Subgroups — Dic₁₅₁₃₅ #72292604

Order 60540.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₁₀₀₉	C₂	1	1	yes	maximal, characteristic
2	Dic₅₀₄₅	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₀₀₉	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₃₀₂₇	—	5	1	no	maximal, Hall
5	C₂×C₅×C₁₀₀₉	D₃	1	1	yes	characteristic
6	C₂×C₃×C₁₀₀₉	D₅	1	1	yes	characteristic
7	C₅×C₁₀₀₉	Dic₃	1	1	yes	characteristic, complemented, Hall
8	Dic₁₀₀₉	—	15	1	no	Hall
9	C₃×C₁₀₀₉	Dic₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₀₀₉	D₁₅	1	1	yes	characteristic
11	C₁₀₀₉	Dic₁₅	1	1	yes	characteristic, complemented, Sylow
12	Dic₁₅	—	1009	1	no	maximal, Hall
13	C₂×C₃×C₅	D₁₀₀₉	1	1	yes	characteristic
14	Dic₅	—	3027	1	no	Hall
15	C₃×C₅	Dic₁₀₀₉	1	1	yes	characteristic, complemented, Hall
16	Dic₃	—	5045	1	no	Hall
17	C₂×C₅	D₃₀₂₇	1	1	yes	characteristic
18	C₂×C₃	D₅₀₄₅	1	1	yes	characteristic
19	C₅	Dic₃₀₂₇	1	1	yes	characteristic, complemented, Sylow
20	C₄	—	15135	1	no	Sylow
21	C₃	Dic₅₀₄₅	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₁₅₁₃₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₅₁₃₅
commutator, hypocenter	C₃×C₅×C₁₀₀₉	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₅×C₁₀₀₉	C₂
LCS	G ▷ C₃×C₅×C₁₀₀₉
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.