Subgroups — Dic₂₀₄₅⋊C₃ #37589340

Order 24540.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₄₀₉⋊C₃	C₂	1	1	yes	maximal, characteristic
2	Dic₂₀₄₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₄₀₉⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₄₀₉⋊C₃	—	5	1	no	maximal, Hall
5	C₂×C₅×C₄₀₉	C₂×C₃	1	1	yes	characteristic
6	C₂×C₄₀₉⋊C₃	D₅	1	1	yes	characteristic
7	C₅×C₄₀₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	Dic₄₀₉	—	5	1	no	Hall
9	C₄₀₉⋊C₃	Dic₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₄₀₉	C₃×D₅	1	1	yes	characteristic
11	C₄₀₉	C₃×Dic₅	1	1	yes	characteristic, complemented, Sylow
12	C₃×Dic₅	—	409	1	no	maximal, Hall
13	C₂×C₃×C₅	—	818	1	no	—
14	Dic₅	—	409	1	no	Hall
15	C₃×C₅	—	818	1	no	Hall
16	C₃×C₄	—	2045	1	no	Hall
17	C₂×C₅	D₄₀₉⋊C₃	1	1	yes	characteristic
18	C₂×C₃	—	818	1	no	—
19	C₅	Dic₄₀₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
20	C₄	—	2045	1	no	Sylow
21	C₃	—	818	1	no	Sylow
22	C₂	C₅⋊(D₄₀₉⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₅⋊(D₄₀₉⋊C₃)
commutator, hypocenter	C₅×C₄₀₉	C₃×C₄
Fitting, socle, cosocle	C₂×C₅×C₄₀₉	C₂×C₃
prime radical	C₂×C₅×C₄₀₉⋊C₃	C₂
LCS	G ▷ C₅×C₄₀₉
UCS	C₁ ◁ C₂

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.