Subgroups — C₁₀₉×Dic₆₉ #44473783

Order 30084.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂₃×C₁₀₉	C₂	1	1	yes	maximal, characteristic
2	Dic₂₃×C₁₀₉	—	3	1	no	maximal, Hall
3	C₃×C₂₃×C₁₀₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₂₃×C₁₀₉	D₃	1	1	yes	characteristic
5	C₂₃×C₁₀₉	Dic₃	1	1	yes	characteristic, complemented, Hall
6	Dic₃×C₁₀₉	—	23	1	no	maximal, Hall
7	C₂×C₃×C₁₀₉	D₂₃	1	1	yes	characteristic
8	C₄×C₁₀₉	—	69	1	no	Hall
9	C₃×C₁₀₉	Dic₂₃	1	1	yes	characteristic, complemented, Hall
10	Dic₆₉	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₁₀₉	D₆₉	1	1	yes	characteristic
12	C₂×C₃×C₂₃	C₂×C₁₀₉	1	1	yes	characteristic
13	C₁₀₉	Dic₆₉	1	1	yes	characteristic, direct product factor, Sylow
14	Dic₂₃	—	3	1	no	Hall
15	C₃×C₂₃	C₄×C₁₀₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₂₃	D₃×C₁₀₉	1	1	yes	characteristic
17	C₂₃	Dic₃×C₁₀₉	1	1	yes	characteristic, complemented, Sylow
18	Dic₃	—	23	1	no	Hall
19	C₂×C₃	D₂₃×C₁₀₉	1	1	yes	characteristic
20	C₄	—	69	1	no	Sylow
21	C₃	Dic₂₃×C₁₀₉	1	1	yes	characteristic, complemented, Sylow
22	C₂	C₁₀₉×D₆₉	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.