Subgroups — C₉⋊#16813738 #45656382

Order 32580.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×D₉₀₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#16813738	—	3	1	no	maximal
3	C₅×C₉×C₁₈₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₉⋊#10624382	—	5	1	no	maximal, Hall
5	C₃×D₉₀₅	D₃	1	1	yes	characteristic
6	#16813738	—	9	1	no	Hall
7	C₉×D₁₈₁	—	5	1	no	—
8	C₃×C₅×C₁₈₁	Dic₃	1	1	yes	characteristic
9	C₃⋊#10624382	—	15	1	no	—
10	D₉₀₅	D₉	1	1	yes	characteristic
11	C₉×C₁₈₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₃×D₁₈₁	—	5	1	no	—
13	C₅×C₁₈₁	Dic₉	1	1	yes	characteristic, complemented, Hall
14	#10624382	—	45	1	no	Hall
15	C₃×C₁₈₁	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
16	D₁₈₁	—	5	1	no	—
17	C₁₈₁	C₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
18	C₉⋊AGL(1,𝔽₅)	—	181	1	no	maximal, Hall
19	C₉×D₅	—	181	1	no	—
20	ΓL(1,𝔽₁₆)	—	543	1	no	—
21	C₅×C₉	#10624382	1	1	yes	characteristic, complemented, Hall
22	Dic₉	—	905	1	no	Hall
23	C₃×D₅	—	181	1	no	—
24	AGL(1,𝔽₅)	—	1629	1	no	Hall
25	C₂×C₉	—	905	1	no	—
26	C₃×C₅	C₃⋊#10624382	1	1	yes	characteristic
27	Dic₃	—	2715	1	no	—
28	D₅	—	181	1	no	—
29	C₉	#16813738	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃	—	905	1	no	—
31	C₅	C₉⋊#10624382	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	8145	1	no	Sylow
33	C₃	C₃⋊#16813738	1	1	yes	characteristic
34	C₂	—	905	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₅×C₉×C₁₈₁	C₄
Frattini	C₃	C₃⋊#16813738
socle	C₃×C₅×C₁₈₁	Dic₃
prime radical	C₃×D₉₀₅	D₃
cosocle	C₉×D₉₀₅	C₂
LCS	G ▷ C₅×C₉×C₁₈₁
UCS	C₁

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.