Subgroups — C₁₁⋊(C₄₉⋊AGL(1,𝔽₅)) #24924709

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	Dic₅₃₉	—	5	1	no	maximal, Hall
4	C₇⋊(C₁₁⋊AGL(1,𝔽₅))	—	7	1	no	maximal
5	C₂×C₁₁×C₄₉	—	5	1	no	—
6	C₄₉⋊AGL(1,𝔽₅)	—	11	1	no	maximal, Hall
7	C₇×D₅×C₁₁	D₇	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	Dic₇	1	1	yes	characteristic
11	Dic₇₇	—	35	1	no	—
12	C₅×C₄₉	Dic₁₁	1	1	yes	characteristic, complemented, Hall
13	C₁₁⋊AGL(1,𝔽₅)	—	49	1	no	Hall
14	Dic₄₉	—	55	1	no	Hall
15	C₂×C₇×C₁₁	—	5	1	no	—
16	C₇⋊AGL(1,𝔽₅)	—	77	1	no	—
17	D₅×C₁₁	D₄₉	1	1	yes	characteristic
18	C₂×C₄₉	—	5	1	no	—
19	C₇×C₁₁	C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic
20	C₇×D₅	D₇₇	1	1	yes	characteristic
21	C₅×C₁₁	Dic₄₉	1	1	yes	characteristic, complemented, Hall
22	C₄₉	C₁₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
23	Dic₁₁	—	245	1	no	Hall
24	C₅×C₇	Dic₇₇	1	1	yes	characteristic
25	Dic₇	—	385	1	no	—
26	C₂×C₁₁	—	5	1	no	—
27	AGL(1,𝔽₅)	—	539	1	no	Hall
28	C₂×C₇	—	5	1	no	—
29	C₁₁	C₄₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
30	D₅	D₅₃₉	1	1	yes	characteristic
31	C₇	C₇⋊(C₁₁⋊AGL(1,𝔽₅))	1	1	yes	characteristic
32	C₅	Dic₅₃₉	1	1	yes	characteristic, complemented, Sylow
33	C₄	—	2695	1	no	Sylow
34	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₅×C₁₁×C₄₉	C₄
Frattini	C₇	C₇⋊(C₁₁⋊AGL(1,𝔽₅))
socle	C₅×C₇×C₁₁	Dic₇
prime radical	C₇×D₅×C₁₁	D₇
cosocle	D₅×C₁₁×C₄₉	C₂
LCS	G ▷ C₅×C₁₁×C₄₉
UCS	C₁

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