Subgroups — C₂₃⋊(C₄₃⋊AGL(1,𝔽₅)) #34089915

Order 19780.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₂₃×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₂₃×C₄₃	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₉₈₉	—	5	1	no	maximal, Hall
4	C₂×C₂₃×C₄₃	—	5	1	no	—
5	C₂₃×C₄₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
6	C₄₃⋊AGL(1,𝔽₅)	—	23	1	no	maximal, Hall
7	C₂₃⋊AGL(1,𝔽₅)	—	43	1	no	maximal, Hall
8	D₅×C₄₃	D₂₃	1	1	yes	characteristic
9	D₅×C₂₃	D₄₃	1	1	yes	characteristic
10	C₅×C₄₃	Dic₂₃	1	1	yes	characteristic, complemented, Hall
11	Dic₄₃	—	115	1	no	Hall
12	C₅×C₂₃	Dic₄₃	1	1	yes	characteristic, complemented, Hall
13	Dic₂₃	—	215	1	no	Hall
14	C₂×C₄₃	—	5	1	no	—
15	C₂×C₂₃	—	5	1	no	—
16	C₄₃	C₂₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
17	C₂₃	C₄₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
18	AGL(1,𝔽₅)	—	989	1	no	Hall
19	D₅	D₉₈₉	1	1	yes	characteristic
20	C₅	Dic₉₈₉	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	4945	1	no	Sylow
22	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₂₃×C₄₃	C₄
prime radical, cosocle	D₅×C₂₃×C₄₃	C₂
LCS	G ▷ C₅×C₂₃×C₄₃
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.