Subgroups — #89166

Order 440.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅₅	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₁₁	C₂²	1	1	yes	characteristic
5	D₅₅	C₄	1	2	yes	complemented
6	C₄×D₁₁	—	5	1	no	maximal, Hall
7	C₅×C₁₁	C₂×C₄	1	1	yes	characteristic, complemented, Hall
8	C₂×D₁₁	—	5	1	no	—
9	C₄×C₁₁	—	5	1	no	—
10	Dic₁₁	D₅	1	1	yes	characteristic, complemented
11	C₄×D₅	—	11	1	no	maximal, Hall
12	C₂×C₁₁	C₂×D₅	1	1	yes	characteristic
13	D₁₁	—	5	2	no	—
14	C₂×D₅	—	11	1	no	—
15	C₄×C₅	—	11	1	no	—
16	Dic₅	D₁₁	1	1	yes	characteristic, complemented
17	C₁₁	C₄×D₅	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₅	C₂×D₁₁	1	1	yes	characteristic
19	D₅	—	11	2	no	—
20	C₂×C₄	—	55	1	no	Sylow
21	C₅	C₄×D₁₁	1	1	yes	characteristic, complemented, Sylow
22	C₂²	—	55	1	no	—
23	C₄	—	5	1	no	—
24	C₄	—	11	1	no	—
25	C₂	—	55	2	no	—
26	C₂	D₅×D₁₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅×D₁₁
commutator, hypocenter	C₅×C₁₁	C₂×C₄
Fitting, socle, cosocle	C₂×C₅×C₁₁	C₂²
prime radical	C₂×D₅₅	C₂
LCS	G ▷ 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.