Subgroups — C₄₃×C₂₃⋊AGL(1,𝔽₅) #34089914

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	C₄₃×Dic₂₃	—	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	AGL(1,𝔽₅)×C₄₃	—	23	1	no	maximal, Hall
7	C₂₃⋊AGL(1,𝔽₅)	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	D₅×C₄₃	D₂₃	1	1	yes	characteristic
9	D₅×C₂₃	C₂×C₄₃	1	1	yes	characteristic
10	C₅×C₄₃	Dic₂₃	1	1	yes	characteristic, complemented, Hall
11	C₄×C₄₃	—	115	1	no	Hall
12	C₅×C₂₃	C₄×C₄₃	1	1	yes	characteristic, complemented, Hall
13	Dic₂₃	—	5	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, direct product factor, Sylow
17	C₂₃	AGL(1,𝔽₅)×C₄₃	1	1	yes	characteristic, complemented, Sylow
18	AGL(1,𝔽₅)	—	23	1	no	Hall
19	D₅	C₄₃×D₂₃	1	1	yes	characteristic
20	C₅	C₄₃×Dic₂₃	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	115	1	no	Sylow
22	C₂	—	5	1	no	—

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.