Subgroups — C₂₃⋊#10596814 #27211113

Order 13340.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×D₁₄₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₂₃×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₂₃⋊#1181	—	5	1	no	maximal, Hall
4	C₂₃×D₂₉	—	5	1	no	—
5	C₂₃×C₂₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
6	#10596814	—	23	1	no	maximal, Hall
7	C₂₃⋊AGL(1,𝔽₅)	—	29	1	no	maximal, Hall
8	D₁₄₅	D₂₃	1	1	yes	characteristic
9	D₅×C₂₃	—	29	1	no	—
10	C₅×C₂₉	Dic₂₃	1	1	yes	characteristic, complemented, Hall
11	#1181	—	115	1	no	Hall
12	C₅×C₂₃	#1181	1	1	yes	characteristic, complemented, Hall
13	Dic₂₃	—	145	1	no	Hall
14	D₂₉	—	5	1	no	—
15	C₂×C₂₃	—	145	1	no	—
16	C₂₉	C₂₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
17	C₂₃	#10596814	1	1	yes	characteristic, complemented, Sylow
18	AGL(1,𝔽₅)	—	667	1	no	Hall
19	D₅	—	29	1	no	—
20	C₅	C₂₃⋊#1181	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	3335	1	no	Sylow
22	C₂	—	145	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₂₃×C₂₉	C₄
prime radical, cosocle	C₂₃×D₁₄₅	C₂
LCS	G ▷ C₅×C₂₃×C₂₉
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.