Subgroups — SL(2,𝔽₁₆) #72209607

Order 4080.

21 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	AGL(1,𝔽₁₆)	—	17	1	no	maximal, Hall
2	C₂⁴⋊C₅	—	17	1	no	Hall
3	A₅	—	68	1	no	maximal
4	C₂²⋊A₄	—	17	1	no	Hall
5	D₁₇	—	120	1	no	maximal
6	D₁₅	—	136	1	no	maximal
7	C₁₇	—	120	1	no	Sylow
8	C₂⁴	—	17	1	no	Sylow
9	C₃×C₅	—	136	1	no	Hall
10	A₄	—	340	1	no	—
11	D₅	—	408	1	no	—
12	C₂³	—	255	1	no	—
13	D₃	—	680	1	no	—
14	C₅	—	136	1	no	Sylow
15	C₂²	—	85	1	no	—
16	C₂²	—	255	2	no	—
17	C₃	—	136	1	no	Sylow
18	C₂	—	255	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	G	C₁
LCS	G
UCS	C₁

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