Subgroups — D₃×AGL(1,𝔽₅) #1226

Order 120.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×D₅	C₂	1	1	yes	maximal, characteristic
2	ΓL(1,𝔽₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×AGL(1,𝔽₅)	—	3	1	no	maximal, Hall
5	D₁₅	C₄	1	1	yes	characteristic, complemented
6	C₃×D₅	C₂²	1	1	yes	characteristic
7	C₅×D₃	C₄	1	1	yes	characteristic, complemented
8	C₄×D₃	—	5	1	no	maximal, Hall
9	C₂×D₅	—	3	1	no	—
10	AGL(1,𝔽₅)	—	3	1	no	—
11	AGL(1,𝔽₅)	D₃	1	1	yes	characteristic, direct product factor
12	C₃×C₅	C₂×C₄	1	1	yes	characteristic, complemented, Hall
13	C₂×D₃	—	5	1	no	—
14	C₃×C₄	—	5	1	no	—
15	Dic₃	—	5	1	no	—
16	C₂×C₅	—	3	1	no	—
17	D₅	—	3	1	no	—
18	D₅	C₂×D₃	1	1	yes	characteristic
19	C₂×C₄	—	15	1	no	Sylow
20	C₂×C₃	—	5	1	no	—
21	D₃	—	5	1	no	—
22	D₃	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
23	C₅	C₄×D₃	1	1	yes	characteristic, complemented, Sylow
24	C₂²	—	15	1	no	—
25	C₄	—	5	1	no	—
26	C₄	—	15	1	no	—
27	C₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
28	C₂	—	3	1	no	—
29	C₂	—	5	1	no	—
30	C₂	—	15	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅	C₂×C₄
prime radical	D₃×D₅	C₂
cosocle	C₃×D₅	C₂²
LCS	G ▷ C₃×C₅
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.