Subgroups — C₁₁×C₁₃×ΓL(1,𝔽₁₆) #22575147

Order 8580.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₃×AGL(1,𝔽₅)	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₁×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁×Dic₃×C₁₃	—	5	1	no	maximal, Hall
5	D₅×C₁₁×C₁₃	D₃	1	1	yes	characteristic
6	C₂×C₃×C₁₁×C₁₃	—	5	1	no	—
7	C₁₃×ΓL(1,𝔽₁₆)	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×C₁₁×C₁₃	Dic₃	1	1	yes	characteristic, complemented, Hall
9	C₁₁×ΓL(1,𝔽₁₆)	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₄×C₁₁×C₁₃	—	15	1	no	Hall
11	C₃×C₁₁×C₁₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₃×D₅×C₁₃	C₂×C₁₁	1	1	yes	characteristic
13	C₃×D₅×C₁₁	C₂×C₁₃	1	1	yes	characteristic
14	C₂×C₁₁×C₁₃	—	5	1	no	—
15	C₁₃×AGL(1,𝔽₅)	—	3	1	no	Hall
16	C₁₁×AGL(1,𝔽₅)	—	3	1	no	Hall
17	C₃×C₅×C₁₃	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
18	C₃×C₅×C₁₁	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
19	Dic₃×C₁₃	—	5	1	no	Hall
20	C₁₁×C₁₃	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, direct product factor, Hall
21	C₁₁×Dic₃	—	5	1	no	Hall
22	D₅×C₁₃	D₃×C₁₁	1	1	yes	characteristic
23	D₅×C₁₁	D₃×C₁₃	1	1	yes	characteristic
24	C₂×C₃×C₁₃	—	5	1	no	—
25	C₂×C₃×C₁₁	—	5	1	no	—
26	C₅×C₁₃	C₁₁×Dic₃	1	1	yes	characteristic, complemented, Hall
27	ΓL(1,𝔽₁₆)	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
28	C₅×C₁₁	Dic₃×C₁₃	1	1	yes	characteristic, complemented, Hall
29	C₄×C₁₃	—	15	1	no	Hall
30	C₄×C₁₁	—	15	1	no	Hall
31	C₃×C₁₃	C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
32	C₃×C₁₁	C₁₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
33	C₃×D₅	C₂×C₁₁×C₁₃	1	1	yes	characteristic
34	C₂×C₁₃	—	5	1	no	—
35	C₂×C₁₁	—	5	1	no	—
36	AGL(1,𝔽₅)	—	3	1	no	Hall
37	C₃×C₅	C₄×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Hall
38	C₁₃	C₁₁×ΓL(1,𝔽₁₆)	1	1	yes	characteristic, direct product factor, Sylow
39	Dic₃	—	5	1	no	Hall
40	C₁₁	C₁₃×ΓL(1,𝔽₁₆)	1	1	yes	characteristic, direct product factor, Sylow
41	D₅	D₃×C₁₁×C₁₃	1	1	yes	characteristic
42	C₂×C₃	—	5	1	no	—
43	C₅	C₁₁×Dic₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	15	1	no	Sylow
45	C₃	C₁₁×C₁₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁×C₁₃	ΓL(1,𝔽₁₆)
commutator, hypocenter	C₃×C₅	C₄×C₁₁×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₁₃	C₄
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₁₁×C₁₃

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₁₁×C₁₃	C₄	semidirect
7. C₁₃×ΓL(1,𝔽₁₆)	C₁₁	direct (N × H)
8. C₅×C₁₁×C₁₃	Dic₃	semidirect
9. C₁₁×ΓL(1,𝔽₁₆)	C₁₃	direct (N × H)
11. C₃×C₁₁×C₁₃	AGL(1,𝔽₅)	semidirect
17. C₃×C₅×C₁₃	C₄×C₁₁	semidirect
18. C₃×C₅×C₁₁	C₄×C₁₃	semidirect
20. C₁₁×C₁₃	ΓL(1,𝔽₁₆)	direct (N × H)
26. C₅×C₁₃	C₁₁×Dic₃	semidirect
27. ΓL(1,𝔽₁₆)	C₁₁×C₁₃	direct (N × H)
28. C₅×C₁₁	Dic₃×C₁₃	semidirect
31. C₃×C₁₃	C₁₁×AGL(1,𝔽₅)	semidirect
32. C₃×C₁₁	C₁₃×AGL(1,𝔽₅)	semidirect
37. C₃×C₅	C₄×C₁₁×C₁₃	semidirect
38. C₁₃	C₁₁×ΓL(1,𝔽₁₆)	direct (N × H)
40. C₁₁	C₁₃×ΓL(1,𝔽₁₆)	direct (N × H)
43. C₅	C₁₁×Dic₃×C₁₃	semidirect
45. C₃	C₁₁×C₁₃×AGL(1,𝔽₅)	semidirect

Subgroups — C11×C13×ΓL(1,𝔽16) #22575147

Conjugacy classes of subgroups

Complements

Subgroups — C₁₁×C₁₃×ΓL(1,𝔽₁₆) #22575147