Subgroups — C₁₁×C₂²⋊AGL(1,𝔽₅) #11724973

Order 880.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₅×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×AGL(1,𝔽₅)	C₂	1	2	yes	maximal, complemented
3	C₂²×C₅×C₁₁	C₄	1	1	yes	characteristic, complemented
4	C₂×D₅×C₁₁	—	2	2	no	—
5	C₂×D₅×C₁₁	C₄	1	1	yes	characteristic, complemented
6	C₂×D₅×C₁₁	C₂²	1	1	yes	characteristic
7	C₁₁×AGL(1,𝔽₅)	—	2	2	no	—
8	C₁₁×C₂²⋊C₄	—	5	1	no	maximal, Hall
9	C₂×C₅×C₁₁	—	2	1	no	—
10	C₂×C₅×C₁₁	C₂×C₄	1	1	yes	characteristic
11	D₅×C₁₁	—	2	1	no	—
12	D₅×C₁₁	D₄	1	2	yes	—
13	C₂³×C₁₁	—	5	1	no	—
14	C₂×C₄×C₁₁	—	5	2	no	—
15	C₂²⋊AGL(1,𝔽₅)	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₅×C₁₁	C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
17	C₂²×C₁₁	—	5	1	no	—
18	C₂²×C₁₁	—	5	1	no	—
19	C₂²×C₁₁	—	10	2	no	—
20	C₂²×C₁₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
21	C₄×C₁₁	—	10	2	no	—
22	C₂²×D₅	C₂×C₁₁	1	1	yes	characteristic
23	C₂×AGL(1,𝔽₅)	C₂×C₁₁	1	2	yes	complemented
24	C₂×C₁₁	—	2	1	no	—
25	C₂×C₁₁	—	5	2	no	—
26	C₂×C₁₁	—	10	1	no	—
27	C₂×C₁₁	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
28	C₂²×C₅	C₄×C₁₁	1	1	yes	characteristic, complemented
29	C₂×D₅	—	2	2	no	—
30	C₂×D₅	C₄×C₁₁	1	1	yes	characteristic, complemented
31	C₂×D₅	C₂²×C₁₁	1	1	yes	characteristic
32	AGL(1,𝔽₅)	—	2	2	no	—
33	C₂²⋊C₄	—	5	1	no	Sylow
34	C₁₁	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
35	C₂×C₅	—	2	1	no	—
36	C₂×C₅	C₂×C₄×C₁₁	1	1	yes	characteristic
37	D₅	—	2	1	no	—
38	D₅	D₄×C₁₁	1	2	yes	—
39	C₂³	—	5	1	no	—
40	C₂×C₄	—	5	2	no	—
41	C₅	C₁₁×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
42	C₂²	—	5	1	no	—
43	C₂²	—	5	1	no	—
44	C₂²	—	10	2	no	—
45	C₂²	C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
46	C₄	—	10	2	no	—
47	C₂	—	2	1	no	—
48	C₂	—	5	2	no	—
49	C₂	—	10	1	no	—
50	C₂	C₂×C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×AGL(1,𝔽₅)	C₂	semidirect
3. C₂²×C₅×C₁₁	C₄	semidirect
5. C₂×D₅×C₁₁	C₄	semidirect
15. C₂²⋊AGL(1,𝔽₅)	C₁₁	direct (N × H)
16. C₅×C₁₁	C₂²⋊C₄	semidirect
20. C₂²×C₁₁	AGL(1,𝔽₅)	semidirect
23. C₂×AGL(1,𝔽₅)	C₂×C₁₁	semidirect
28. C₂²×C₅	C₄×C₁₁	semidirect
30. C₂×D₅	C₄×C₁₁	semidirect
34. C₁₁	C₂²⋊AGL(1,𝔽₅)	direct (N × H)
41. C₅	C₁₁×C₂²⋊C₄	semidirect
45. C₂²	C₁₁×AGL(1,𝔽₅)	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₅×C₁₁	2
C₂×C₁₁×AGL(1,𝔽₅)	2
C₁₁×C₂²⋊C₄	5
C₂²⋊AGL(1,𝔽₅)	11

Subgroups — C11×C22⋊AGL(1,𝔽5) #11724973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₂²⋊AGL(1,𝔽₅) #11724973