Subgroups — C₃×C₅×Dic₄₀₉ #37589331

Order 24540.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₄₀₉	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₄₀₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₄₀₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×Dic₄₀₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₄₀₉	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃×C₄₀₉	C₂×C₅	1	1	yes	characteristic
7	C₅×C₄₀₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	Dic₄₀₉	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₄₀₉	C₄×C₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₄₀₉	C₂×C₃×C₅	1	1	yes	characteristic
11	C₄₀₉	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Sylow
12	C₃×C₄×C₅	—	409	1	no	maximal, Hall
13	C₂×C₃×C₅	D₄₀₉	1	1	yes	characteristic
14	C₄×C₅	—	409	1	no	Hall
15	C₃×C₅	Dic₄₀₉	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₄	—	409	1	no	Hall
17	C₂×C₅	C₃×D₄₀₉	1	1	yes	characteristic
18	C₂×C₃	C₅×D₄₀₉	1	1	yes	characteristic
19	C₅	C₃×Dic₄₀₉	1	1	yes	characteristic, direct product factor, Sylow
20	C₄	—	409	1	no	Sylow
21	C₃	C₅×Dic₄₀₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×C₅×D₄₀₉	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.