Subgroups — C₄₉⋊(Dic₁₁⋊C₅) #24924691

Order 10780.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₉×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₄₉×C₁₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₅₃₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₇⋊(Dic₁₁⋊C₅)	—	7	1	no	maximal
5	C₂×C₁₁×C₄₉	C₂×C₅	1	1	yes	characteristic
6	C₅×Dic₄₉	—	11	1	no	maximal, Hall
7	C₂×C₇×C₁₁⋊C₅	D₇	1	1	yes	characteristic
8	C₁₁×C₄₉	C₄×C₅	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅×C₄₉	—	11	1	no	—
10	C₇×C₁₁⋊C₅	Dic₇	1	1	yes	characteristic
11	Dic₇₇	—	7	1	no	—
12	C₅×C₄₉	—	11	1	no	Hall
13	Dic₁₁⋊C₅	—	49	1	no	Hall
14	Dic₄₉	—	11	1	no	Hall
15	C₂×C₇×C₁₁	C₅×D₇	1	1	yes	characteristic
16	C₅×Dic₇	—	77	1	no	—
17	C₂×C₁₁⋊C₅	D₄₉	1	1	yes	characteristic
18	C₂×C₄₉	AGL(1,𝔽₁₁)	1	1	yes	characteristic
19	C₇×C₁₁	C₅×Dic₇	1	1	yes	characteristic
20	C₂×C₅×C₇	—	11	1	no	—
21	C₁₁⋊C₅	Dic₄₉	1	1	yes	characteristic, complemented, Hall
22	C₄₉	Dic₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
23	Dic₁₁	—	49	1	no	Hall
24	C₅×C₇	—	11	1	no	—
25	Dic₇	—	77	1	no	—
26	C₂×C₁₁	C₅×D₄₉	1	1	yes	characteristic
27	C₄×C₅	—	539	1	no	Hall
28	C₂×C₇	C₇⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic
29	C₁₁	C₅×Dic₄₉	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₅	—	11	1	no	—
31	C₇	C₇⋊(Dic₁₁⋊C₅)	1	1	yes	characteristic
32	C₅	—	11	1	no	Sylow
33	C₄	—	539	1	no	Sylow
34	C₂	C₄₉⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic

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