Subgroups — (C₁₁⋊C₅)⋊Dic₁₀₉ #37561839

Order 23980.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁⋊C₅×C₁₀₉	C₂	1	1	yes	maximal, characteristic
2	C₁₁⋊C₅×C₁₀₉	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₁₉₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₁₁×C₁₀₉	C₂×C₅	1	1	yes	characteristic
5	C₅×Dic₁₀₉	—	11	1	no	maximal, Hall
6	C₁₁×C₁₀₉	C₄×C₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₅×C₁₀₉	—	11	1	no	—
8	C₅×C₁₀₉	—	11	1	no	Hall
9	Dic₁₀₉	—	55	1	no	Hall
10	Dic₁₁⋊C₅	—	109	1	no	maximal, Hall
11	C₂×C₁₀₉	AGL(1,𝔽₁₁)	1	1	yes	characteristic
12	C₂×C₁₁⋊C₅	D₁₀₉	1	1	yes	characteristic
13	C₁₀₉	Dic₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
14	C₁₁⋊C₅	Dic₁₀₉	1	1	yes	characteristic, complemented, Hall
15	Dic₁₁	—	109	1	no	Hall
16	C₂×C₁₁	C₅×D₁₀₉	1	1	yes	characteristic
17	C₄×C₅	—	1199	1	no	Hall
18	C₁₁	C₅×Dic₁₀₉	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅	—	11	1	no	—
20	C₅	—	11	1	no	Sylow
21	C₄	—	5995	1	no	Sylow
22	C₂	(C₁₁⋊C₅)⋊D₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	(C₁₁⋊C₅)⋊D₁₀₉
commutator, hypocenter	C₁₁×C₁₀₉	C₄×C₅
Fitting, socle, cosocle	C₂×C₁₁×C₁₀₉	C₂×C₅
prime radical	C₂×C₁₁⋊C₅×C₁₀₉	C₂
LCS	G ▷ C₁₁×C₁₀₉
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.