Subgroups — C₄₉×C₁₁⋊AGL(1,𝔽₅) #24924707

Order 10780.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₁₁×C₄₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₁×C₄₉	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₁×C₄₉	—	5	1	no	maximal, Hall
4	C₇×C₁₁⋊AGL(1,𝔽₅)	C₇	1	1	yes	maximal, characteristic
5	C₂×C₁₁×C₄₉	—	5	1	no	—
6	AGL(1,𝔽₅)×C₄₉	—	11	1	no	maximal, Hall
7	C₇×D₅×C₁₁	C₂×C₇	1	1	yes	characteristic
8	C₁₁×C₄₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
9	D₅×C₄₉	D₁₁	1	1	yes	characteristic
10	C₅×C₇×C₁₁	C₄×C₇	1	1	yes	characteristic
11	C₇×Dic₁₁	—	5	1	no	—
12	C₅×C₄₉	Dic₁₁	1	1	yes	characteristic, complemented, Hall
13	C₁₁⋊AGL(1,𝔽₅)	C₄₉	1	1	yes	characteristic, direct product factor, Hall
14	C₄×C₄₉	—	55	1	no	Hall
15	C₂×C₇×C₁₁	—	5	1	no	—
16	C₇×AGL(1,𝔽₅)	—	11	1	no	—
17	D₅×C₁₁	C₂×C₄₉	1	1	yes	characteristic
18	C₂×C₄₉	—	5	1	no	—
19	C₇×C₁₁	C₇×AGL(1,𝔽₅)	1	1	yes	characteristic
20	C₇×D₅	C₇×D₁₁	1	1	yes	characteristic
21	C₅×C₁₁	C₄×C₄₉	1	1	yes	characteristic, complemented, Hall
22	C₄₉	C₁₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
23	Dic₁₁	—	5	1	no	Hall
24	C₅×C₇	C₇×Dic₁₁	1	1	yes	characteristic
25	C₄×C₇	—	55	1	no	—
26	C₂×C₁₁	—	5	1	no	—
27	AGL(1,𝔽₅)	—	11	1	no	Hall
28	C₂×C₇	—	5	1	no	—
29	C₁₁	AGL(1,𝔽₅)×C₄₉	1	1	yes	characteristic, complemented, Sylow
30	D₅	D₁₁×C₄₉	1	1	yes	characteristic
31	C₇	C₇×C₁₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic
32	C₅	Dic₁₁×C₄₉	1	1	yes	characteristic, complemented, Sylow
33	C₄	—	55	1	no	Sylow
34	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₄₉	C₁₁⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅×C₁₁	C₄×C₄₉
Frattini	C₇	C₇×C₁₁⋊AGL(1,𝔽₅)
Fitting	C₅×C₁₁×C₄₉	C₄
socle	C₅×C₇×C₁₁	C₄×C₇
prime radical, cosocle	C₇×D₅×C₁₁	C₂×C₇
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₄₉

Complements

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

N	H ≅ G/N	type
2. C₅×C₁₁×C₄₉	C₄	semidirect
8. C₁₁×C₄₉	AGL(1,𝔽₅)	semidirect
12. C₅×C₄₉	Dic₁₁	semidirect
13. C₁₁⋊AGL(1,𝔽₅)	C₄₉	direct (N × H)
21. C₅×C₁₁	C₄×C₄₉	semidirect
22. C₄₉	C₁₁⋊AGL(1,𝔽₅)	direct (N × H)
29. C₁₁	AGL(1,𝔽₅)×C₄₉	semidirect
32. C₅	Dic₁₁×C₄₉	semidirect

Subgroups — C49×C11⋊AGL(1,𝔽5) #24924707

Conjugacy classes of subgroups

Complements

Subgroups — C₄₉×C₁₁⋊AGL(1,𝔽₅) #24924707