Subgroups — #89170

Order 440.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₅₅	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₁₁	C₂	1	1	yes	maximal, characteristic
3	C₁₁×Dic₅	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×C₁₁	C₂²	1	1	yes	characteristic
5	Dic₂₂	—	5	1	no	maximal, Hall
6	C₅×C₁₁	Q₈	1	1	yes	characteristic, complemented, Hall
7	C₄×C₁₁	—	5	1	no	—
8	Dic₁₁	—	5	1	no	—
9	Dic₁₁	D₅	1	1	yes	characteristic
10	Dic₁₀	—	11	1	no	maximal, Hall
11	C₂×C₁₁	C₂×D₅	1	1	yes	characteristic
12	C₄×C₅	—	11	1	no	—
13	Dic₅	—	11	1	no	—
14	Dic₅	D₁₁	1	1	yes	characteristic
15	C₁₁	Dic₁₀	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₅	C₂×D₁₁	1	1	yes	characteristic
17	Q₈	—	55	1	no	Sylow
18	C₅	Dic₂₂	1	1	yes	characteristic, complemented, Sylow
19	C₄	—	5	1	no	—
20	C₄	—	11	1	no	—
21	C₄	—	55	1	no	—
22	C₂	D₅×D₁₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅×D₁₁
commutator, Fitting, socle, prime radical, cosocle	C₂×C₅×C₁₁	C₂²
hypocenter	C₅×C₁₁	Q₈
LCS	G ▷ C₂×C₅×C₁₁ ▷ C₅×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.