Subgroups — SL(2,𝔽₉) #10623940

Order 720.

27 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	SL(2,𝔽₅)	—	6	2	no	maximal
2	#622	—	10	1	no	maximal
3	#226	—	15	2	no	maximal
4	C₃⋊Dic₃	—	10	1	no	—
5	SL(2,𝔽₃)	—	15	2	no	—
6	Dic₅	—	36	1	no	—
7	C₂×C₃²	—	10	1	no	—
8	Q₁₆	—	45	1	no	Sylow
9	Dic₃	—	60	2	no	—
10	C₂×C₅	—	36	1	no	—
11	C₃²	—	10	1	no	Sylow
12	Q₈	—	15	2	no	—
13	C₈	—	45	1	no	—
14	C₂×C₃	—	20	2	no	—
15	C₅	—	36	1	no	Sylow
16	C₄	—	45	1	no	—
17	C₃	—	20	2	no	—
18	C₂	A₆	1	1	yes	maximal normal, characteristic

	subgroup	G/H
center, Frattini, Fitting, socle, cosocle, hypercenter	C₂	A₆
commutator, hypocenter	G	C₁
LCS	G
UCS	C₁ ◁ C₂

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