Subgroups — A₄×AGL(1,𝔽₅) #6832

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)	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×A₄	C₄	1	1	yes	characteristic, complemented
4	C₃×AGL(1,𝔽₅)	—	4	1	no	maximal
5	C₄×A₄	—	5	1	no	maximal, Hall
6	C₂²×D₅	C₂×C₃	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	C₃×C₄	1	1	yes	characteristic, complemented
12	C₂×D₅	—	3	1	no	—
13	C₂×D₅	—	3	1	no	—
14	AGL(1,𝔽₅)	—	3	1	no	—
15	AGL(1,𝔽₅)	A₄	1	1	yes	characteristic, direct product factor
16	C₂²×C₄	—	5	1	no	Sylow
17	C₃×C₅	—	4	1	no	Hall
18	A₄	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
19	C₃×C₄	—	20	1	no	—
20	C₂×C₅	—	3	1	no	—
21	D₅	—	3	1	no	—
22	D₅	C₂×A₄	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	C₄×A₄	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	15	1	no	—
29	C₂²	—	15	1	no	—
30	C₂²	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
31	C₄	—	5	1	no	—
32	C₄	—	15	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, Fitting, socle, hypocenter	C₂²×C₅	C₃×C₄
prime radical	D₅×A₄	C₂
cosocle	C₂²×D₅	C₂×C₃
LCS	G ▷ C₂²×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.