Subgroups — C₂₃⋊(#261⋊C₉) #24924479

Order 10764.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×D₁₃⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₂₃⋊#261	C₃	1	1	yes	maximal, characteristic
3	C₂₃×C₁₃⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₂₃×D₁₃	C₂×C₃	1	1	yes	characteristic
5	C₂₃⋊#261	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₃×C₂₃	C₃×C₄	1	1	yes	characteristic
7	C₉×Dic₂₃	—	13	1	no	maximal, Hall
8	C₂₃×D₁₃	C₂×C₉	1	1	yes	characteristic
9	#261⋊C₉	—	23	1	no	maximal, Hall
10	C₂×C₉×C₂₃	—	13	1	no	—
11	C₁₃×C₂₃	C₄×C₉	1	1	yes	characteristic, complemented, Hall
12	C₃×Dic₂₃	—	13	1	no	—
13	D₁₃⋊C₉	D₂₃	1	1	yes	characteristic
14	C₉×C₂₃	—	13	1	no	Hall
15	C₃×#261	—	23	1	no	—
16	C₂×C₃×C₂₃	—	13	1	no	—
17	C₁₃⋊C₉	Dic₂₃	1	1	yes	characteristic, complemented, Hall
18	Dic₂₃	—	13	1	no	Hall
19	C₃×D₁₃	C₃×D₂₃	1	1	yes	characteristic
20	C₃×C₂₃	AGL(1,𝔽₁₃)	1	1	yes	characteristic
21	#261	—	23	1	no	Hall
22	C₂×C₂₃	—	13	1	no	—
23	C₃×C₁₃	C₃×Dic₂₃	1	1	yes	characteristic
24	C₄×C₉	—	299	1	no	Hall
25	D₁₃	C₉×D₂₃	1	1	yes	characteristic
26	C₂₃	#261⋊C₉	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₉	—	13	1	no	—
28	C₁₃	C₉×Dic₂₃	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₄	—	299	1	no	—
30	C₉	—	13	1	no	Sylow
31	C₂×C₃	—	13	1	no	—
32	C₄	—	299	1	no	Sylow
33	C₃	C₂₃⋊AGL(1,𝔽₁₃)	1	1	yes	characteristic
34	C₂	—	13	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₂₃⋊AGL(1,𝔽₁₃)
commutator, hypocenter	C₁₃×C₂₃	C₄×C₉
Fitting, socle	C₃×C₁₃×C₂₃	C₃×C₄
prime radical, cosocle	C₃×C₂₃×D₁₃	C₂×C₃
LCS	G ▷ C₁₃×C₂₃
UCS	C₁ ◁ C₃

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