Subgroups — C₁₁×AGL(1,𝔽₅)×C₄₉ #24924706

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	C₄×C₁₁×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	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₇×D₅×C₁₁	C₂×C₇	1	1	yes	characteristic
8	C₁₁×C₄₉	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Hall
9	D₅×C₄₉	C₂×C₁₁	1	1	yes	characteristic
10	C₅×C₇×C₁₁	C₄×C₇	1	1	yes	characteristic
11	C₄×C₇×C₁₁	—	5	1	no	—
12	C₅×C₄₉	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
13	C₁₁×AGL(1,𝔽₅)	C₄₉	1	1	yes	characteristic, direct product factor, Hall
14	C₄×C₄₉	—	5	1	no	Hall
15	C₂×C₇×C₁₁	—	5	1	no	—
16	C₇×AGL(1,𝔽₅)	C₇×C₁₁	1	1	yes	characteristic
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	C₂×C₇×C₁₁	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	C₄×C₁₁	—	5	1	no	Hall
24	C₅×C₇	C₄×C₇×C₁₁	1	1	yes	characteristic
25	C₄×C₇	—	5	1	no	—
26	C₂×C₁₁	—	5	1	no	—
27	AGL(1,𝔽₅)	C₁₁×C₄₉	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₇	—	5	1	no	—
29	C₁₁	AGL(1,𝔽₅)×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
30	D₅	C₂×C₁₁×C₄₉	1	1	yes	characteristic
31	C₇	C₇×C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic
32	C₅	C₄×C₁₁×C₄₉	1	1	yes	characteristic, complemented, Sylow
33	C₄	—	5	1	no	Sylow
34	C₂	—	5	1	no	—

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

Complements

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

N	H ≅ G/N	type
2. C₅×C₁₁×C₄₉	C₄	semidirect
6. AGL(1,𝔽₅)×C₄₉	C₁₁	direct (N × H)
8. C₁₁×C₄₉	AGL(1,𝔽₅)	direct (N × H)
12. C₅×C₄₉	C₄×C₁₁	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)
27. AGL(1,𝔽₅)	C₁₁×C₄₉	direct (N × H)
29. C₁₁	AGL(1,𝔽₅)×C₄₉	direct (N × H)
32. C₅	C₄×C₁₁×C₄₉	semidirect

Subgroups — C11×AGL(1,𝔽5)×C49 #24924706

Conjugacy classes of subgroups

Complements

Subgroups — C₁₁×AGL(1,𝔽₅)×C₄₉ #24924706