Subgroups — C₅₃×Dic₃₃ #20296167

Order 6996.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₁×C₅₃	C₂	1	1	yes	maximal, characteristic
2	Dic₁₁×C₅₃	—	3	1	no	maximal, Hall
3	C₃×C₁₁×C₅₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁×C₅₃	D₃	1	1	yes	characteristic
5	Dic₃×C₅₃	—	11	1	no	maximal, Hall
6	C₁₁×C₅₃	Dic₃	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₅₃	D₁₁	1	1	yes	characteristic
8	C₄×C₅₃	—	33	1	no	Hall
9	C₃×C₅₃	Dic₁₁	1	1	yes	characteristic, complemented, Hall
10	Dic₃₃	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₅₃	D₃₃	1	1	yes	characteristic
12	C₂×C₃×C₁₁	C₂×C₅₃	1	1	yes	characteristic
13	C₅₃	Dic₃₃	1	1	yes	characteristic, direct product factor, Sylow
14	Dic₁₁	—	3	1	no	Hall
15	C₃×C₁₁	C₄×C₅₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₁	D₃×C₅₃	1	1	yes	characteristic
17	Dic₃	—	11	1	no	Hall
18	C₁₁	Dic₃×C₅₃	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	D₁₁×C₅₃	1	1	yes	characteristic
20	C₄	—	33	1	no	Sylow
21	C₃	Dic₁₁×C₅₃	1	1	yes	characteristic, complemented, Sylow
22	C₂	C₅₃×D₃₃	1	1	yes	characteristic

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