Subgroups — #13088276

Order 1440.

33 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	SL(2,𝔽₉)	C₂	1	1	yes	maximal, characteristic, complemented
2	#3771	—	10	1	no	maximal
3	SL(2,𝔽₅)	—	12	1	no	—
4	#622	—	10	1	no	—
5	#226	—	30	1	no	—
6	C₂²⋊D₅	—	36	1	no	maximal
7	C₃⋊Dic₃	—	10	1	no	—
8	SD₃₂	—	45	1	no	maximal, Sylow
9	SL(2,𝔽₃)	—	30	1	no	—
10	C₂²×C₅	—	36	1	no	—
11	C₂×D₅	—	36	1	no	—
12	Dic₅	—	36	1	no	—
13	C₂×C₃²	—	10	1	no	—
14	Q₁₆	—	45	1	no	—
15	D₈	—	45	1	no	—
16	C₁₆	—	45	1	no	—
17	Dic₃	—	120	1	no	—
18	C₂×C₅	—	36	1	no	—
19	C₂×C₅	—	72	1	no	—
20	D₅	—	72	1	no	—
21	C₃²	—	10	1	no	Sylow
22	Q₈	—	30	1	no	—
23	D₄	—	90	1	no	—
24	C₈	—	45	1	no	—
25	C₂×C₃	—	40	1	no	—
26	C₅	—	36	1	no	Sylow
27	C₂²	—	36	1	no	—
28	C₄	—	45	1	no	—
29	C₃	—	40	1	no	—
30	C₂	—	72	1	no	—
31	C₂	PGL(2,𝔽₉)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, Fitting, socle, hypercenter	C₂	PGL(2,𝔽₉)
commutator, cosocle, hypocenter	SL(2,𝔽₉)	C₂
LCS	G ▷ SL(2,𝔽₉)
UCS	C₁ ◁ C₂

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

N	H ≅ G/N	type
1. SL(2,𝔽₉)	C₂	semidirect

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