Subgroups — C₃×Dic₁₃×C₁₀₃ #30632537

Order 16068.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₃×C₁₀₃	C₂	1	1	yes	maximal, characteristic
2	Dic₁₃×C₁₀₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₃×C₁₀₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₃×C₁₀₃	C₂×C₃	1	1	yes	characteristic
5	C₁₃×C₁₀₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×C₄×C₁₀₃	—	13	1	no	maximal, Hall
7	C₂×C₃×C₁₀₃	D₁₃	1	1	yes	characteristic
8	C₄×C₁₀₃	—	13	1	no	Hall
9	C₃×C₁₀₃	Dic₁₃	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₀₃	C₃×D₁₃	1	1	yes	characteristic
11	C₃×Dic₁₃	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₀₃	C₃×Dic₁₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₃×C₁₃	C₂×C₁₀₃	1	1	yes	characteristic
14	Dic₁₃	C₃×C₁₀₃	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₁₃	C₄×C₁₀₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₃	C₂×C₃×C₁₀₃	1	1	yes	characteristic
17	C₁₃	C₃×C₄×C₁₀₃	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	13	1	no	Hall
19	C₂×C₃	D₁₃×C₁₀₃	1	1	yes	characteristic
20	C₄	—	13	1	no	Sylow
21	C₃	Dic₁₃×C₁₀₃	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×D₁₃×C₁₀₃	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.