Subgroups — C₃⋊#14583754 #22551978

Order 8268.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₃×C₅₃	C₂	1	1	yes	maximal, characteristic
2	#14583754	—	3	1	no	maximal, Hall
3	C₃×C₁₃×C₅₃	C₄	1	1	yes	characteristic, complemented, Hall
4	D₁₃×C₅₃	D₃	1	1	yes	characteristic
5	C₁₃×C₅₃	Dic₃	1	1	yes	characteristic, complemented, Hall
6	Dic₁₅₉	—	13	1	no	maximal, Hall
7	C₂×C₃×C₅₃	—	13	1	no	—
8	Dic₅₃	—	39	1	no	Hall
9	C₃×C₅₃	#261	1	1	yes	characteristic, complemented, Hall
10	C₃⋊#261	—	53	1	no	maximal, Hall
11	C₂×C₅₃	—	13	1	no	—
12	C₃×D₁₃	D₅₃	1	1	yes	characteristic
13	C₅₃	C₃⋊#261	1	1	yes	characteristic, complemented, Sylow
14	#261	—	159	1	no	Hall
15	C₃×C₁₃	Dic₅₃	1	1	yes	characteristic, complemented, Hall
16	D₁₃	D₁₅₉	1	1	yes	characteristic
17	C₁₃	Dic₁₅₉	1	1	yes	characteristic, complemented, Sylow
18	Dic₃	—	689	1	no	Hall
19	C₂×C₃	—	13	1	no	—
20	C₄	—	2067	1	no	Sylow
21	C₃	#14583754	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	13	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₁₃×C₅₃	C₄
LCS	G ▷ C₃×C₁₃×C₅₃
UCS	C₁

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