Subgroups — A₅⋊C₄ #6730

Order 240.

35 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×A₅	C₂	1	1	yes	maximal, characteristic
2	A₅	C₄	1	1	yes	characteristic, complemented
3	SL(2,ℤ/4)	—	5	1	no	maximal, Hall
4	C₂×AGL(1,𝔽₅)	—	6	1	no	maximal
5	C₂×A₄	—	5	1	no	—
6	C₄×D₃	—	10	1	no	maximal
7	C₂×D₅	—	6	1	no	—
8	AGL(1,𝔽₅)	—	6	2	no	—
9	C₂²⋊C₄	—	15	1	no	Sylow
10	C₂×D₃	—	10	1	no	—
11	A₄	—	5	1	no	—
12	C₃×C₄	—	10	1	no	—
13	Dic₃	—	10	1	no	—
14	C₂×C₅	—	6	1	no	—
15	D₅	—	6	1	no	—
16	D₅	—	6	1	no	—
17	C₂³	—	5	1	no	—
18	C₂×C₄	—	15	1	no	—
19	C₂×C₄	—	15	1	no	—
20	C₂×C₃	—	10	1	no	—
21	D₃	—	10	1	no	—
22	D₃	—	10	1	no	—
23	C₅	—	6	1	no	Sylow
24	C₂²	—	5	1	no	—
25	C₂²	—	15	1	no	—
26	C₂²	—	15	1	no	—
27	C₄	—	10	1	no	—
28	C₄	—	30	1	no	—
29	C₃	—	10	1	no	Sylow
30	C₂	—	15	1	no	—
31	C₂	—	15	1	no	—
32	C₂	S₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, Fitting, hypercenter	C₂	S₅
commutator, hypocenter	A₅	C₄
socle, prime radical, cosocle	C₂×A₅	C₂
LCS	G ▷ A₅
UCS	C₁ ◁ C₂

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. A₅	C₄	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.