Subgroups — Dic₃×C₁₁⋊C₅ #10620332

Order 660.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₁⋊C₅	—	3	1	no	maximal, Hall
3	C₃×C₁₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁×Dic₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₁₁⋊C₅	D₃	1	1	yes	characteristic
6	C₂×C₃×C₁₁	C₂×C₅	1	1	yes	characteristic
7	C₅×Dic₃	—	11	1	no	maximal, Hall
8	C₁₁⋊C₅	Dic₃	1	1	yes	characteristic, direct product factor, Hall
9	C₄×C₁₁	—	3	1	no	Hall
10	C₃×C₁₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₅	—	11	1	no	—
12	C₂×C₁₁	C₅×D₃	1	1	yes	characteristic
13	C₄×C₅	—	33	1	no	Hall
14	C₃×C₅	—	11	1	no	Hall
15	Dic₃	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
16	C₁₁	C₅×Dic₃	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₅	—	11	1	no	—
18	C₂×C₃	C₂×C₁₁⋊C₅	1	1	yes	characteristic
19	C₅	—	11	1	no	Sylow
20	C₄	—	3	1	no	Sylow
21	C₃	C₄×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₃×C₁₁⋊C₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×C₁₁⋊C₅
commutator, hypocenter	C₃×C₁₁	C₄×C₅
Fitting, socle, cosocle	C₂×C₃×C₁₁	C₂×C₅
prime radical	C₂×C₃×C₁₁⋊C₅	C₂
LCS	G ▷ C₃×C₁₁
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.