Subgroups — AΓL(1,𝔽₁₆) #11757164

Order 960.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	((C₂⁴⋊C₅)⋊C₂)⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#66297	—	3	1	no	maximal, Hall
3	AGL(1,𝔽₁₆)	C₄	1	1	yes	characteristic, complemented
4	#4625	—	5	1	no	maximal, Hall
5	(C₂⁴⋊C₅)⋊C₂	D₃	1	1	yes	characteristic
6	#120⋊C₃	—	5	1	no	—
7	C₂⁴⋊C₅	Dic₃	1	1	yes	characteristic, complemented
8	AΣL(1,𝔽₁₆)	—	15	1	no	Sylow
9	ΓL(1,𝔽₁₆)	—	16	1	no	maximal
10	C₂²⋊A₄	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
11	SL(2,ℤ/4)	—	20	1	no	—
12	#120	—	5	1	no	—
13	#100	—	15	1	no	—
14	#99	—	15	1	no	—
15	C₃×D₅	—	16	1	no	—
16	C₂×A₄	—	20	1	no	—
17	AGL(1,𝔽₅)	—	48	1	no	—
18	C₂⁴	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
19	C₂×D₄	—	15	1	no	—
20	M₁₆	—	30	1	no	—
21	C₂²⋊C₄	—	15	1	no	—
22	C₂²⋊C₄	—	30	1	no	—
23	C₃×C₅	—	16	1	no	Hall
24	A₄	—	20	1	no	—
25	Dic₃	—	80	1	no	—
26	D₅	—	16	1	no	—
27	C₂³	—	5	1	no	—
28	C₂³	—	15	1	no	—
29	D₄	—	60	1	no	—
30	C₂×C₄	—	15	1	no	—
31	C₂×C₄	—	60	1	no	—
32	C₈	—	60	1	no	—
33	C₂×C₃	—	80	1	no	—
34	C₅	—	16	1	no	Sylow
35	C₂²	—	5	1	no	—
36	C₂²	—	30	1	no	—
37	C₂²	—	30	1	no	—
38	C₄	—	30	1	no	—
39	C₄	—	120	1	no	—
40	C₃	—	16	1	no	Sylow
41	C₂	—	15	1	no	—
42	C₂	—	20	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	AGL(1,𝔽₁₆)	C₄
Fitting, socle	C₂⁴	ΓL(1,𝔽₁₆)
prime radical, cosocle	((C₂⁴⋊C₅)⋊C₂)⋊C₃	C₂
LCS	G ▷ AGL(1,𝔽₁₆)
UCS	C₁

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

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