Subgroups — C₃⋊#3928 #90930

Order 480.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#672	C₂	1	1	yes	maximal, characteristic
2	#3928	—	3	1	no	maximal, Hall
3	C₃×C₅×C₈	C₄	1	1	yes	characteristic
4	C₃⋊C₃₂	—	5	1	no	maximal, Hall
5	#672	D₃	1	1	yes	characteristic
6	C₃×C₄×C₅	C₈	1	1	yes	characteristic
7	C₃×C₁₆	—	5	1	no	—
8	C₅×C₈	Dic₃	1	1	yes	characteristic
9	C₃₂	—	15	1	no	Sylow
10	C₂×C₃×C₅	C₁₆	1	1	yes	characteristic
11	C₃×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
12	C₄×C₅	C₃⋊C₈	1	1	yes	characteristic
13	C₁₆	—	5	1	no	—
14	C₃×C₅	C₃₂	1	1	yes	characteristic, complemented, Hall
15	C₃×C₄	#170	1	1	yes	characteristic
16	C₂×C₅	C₃⋊C₁₆	1	1	yes	characteristic
17	C₈	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
18	C₂×C₃	#674	1	1	yes	characteristic
19	C₅	C₃⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
20	C₄	C₃⋊#170	1	1	yes	characteristic
21	C₃	#3928	1	1	yes	characteristic, complemented, Sylow
22	C₂	C₃⋊#674	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₈	ΓL(1,𝔽₁₆)
commutator, hypocenter	C₃×C₅	C₃₂
Fitting	C₃×C₅×C₈	C₄
socle, prime radical	C₂×C₃×C₅	C₁₆
cosocle	C₃×#672	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₈

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.