Subgroups — C₅×C₁₁×Dic₁₀₉ #37561830

Order 23980.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₁×C₁₀₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₁×C₁₀₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁×Dic₁₀₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₁₁×C₁₀₉	C₂×C₅	1	1	yes	characteristic
5	C₅×Dic₁₀₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×C₁₀₉	C₄×C₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₅×C₁₀₉	C₂×C₁₁	1	1	yes	characteristic
8	C₅×C₁₀₉	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
9	Dic₁₀₉	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
10	C₄×C₅×C₁₁	—	109	1	no	maximal, Hall
11	C₂×C₁₀₉	C₂×C₅×C₁₁	1	1	yes	characteristic
12	C₂×C₅×C₁₁	D₁₀₉	1	1	yes	characteristic
13	C₁₀₉	C₄×C₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
14	C₅×C₁₁	Dic₁₀₉	1	1	yes	characteristic, direct product factor, Hall
15	C₄×C₁₁	—	109	1	no	Hall
16	C₂×C₁₁	C₅×D₁₀₉	1	1	yes	characteristic
17	C₄×C₅	—	109	1	no	Hall
18	C₁₁	C₅×Dic₁₀₉	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₅	C₁₁×D₁₀₉	1	1	yes	characteristic
20	C₅	C₁₁×Dic₁₀₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	109	1	no	Sylow
22	C₂	C₅×C₁₁×D₁₀₉	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.