Subgroups — C₂×C₅⋊(D₄₀₉⋊C₃) #37589350

Order 24540.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊(D₄₀₉⋊C₃)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₄₀₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₀₄₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×C₄₀₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₄₀₉⋊C₃	—	5	1	no	maximal, Hall
6	C₂×C₅×C₄₀₉	C₂×C₃	1	1	yes	characteristic, complemented
7	D₂₀₄₅	C₂×C₃	1	2	yes	complemented
8	C₂×C₄₀₉⋊C₃	D₅	1	1	yes	characteristic, complemented
9	D₄₀₉⋊C₃	—	5	2	no	—
10	C₅×C₄₀₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×D₄₀₉	—	5	1	no	Hall
12	C₄₀₉⋊C₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
13	C₂×C₄₀₉	C₃×D₅	1	1	yes	characteristic, complemented
14	D₄₀₉	—	5	2	no	—
15	C₄₀₉	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃×D₅	—	409	1	no	maximal, Hall
17	C₂×C₃×C₅	—	818	1	no	—
18	C₃×D₅	—	409	2	no	—
19	C₂×D₅	—	409	1	no	Hall
20	C₃×C₅	—	818	1	no	Hall
21	C₂²×C₃	—	2045	1	no	Hall
22	C₂×C₅	D₄₀₉⋊C₃	1	1	yes	characteristic, complemented
23	D₅	—	409	2	no	—
24	C₂×C₃	—	818	1	no	—
25	C₂×C₃	—	2045	2	no	—
26	C₅	C₂×D₄₀₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₂²	—	2045	1	no	Sylow
28	C₃	—	818	1	no	Sylow
29	C₂	—	2045	2	no	—
30	C₂	C₅⋊(D₄₀₉⋊C₃)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₅⋊(D₄₀₉⋊C₃)
commutator, cosocle, hypocenter	C₅×C₄₀₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₄₀₉	C₂×C₃
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.