Subgroups — A₄⋊AGL(1,𝔽₅) #6831

Order 240.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×A₄	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊AGL(1,𝔽₅)	—	3	1	no	maximal, Hall
3	C₅×A₄	C₄	1	1	yes	characteristic, complemented
4	ΓL(1,𝔽₁₆)	—	4	1	no	maximal
5	SL(2,ℤ/4)	—	5	1	no	maximal, Hall
6	C₂²×D₅	D₃	1	1	yes	characteristic
7	C₂×AGL(1,𝔽₅)	—	3	1	no	—
8	C₂×AGL(1,𝔽₅)	—	3	1	no	—
9	C₃×D₅	—	4	1	no	—
10	C₂×A₄	—	5	1	no	—
11	C₂²×C₅	Dic₃	1	1	yes	characteristic, complemented
12	C₂×D₅	—	3	1	no	—
13	C₂×D₅	—	3	1	no	—
14	AGL(1,𝔽₅)	—	6	1	no	—
15	AGL(1,𝔽₅)	—	6	1	no	—
16	C₂²⋊C₄	—	15	1	no	Sylow
17	C₃×C₅	—	4	1	no	Hall
18	A₄	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
19	Dic₃	—	20	1	no	—
20	C₂×C₅	—	3	1	no	—
21	D₅	—	3	1	no	—
22	D₅	S₄	1	1	yes	characteristic
23	C₂³	—	5	1	no	—
24	C₂×C₄	—	15	1	no	—
25	C₂×C₄	—	15	1	no	—
26	C₂×C₃	—	20	1	no	—
27	C₅	SL(2,ℤ/4)	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	15	1	no	—
29	C₂²	—	15	1	no	—
30	C₂²	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
31	C₄	—	30	1	no	—
32	C₄	—	30	1	no	—
33	C₃	—	4	1	no	Sylow
34	C₂	—	3	1	no	—
35	C₂	—	5	1	no	—
36	C₂	—	15	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	C₅×A₄	C₄
Fitting, socle	C₂²×C₅	Dic₃
prime radical, cosocle	D₅×A₄	C₂
LCS	G ▷ C₅×A₄
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.