C₂×C₅	—	13	1	no	—
42	C₂×C₃	—	13	1	no	—
43	C₅	C₄₁×AGL(1,𝔽₁₃)	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	—	13	1	no	Sylow
45	C₃	—	13	1	no	Sylow
46	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₄₁	AGL(1,𝔽₁₃)
commutator, hypocenter	C₁₃	C₃×C₄×C₅×C₄₁
Frattini	C₁	G
Fitting, socle	C₅×C₁₃×C₄₁	C₃×C₄
prime radical	C₅×C₄₁×D₁₃⋊C₃	C₂
cosocle	D₁₃	C₂×C₃×C₅×C₄₁
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₅×C₄₁

Complements

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

N	H ≅ G/N	type
2. C₅×C₄₁×#261	C₃	semidirect
3. C₅×C₁₃⋊C₃×C₄₁	C₄	semidirect
4. C₄₁×AGL(1,𝔽₁₃)	C₅	direct (N × H)
7. C₅×C₁₃×C₄₁	C₃×C₄	semidirect
9. C₄₁×#261	C₃×C₅	semidirect
10. C₁₃⋊C₃×C₄₁	C₄×C₅	semidirect
14. C₅×AGL(1,𝔽₁₃)	C₄₁	direct (N × H)
16. C₁₃×C₄₁	C₃×C₄×C₅	semidirect
20. C₅×#261	C₃×C₄₁	semidirect
22. C₅×C₄₁	AGL(1,𝔽₁₃)	direct (N × H)
23. C₅×C₁₃⋊C₃	C₄×C₄₁	semidirect
25. AGL(1,𝔽₁₃)	C₅×C₄₁	direct (N × H)
30. C₅×C₁₃	C₃×C₄×C₄₁	semidirect
32. #261	C₃×C₅×C₄₁	semidirect
33. C₄₁	C₅×AGL(1,𝔽₁₃)	direct (N × H)
34. C₁₃⋊C₃	C₄×C₅×C₄₁	semidirect
39. C₁₃	C₃×C₄×C₅×C₄₁	semidirect
43. C₅	C₄₁×AGL(1,𝔽₁₃)	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×C₄₁×D₁₃⋊C₃	2
C₅×C₄₁×#261	3
C₄₁×AGL(1,𝔽₁₃)	5
C₃×C₄×C₅×C₄₁	13
C₅×AGL(1,𝔽₁₃)	41

Subgroups — C5×C41×AGL(1,𝔽13) #44544342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₄₁×AGL(1,𝔽₁₃) #44544342