Subgroups — D₁₁⋊(C₂⁴⋊C₅) #13183465

Order 1760.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁⋊(C₂⁴⋊C₅)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×D₁₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂⁴×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
4	C₂³×D₁₁	—	5	3	no	—
5	C₂³×D₁₁	—	5	3	no	—
6	C₂×C₂⁴⋊C₅	—	11	1	no	maximal, Hall
7	AGL(1,𝔽₁₁)	—	16	1	no	maximal
8	C₂³×C₁₁	—	5	3	no	—
9	C₂²×D₁₁	—	5	12	no	—
10	C₂²×D₁₁	—	5	3	no	—
11	C₂²×D₁₁	—	5	1	no	—
12	C₂²×D₁₁	—	5	6	no	—
13	C₂²×D₁₁	—	5	6	no	—
14	C₂⁴⋊C₅	—	11	1	no	—
15	C₁₁⋊C₅	—	16	1	no	Hall
16	C₂²×C₁₁	—	5	6	no	—
17	C₂²×C₁₁	—	5	1	no	—
18	C₂×D₁₁	—	5	12	no	—
19	C₂×D₁₁	—	5	3	no	—
20	C₂×D₁₁	—	5	3	no	—
21	C₂×D₁₁	—	5	6	no	—
22	C₂⁵	—	11	1	no	Sylow
23	C₂×C₁₁	—	5	3	no	—
24	D₁₁	—	5	3	no	—
25	D₁₁	C₂⁴⋊C₅	1	1	yes	characteristic, complemented
26	C₂⁴	—	55	3	no	—
27	C₂⁴	—	55	3	no	—
28	C₂⁴	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
29	C₁₁	C₂×C₂⁴⋊C₅	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₅	—	176	1	no	—
31	C₂³	—	5	3	no	—
32	C₂³	—	55	6	no	—
33	C₂³	—	55	6	no	—
34	C₂³	—	55	12	no	—
35	C₂³	—	55	1	no	—
36	C₂³	—	55	3	no	—
37	C₅	—	176	1	no	Sylow
38	C₂²	—	5	6	no	—
39	C₂²	—	5	1	no	—
40	C₂²	—	55	3	no	—
41	C₂²	—	55	6	no	—
42	C₂²	—	55	12	no	—
43	C₂²	—	55	3	no	—
44	C₂	—	5	3	no	—
45	C₂	—	11	1	no	—
46	C₂	—	55	3	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂⁴×C₁₁	C₂×C₅
LCS	G ▷ C₂⁴×C₁₁
UCS	C₁

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.