Subgroups — #19154606⋊C₃ #31798685

Order 17628.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₁₃⋊C₃)⋊D₁₁₃	C₂	1	1	yes	maximal, characteristic
2	#19154606	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃⋊C₃×C₁₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	D₁₄₆₉	C₂×C₃	1	1	yes	characteristic
5	C₁₃×C₁₁₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×#90673	—	13	1	no	maximal, Hall
7	C₃×D₁₁₃	—	13	1	no	—
8	#90673	—	13	1	no	Hall
9	C₃×C₁₁₃	—	52	1	no	Hall
10	D₁₁₃	—	13	1	no	—
11	AGL(1,𝔽₁₃)	—	113	1	no	maximal, Hall
12	C₁₁₃	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Sylow
13	D₁₃⋊C₃	—	113	1	no	—
14	#261	—	113	1	no	Hall
15	C₁₃⋊C₃	#90673	1	1	yes	characteristic, complemented, Hall
16	D₁₃	—	113	1	no	—
17	C₁₃	C₃×#90673	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	1469	1	no	Hall
19	C₂×C₃	—	1469	1	no	—
20	C₄	—	1469	1	no	Sylow
21	C₃	—	52	1	no	Sylow
22	C₂	—	1469	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₃×C₁₁₃	C₃×C₄
prime radical	(C₁₃⋊C₃)⋊D₁₁₃	C₂
cosocle	D₁₄₆₉	C₂×C₃
LCS	G ▷ C₁₃×C₁₁₃
UCS	C₁

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.