Subgroups — C₅×Dic₁₄₀₃ #43242597

Order 28060.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₂₃×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₂₃×C₆₁	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₄₀₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₂₃×C₆₁	C₂×C₅	1	1	yes	characteristic
5	C₂₃×C₆₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
6	C₅×Dic₆₁	—	23	1	no	maximal, Hall
7	C₂×C₅×C₆₁	D₂₃	1	1	yes	characteristic
8	C₅×Dic₂₃	—	61	1	no	maximal, Hall
9	C₅×C₆₁	Dic₂₃	1	1	yes	characteristic, complemented, Hall
10	Dic₆₁	—	23	1	no	Hall
11	C₂×C₅×C₂₃	D₆₁	1	1	yes	characteristic
12	C₂×C₆₁	C₅×D₂₃	1	1	yes	characteristic
13	C₅×C₂₃	Dic₆₁	1	1	yes	characteristic, complemented, Hall
14	Dic₂₃	—	61	1	no	Hall
15	C₆₁	C₅×Dic₂₃	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₂₃	C₅×D₆₁	1	1	yes	characteristic
17	C₂₃	C₅×Dic₆₁	1	1	yes	characteristic, complemented, Sylow
18	C₄×C₅	—	1403	1	no	Hall
19	C₂×C₅	D₁₄₀₃	1	1	yes	characteristic
20	C₅	Dic₁₄₀₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	1403	1	no	Sylow
22	C₂	C₅×D₁₄₀₃	1	1	yes	characteristic

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.