Subgroups — C₁₁×C₁₃×Dic₅₃ #44476331

Order 30316.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₁₃×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₃×C₅₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₃×Dic₅₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₁×Dic₅₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₃×C₅₃	C₂×C₁₁	1	1	yes	characteristic
6	C₂×C₁₁×C₅₃	C₂×C₁₃	1	1	yes	characteristic
7	C₁₃×C₅₃	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
8	C₁₁×C₅₃	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
9	C₄×C₁₁×C₁₃	—	53	1	no	maximal, Hall
10	C₂×C₁₁×C₁₃	D₅₃	1	1	yes	characteristic
11	Dic₅₃	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
12	C₁₁×C₁₃	Dic₅₃	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₅₃	C₂×C₁₁×C₁₃	1	1	yes	characteristic
14	C₅₃	C₄×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Sylow
15	C₄×C₁₃	—	53	1	no	Hall
16	C₄×C₁₁	—	53	1	no	Hall
17	C₂×C₁₃	C₁₁×D₅₃	1	1	yes	characteristic
18	C₂×C₁₁	C₁₃×D₅₃	1	1	yes	characteristic
19	C₁₃	C₁₁×Dic₅₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₁₁	C₁₃×Dic₅₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	53	1	no	Sylow
22	C₂	C₁₁×C₁₃×D₅₃	1	1	yes	characteristic

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.