Subgroups — C₂×D₅×D₁₁ #89194

Order 440.

64 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, complemented
2	C₂×D₅×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₁₁	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₅×C₁₁	C₂²	1	1	yes	characteristic, complemented
6	D₅₅	C₂²	1	2	yes	complemented
7	C₅×D₁₁	C₂²	1	2	yes	complemented
8	D₅×C₁₁	C₂²	1	2	yes	complemented
9	C₂²×D₁₁	—	5	1	no	maximal, Hall
10	C₅×C₁₁	C₂³	1	1	yes	characteristic, complemented, Hall
11	C₂²×C₁₁	—	5	1	no	—
12	C₂×D₁₁	—	5	1	no	—
13	C₂×D₁₁	—	5	4	no	—
14	C₂×D₁₁	D₅	1	1	yes	characteristic, direct product factor
15	C₂²×D₅	—	11	1	no	maximal, Hall
16	C₂×C₁₁	—	5	2	no	—
17	C₂×C₁₁	C₂×D₅	1	1	yes	characteristic, complemented
18	D₁₁	—	5	2	no	—
19	D₁₁	C₂×D₅	1	2	yes	direct product factor
20	C₂²×C₅	—	11	1	no	—
21	C₂×D₅	—	11	1	no	—
22	C₂×D₅	—	11	4	no	—
23	C₂×D₅	D₁₁	1	1	yes	characteristic, direct product factor
24	C₁₁	C₂²×D₅	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₅	—	11	2	no	—
26	C₂×C₅	C₂×D₁₁	1	1	yes	characteristic, complemented
27	D₅	—	11	2	no	—
28	D₅	C₂×D₁₁	1	2	yes	direct product factor
29	C₂³	—	55	1	no	Sylow
30	C₅	C₂²×D₁₁	1	1	yes	characteristic, complemented, Sylow
31	C₂²	—	5	1	no	—
32	C₂²	—	11	1	no	—
33	C₂²	—	55	4	no	—
34	C₂²	—	55	1	no	—
35	C₂	—	5	2	no	—
36	C₂	—	11	2	no	—
37	C₂	—	55	2	no	—
38	C₂	D₅×D₁₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₅×D₁₁
commutator, cosocle, hypocenter	C₅×C₁₁	C₂³
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₁	C₂²
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.