Subgroups — C₅⋊(D₂₂₉⋊C₉) #35207293

Order 20610.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₂₉⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₁₁₄₅	C₃	1	1	yes	maximal, characteristic
3	D₂₂₉⋊C₉	—	5	1	no	maximal, Hall
4	C₃×C₅×C₂₂₉	C₂×C₃	1	1	yes	characteristic
5	D₁₁₄₅	C₉	1	1	yes	characteristic, complemented, Hall
6	C₂₂₉⋊C₉	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃×D₂₂₉	—	5	1	no	—
8	C₅×C₂₂₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₃×C₂₂₉	C₃×D₅	1	1	yes	characteristic
10	D₂₂₉	—	5	1	no	Hall
11	C₂₂₉	C₉×D₅	1	1	yes	characteristic, complemented, Sylow
12	C₉×D₅	—	229	1	no	maximal, Hall
13	C₅×C₉	—	229	1	no	Hall
14	C₃×D₅	—	687	1	no	—
15	C₂×C₉	—	1145	1	no	Hall
16	C₃×C₅	D₂₂₉⋊C₃	1	1	yes	characteristic
17	D₅	—	687	1	no	Hall
18	C₉	—	229	1	no	Sylow
19	C₂×C₃	—	3435	1	no	—
20	C₅	D₂₂₉⋊C₉	1	1	yes	characteristic, complemented, Sylow
21	C₃	C₅⋊(D₂₂₉⋊C₃)	1	1	yes	characteristic
22	C₂	—	3435	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₅⋊(D₂₂₉⋊C₃)
commutator, hypocenter	C₅×C₂₂₉	C₂×C₉
Fitting, socle, cosocle	C₃×C₅×C₂₂₉	C₂×C₃
prime radical	C₃×D₁₁₄₅	C₃
LCS	G ▷ C₅×C₂₂₉
UCS	C₁ ◁ C₃

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.