Subgroups — C₃×#14583755 #22551971

Order 8268.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×D₅₃	C₂	1	1	yes	maximal, characteristic
2	#14583755	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₃×C₅₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₃×D₅₃	C₂×C₃	1	1	yes	characteristic
5	C₁₃×C₅₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×#6157	—	13	1	no	maximal, Hall
7	C₃×D₅₃	D₁₃	1	1	yes	characteristic
8	#6157	—	13	1	no	Hall
9	C₃×C₅₃	Dic₁₃	1	1	yes	characteristic, complemented, Hall
10	C₃×Dic₁₃	—	53	1	no	maximal, Hall
11	D₅₃	C₃×D₁₃	1	1	yes	characteristic
12	C₂×C₃×C₁₃	—	53	1	no	—
13	C₅₃	C₃×Dic₁₃	1	1	yes	characteristic, complemented, Sylow
14	Dic₁₃	—	53	1	no	Hall
15	C₃×C₁₃	#6157	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₃	—	53	1	no	—
17	C₁₃	C₃×#6157	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	689	1	no	Hall
19	C₂×C₃	—	53	1	no	—
20	C₄	—	689	1	no	Sylow
21	C₃	#14583755	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	53	1	no	—

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