Subgroups — Dic₃₆₁₅ #28385997

Order 14460.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₂₄₁	C₂	1	1	yes	maximal, characteristic
2	Dic₁₂₀₅	—	3	1	no	maximal, Hall
3	C₃×C₅×C₂₄₁	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₇₂₃	—	5	1	no	maximal, Hall
5	C₂×C₅×C₂₄₁	D₃	1	1	yes	characteristic
6	C₂×C₃×C₂₄₁	D₅	1	1	yes	characteristic
7	C₅×C₂₄₁	Dic₃	1	1	yes	characteristic, complemented, Hall
8	Dic₂₄₁	—	15	1	no	Hall
9	C₃×C₂₄₁	Dic₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₂₄₁	D₁₅	1	1	yes	characteristic
11	C₂₄₁	Dic₁₅	1	1	yes	characteristic, complemented, Sylow
12	Dic₁₅	—	241	1	no	maximal, Hall
13	C₂×C₃×C₅	D₂₄₁	1	1	yes	characteristic
14	Dic₅	—	723	1	no	Hall
15	C₃×C₅	Dic₂₄₁	1	1	yes	characteristic, complemented, Hall
16	Dic₃	—	1205	1	no	Hall
17	C₂×C₅	D₇₂₃	1	1	yes	characteristic
18	C₂×C₃	D₁₂₀₅	1	1	yes	characteristic
19	C₅	Dic₇₂₃	1	1	yes	characteristic, complemented, Sylow
20	C₄	—	3615	1	no	Sylow
21	C₃	Dic₁₂₀₅	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₃₆₁₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃₆₁₅
commutator, hypocenter	C₃×C₅×C₂₄₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₅×C₂₄₁	C₂
LCS	G ▷ C₃×C₅×C₂₄₁
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.