Subgroups — C₉⋊#16812338 #44528131

Order 31140.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×D₈₆₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#16812338	—	3	1	no	maximal
3	C₅×C₉×C₁₇₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₉⋊#10621924	—	5	1	no	maximal, Hall
5	C₃×D₈₆₅	D₃	1	1	yes	characteristic
6	#16812338	—	9	1	no	Hall
7	C₉×D₁₇₃	—	5	1	no	—
8	C₃×C₅×C₁₇₃	Dic₃	1	1	yes	characteristic
9	C₃⋊#10621924	—	15	1	no	—
10	D₈₆₅	D₉	1	1	yes	characteristic
11	C₉×C₁₇₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₃×D₁₇₃	—	5	1	no	—
13	C₅×C₁₇₃	Dic₉	1	1	yes	characteristic, complemented, Hall
14	#10621924	—	45	1	no	Hall
15	C₃×C₁₇₃	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
16	D₁₇₃	—	5	1	no	—
17	C₉⋊AGL(1,𝔽₅)	—	173	1	no	maximal, Hall
18	C₁₇₃	C₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
19	C₉×D₅	—	173	1	no	—
20	ΓL(1,𝔽₁₆)	—	519	1	no	—
21	C₅×C₉	#10621924	1	1	yes	characteristic, complemented, Hall
22	Dic₉	—	865	1	no	Hall
23	C₃×D₅	—	173	1	no	—
24	AGL(1,𝔽₅)	—	1557	1	no	Hall
25	C₂×C₉	—	865	1	no	—
26	C₃×C₅	C₃⋊#10621924	1	1	yes	characteristic
27	Dic₃	—	2595	1	no	—
28	D₅	—	173	1	no	—
29	C₉	#16812338	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃	—	865	1	no	—
31	C₅	C₉⋊#10621924	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	7785	1	no	Sylow
33	C₃	C₃⋊#16812338	1	1	yes	characteristic
34	C₂	—	865	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₅×C₉×C₁₇₃	C₄
Frattini	C₃	C₃⋊#16812338
socle	C₃×C₅×C₁₇₃	Dic₃
prime radical	C₃×D₈₆₅	D₃
cosocle	C₉×D₈₆₅	C₂
LCS	G ▷ C₅×C₉×C₁₇₃
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.