Subgroups — C₄×C₁₁⋊AGL(1,𝔽₅) #11724976

Order 880.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁⋊AGL(1,𝔽₅)	C₂	1	2	yes	maximal
2	C₄×D₅×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₂×D₅×C₁₁	C₂²	1	1	yes	characteristic
4	C₁₁⋊AGL(1,𝔽₅)	C₄	1	4	yes	direct product factor
5	C₄×C₅×C₁₁	C₄	1	1	yes	characteristic, complemented
6	C₁₁×Dic₅	C₄	1	1	yes	characteristic, complemented
7	C₄×Dic₁₁	—	5	1	no	maximal, Hall
8	C₂×C₅×C₁₁	C₂×C₄	1	1	yes	characteristic
9	D₅×C₁₁	C₂×C₄	1	2	yes	—
10	C₂×C₄×C₁₁	—	5	1	no	—
11	C₂×Dic₁₁	—	5	2	no	—
12	C₄×AGL(1,𝔽₅)	—	11	1	no	maximal, Hall
13	C₅×C₁₁	C₄²	1	1	yes	characteristic, complemented, Hall
14	C₂²×C₁₁	—	5	1	no	—
15	C₄×C₁₁	—	5	1	no	—
16	C₄×C₁₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
17	Dic₁₁	—	5	4	no	—
18	C₂×AGL(1,𝔽₅)	—	11	2	no	—
19	C₄×D₅	D₁₁	1	1	yes	characteristic
20	C₂×C₁₁	—	5	2	no	—
21	C₂×C₁₁	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
22	C₂×D₅	C₂×D₁₁	1	1	yes	characteristic
23	AGL(1,𝔽₅)	—	11	4	no	—
24	C₄×C₅	Dic₁₁	1	1	yes	characteristic, complemented
25	Dic₅	Dic₁₁	1	1	yes	characteristic, complemented
26	C₄²	—	55	1	no	Sylow
27	C₁₁	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₅	C₂×Dic₁₁	1	1	yes	characteristic
29	D₅	C₄×D₁₁	1	2	yes	—
30	C₂×C₄	—	5	1	no	—
31	C₂×C₄	—	55	2	no	—
32	C₅	C₄×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
33	C₂²	—	5	1	no	—
34	C₄	—	5	1	no	—
35	C₄	—	55	4	no	—
36	C₄	C₁₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
37	C₂	—	5	2	no	—
38	C₂	C₂×C₁₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄	C₁₁⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅×C₁₁	C₄²
Frattini	C₂	C₂×C₁₁⋊AGL(1,𝔽₅)
Fitting	C₄×C₅×C₁₁	C₄
socle	C₂×C₅×C₁₁	C₂×C₄
prime radical, cosocle	C₂×D₅×C₁₁	C₂²
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₄

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. C₁₁⋊AGL(1,𝔽₅)	C₄	direct (N × H)
5. C₄×C₅×C₁₁	C₄	semidirect
6. C₁₁×Dic₅	C₄	semidirect
13. C₅×C₁₁	C₄²	semidirect
16. C₄×C₁₁	AGL(1,𝔽₅)	semidirect
24. C₄×C₅	Dic₁₁	semidirect
25. Dic₅	Dic₁₁	semidirect
27. C₁₁	C₄×AGL(1,𝔽₅)	semidirect
32. C₅	C₄×Dic₁₁	semidirect
36. C₄	C₁₁⋊AGL(1,𝔽₅)	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₁⋊AGL(1,𝔽₅)	2
C₄×D₅×C₁₁	2
C₄×Dic₁₁	5
C₄×AGL(1,𝔽₅)	11

Subgroups — C4×C11⋊AGL(1,𝔽5) #11724976

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₁⋊AGL(1,𝔽₅) #11724976