Subgroups — Dic₁₀₅ #88286

Order 420.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₇	C₂	1	1	yes	maximal, characteristic
2	Dic₃₅	—	3	1	no	maximal, Hall
3	C₃×C₅×C₇	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₂₁	—	5	1	no	maximal, Hall
5	C₂×C₅×C₇	D₃	1	1	yes	characteristic
6	Dic₁₅	—	7	1	no	maximal, Hall
7	C₂×C₃×C₇	D₅	1	1	yes	characteristic
8	C₅×C₇	Dic₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₅	D₇	1	1	yes	characteristic
10	Dic₇	—	15	1	no	Hall
11	C₃×C₇	Dic₅	1	1	yes	characteristic, complemented, Hall
12	Dic₅	—	21	1	no	Hall
13	C₃×C₅	Dic₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₇	D₁₅	1	1	yes	characteristic
15	Dic₃	—	35	1	no	Hall
16	C₂×C₅	D₂₁	1	1	yes	characteristic
17	C₇	Dic₁₅	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃	D₃₅	1	1	yes	characteristic
19	C₅	Dic₂₁	1	1	yes	characteristic, complemented, Sylow
20	C₄	—	105	1	no	Sylow
21	C₃	Dic₃₅	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₁₀₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₀₅
commutator, hypocenter	C₃×C₅×C₇	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₅×C₇	C₂
LCS	G ▷ C₃×C₅×C₇
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.