Subgroups — PGL(2,𝔽₉) #10624295

Order 720.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	A₆	C₂	1	1	yes	maximal, characteristic, complemented
2	AGL(1,𝔽₉)	—	10	1	no	maximal
3	A₅	—	12	1	no	—
4	#157	—	10	1	no	—
5	S₄	—	30	1	no	—
6	C₂×D₅	—	36	1	no	maximal
7	C₃⋊D₃	—	10	1	no	—
8	D₈	—	45	1	no	maximal, Sylow
9	A₄	—	30	1	no	—
10	C₂×C₅	—	36	1	no	—
11	D₅	—	36	1	no	—
12	D₅	—	36	1	no	—
13	C₃²	—	10	1	no	Sylow
14	D₄	—	45	1	no	—
15	D₄	—	45	1	no	—
16	C₈	—	45	1	no	—
17	D₃	—	120	1	no	—
18	C₅	—	36	1	no	Sylow
19	C₂²	—	30	1	no	—
20	C₂²	—	90	1	no	—
21	C₄	—	45	1	no	—
22	C₃	—	40	1	no	—
23	C₂	—	36	1	no	—
24	C₂	—	45	1	no	—

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

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

N	H ≅ G/N	type
1. A₆	C₂	semidirect

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