Subgroups — C₁₁⋊C₅×D₅₁ #19150511

Order 5610.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₇×C₁₁⋊C₅	—	3	1	no	maximal, Hall
3	C₁₁×D₅₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₇×C₁₁⋊C₅	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₅×D₅₁	—	11	1	no	maximal, Hall
7	C₁₁×D₁₇	—	3	1	no	Hall
8	D₃×C₁₁⋊C₅	—	17	1	no	maximal, Hall
9	C₃×C₅×C₁₇	—	11	1	no	Hall
10	C₁₁×C₁₇	C₅×D₃	1	1	yes	characteristic, complemented, Hall
11	C₅×D₁₇	—	33	1	no	Hall
12	C₃×C₁₁⋊C₅	D₁₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₁⋊C₅	—	51	1	no	Hall
14	D₅₁	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
15	C₅×C₁₇	—	11	1	no	Hall
16	D₃×C₁₁	—	17	1	no	Hall
17	C₁₁⋊C₅	D₅₁	1	1	yes	characteristic, direct product factor, Hall
18	C₃×C₁₇	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Hall
19	D₁₇	—	3	1	no	Hall
20	C₃×C₁₁	C₅×D₁₇	1	1	yes	characteristic, complemented, Hall
21	C₅×D₃	—	187	1	no	Hall
22	C₂×C₁₁	—	51	1	no	Hall
23	C₁₇	D₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
24	C₃×C₅	—	11	1	no	Hall
25	C₁₁	C₅×D₅₁	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	561	1	no	Hall
27	D₃	—	17	1	no	Hall
28	C₅	—	11	1	no	Sylow
29	C₃	D₁₇×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	51	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₁₁×C₁₇	C₂×C₅
LCS	G ▷ C₃×C₁₁×C₁₇
UCS	C₁

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