Subgroups — C₁₃×Dic₁₁×C₅₉ #46798144

Order 33748.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₁₃×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₃×C₅₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄×C₁₃×C₅₉	—	11	1	no	maximal, Hall
4	Dic₁₁×C₅₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₃×C₅₉	D₁₁	1	1	yes	characteristic
6	C₂×C₁₁×C₅₉	C₂×C₁₃	1	1	yes	characteristic
7	C₁₃×C₅₉	Dic₁₁	1	1	yes	characteristic, direct product factor, Hall
8	C₁₁×C₅₉	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
9	C₁₃×Dic₁₁	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₁₁×C₁₃	C₂×C₅₉	1	1	yes	characteristic
11	C₄×C₅₉	—	11	1	no	Hall
12	C₁₁×C₁₃	C₄×C₅₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅₉	C₁₃×D₁₁	1	1	yes	characteristic
14	C₅₉	C₁₃×Dic₁₁	1	1	yes	characteristic, direct product factor, Sylow
15	C₄×C₁₃	—	11	1	no	Hall
16	Dic₁₁	C₁₃×C₅₉	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₁₃	D₁₁×C₅₉	1	1	yes	characteristic
18	C₂×C₁₁	C₂×C₁₃×C₅₉	1	1	yes	characteristic
19	C₁₃	Dic₁₁×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
20	C₁₁	C₄×C₁₃×C₅₉	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	11	1	no	Sylow
22	C₂	C₁₃×D₁₁×C₅₉	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.