Subgroups — C₅₉×Dic₁₃⋊C₃ #22604178

Order 9204.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃⋊C₃×C₅₉	C₂	1	1	yes	maximal, characteristic
2	Dic₁₃×C₅₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃⋊C₃×C₅₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₃×C₅₉	C₂×C₃	1	1	yes	characteristic
5	C₁₃×C₅₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×C₄×C₅₉	—	13	1	no	maximal, Hall
7	C₂×C₃×C₅₉	—	13	1	no	—
8	C₄×C₅₉	—	13	1	no	Hall
9	C₃×C₅₉	—	13	1	no	Hall
10	Dic₁₃⋊C₃	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₅₉	D₁₃⋊C₃	1	1	yes	characteristic
12	C₂×C₁₃⋊C₃	C₂×C₅₉	1	1	yes	characteristic
13	C₅₉	Dic₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
14	Dic₁₃	C₃×C₅₉	1	1	yes	characteristic, complemented, Hall
15	C₁₃⋊C₃	C₄×C₅₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₃	C₂×C₃×C₅₉	1	1	yes	characteristic
17	C₁₃	C₃×C₄×C₅₉	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	13	1	no	Hall
19	C₂×C₃	—	13	1	no	—
20	C₄	—	13	1	no	Sylow
21	C₃	—	13	1	no	Sylow
22	C₂	C₅₉×D₁₃⋊C₃	1	1	yes	characteristic

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