Subgroups — C₃⋊AGL(1,𝔽₁₃) #90855

Order 468.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#261	C₃	1	1	yes	maximal, characteristic, complemented
3	AGL(1,𝔽₁₃)	—	3	1	no	maximal
4	C₃×C₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×D₁₃	C₂×C₃	1	1	yes	characteristic
6	D₁₃⋊C₃	—	2	1	no	—
7	D₁₃⋊C₃	D₃	1	1	yes	characteristic
8	#261	—	3	1	no	Hall
9	C₃×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented
10	C₁₃⋊C₃	—	2	1	no	—
11	C₁₃⋊C₃	Dic₃	1	1	yes	characteristic, complemented
12	C₃×Dic₃	—	13	1	no	maximal, Hall
13	D₁₃	C₃×D₃	1	1	yes	characteristic
14	C₂×C₃²	—	13	1	no	—
15	C₁₃	C₃×Dic₃	1	1	yes	characteristic, complemented, Sylow
16	C₃×C₄	—	39	1	no	—
17	Dic₃	—	13	1	no	—
18	C₃²	—	13	1	no	Sylow
19	C₂×C₃	—	13	1	no	—
20	C₂×C₃	—	13	1	no	—
21	C₂×C₃	—	26	1	no	—
22	C₄	—	39	1	no	Sylow
23	C₃	—	13	1	no	—
24	C₃	—	26	1	no	—
25	C₃	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented
26	C₂	—	13	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₁₃	C₃×C₄
prime radical	C₃×D₁₃⋊C₃	C₂
cosocle	C₃×D₁₃	C₂×C₃
LCS	G ▷ C₃×C₁₃
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.