Subgroups — C₂×AGL(1,𝔽₁₆) #92114

Order 480.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	AGL(1,𝔽₁₆)	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂×C₂⁴⋊C₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₂²⋊A₄	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂⁴⋊C₅	C₂×C₃	1	1	yes	characteristic, complemented
5	C₂²⋊A₄	C₂×C₅	1	1	yes	characteristic, complemented
6	C₂⁵	C₃×C₅	1	1	yes	characteristic, complemented, Sylow
7	C₂×C₃×C₅	—	16	1	no	maximal
8	C₂×A₄	—	20	1	no	—
9	C₂⁴	—	15	1	no	—
10	C₂⁴	—	15	1	no	—
11	C₂⁴	C₂×C₃×C₅	1	1	yes	characteristic, complemented
12	C₃×C₅	—	16	1	no	Hall
13	A₄	—	20	1	no	—
14	C₂×C₅	—	16	1	no	—
15	C₂³	—	5	1	no	—
16	C₂³	—	15	1	no	—
17	C₂³	—	15	1	no	—
18	C₂³	—	15	2	no	—
19	C₂³	—	15	6	no	—
20	C₂×C₃	—	16	1	no	—
21	C₅	—	16	1	no	Sylow
22	C₂²	—	5	1	no	—
23	C₂²	—	15	2	no	—
24	C₂²	—	15	1	no	—
25	C₂²	—	15	6	no	—
26	C₂²	—	15	1	no	—
27	C₃	—	16	1	no	Sylow
28	C₂	—	15	1	no	—
29	C₂	—	15	1	no	—
30	C₂	AGL(1,𝔽₁₆)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	AGL(1,𝔽₁₆)
commutator, cosocle, hypocenter	C₂⁴	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂⁵	C₃×C₅
LCS	G ▷ C₂⁴
UCS	C₁ ◁ C₂

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.