Subgroups — #89167

Order 440.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₅₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₁₁	C₂²	1	1	yes	characteristic
5	C₅×D₁₁	—	2	1	no	—
6	D₅×C₁₁	—	2	1	no	—
7	C₂²⋊D₁₁	—	5	1	no	maximal, Hall
8	C₅×C₁₁	D₄	1	1	yes	characteristic, complemented, Hall
9	C₂²×C₁₁	—	5	1	no	—
10	C₂×D₁₁	D₅	1	1	yes	characteristic, complemented
11	Dic₁₁	—	5	1	no	—
12	C₂²⋊D₅	—	11	1	no	maximal, Hall
13	C₂×C₁₁	—	10	1	no	—
14	C₂×C₁₁	C₂×D₅	1	1	yes	characteristic
15	D₁₁	—	2	1	no	—
16	C₂²×C₅	—	11	1	no	—
17	C₂×D₅	D₁₁	1	1	yes	characteristic, complemented
18	Dic₅	—	11	1	no	—
19	C₁₁	C₂²⋊D₅	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₅	—	22	1	no	—
21	C₂×C₅	C₂×D₁₁	1	1	yes	characteristic
22	D₅	—	2	1	no	—
23	D₄	—	55	1	no	Sylow
24	C₅	C₂²⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
25	C₂²	—	5	1	no	—
26	C₂²	—	11	1	no	—
27	C₄	—	55	1	no	—
28	C₂	—	10	1	no	—
29	C₂	—	22	1	no	—
30	C₂	D₅×D₁₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅×D₁₁
commutator, Fitting, socle, cosocle	C₂×C₅×C₁₁	C₂²
hypocenter	C₅×C₁₁	D₄
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.