Subgroups — C₃⋊#19154607 #31798705

Order 17628.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₃×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	#19154607	—	3	1	no	maximal, Hall
3	C₃×C₁₃×C₁₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	D₁₃×C₁₁₃	D₃	1	1	yes	characteristic
5	C₁₃×C₁₁₃	Dic₃	1	1	yes	characteristic, complemented, Hall
6	Dic₃₃₉	—	13	1	no	maximal, Hall
7	C₂×C₃×C₁₁₃	—	13	1	no	—
8	Dic₁₁₃	—	39	1	no	Hall
9	C₃×C₁₁₃	#261	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₁₃	—	13	1	no	—
11	C₃⋊#261	—	113	1	no	maximal, Hall
12	C₁₁₃	C₃⋊#261	1	1	yes	characteristic, complemented, Sylow
13	C₃×D₁₃	D₁₁₃	1	1	yes	characteristic
14	#261	—	339	1	no	Hall
15	C₃×C₁₃	Dic₁₁₃	1	1	yes	characteristic, complemented, Hall
16	D₁₃	D₃₃₉	1	1	yes	characteristic
17	C₁₃	Dic₃₃₉	1	1	yes	characteristic, complemented, Sylow
18	Dic₃	—	1469	1	no	Hall
19	C₂×C₃	—	13	1	no	—
20	C₄	—	4407	1	no	Sylow
21	C₃	#19154607	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×C₁₁₃	C₄
prime radical, cosocle	C₃×D₁₃×C₁₁₃	C₂
LCS	G ▷ C₃×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.