Subgroups — C₅×D₄×C₁₁ #89187

Order 440.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₁₁	C₂	1	2	yes	maximal, complemented
2	C₄×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₁₁	—	2	2	no	—
4	C₂×C₅×C₁₁	C₂²	1	1	yes	characteristic
5	D₄×C₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₁₁	D₄	1	1	yes	characteristic, direct product factor, Hall
7	C₂²×C₁₁	C₂×C₅	1	2	yes	complemented
8	C₄×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
9	C₅×D₄	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₁₁	—	2	2	no	—
11	C₂×C₁₁	C₂²×C₅	1	1	yes	characteristic
12	C₂²×C₅	C₂×C₁₁	1	2	yes	complemented
13	C₄×C₅	C₂×C₁₁	1	1	yes	characteristic, complemented
14	C₁₁	C₅×D₄	1	1	yes	characteristic, direct product factor, Sylow
15	C₂×C₅	—	2	2	no	—
16	C₂×C₅	C₂²×C₁₁	1	1	yes	characteristic
17	D₄	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
18	C₅	D₄×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₂²	C₂×C₅×C₁₁	1	2	yes	complemented
20	C₄	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented
21	C₂	—	2	2	no	—
22	C₂	C₂²×C₅×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅×C₁₁	C₂²
commutator, Frattini, cosocle	C₂	C₂²×C₅×C₁₁
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₁₁ ◁ G

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.