Subgroups — GL(2,𝔽₅) #91142

Order 480.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6732	C₂	1	1	yes	maximal, characteristic
2	SL(2,𝔽₅)	C₄	1	1	yes	characteristic, complemented
3	GU(2,𝔽₃)	—	5	1	no	maximal, Hall
4	C₄×AGL(1,𝔽₅)	—	6	1	no	maximal
5	#41⋊C₃	—	5	1	no	—
6	ΓL(1,𝔽₂₅)	—	10	1	no	maximal
7	C₂×AGL(1,𝔽₅)	—	6	2	no	—
8	C₄×D₅	—	6	1	no	—
9	#104	—	15	1	no	Sylow
10	C₄×D₃	—	10	1	no	—
11	SL(2,𝔽₃)	—	5	1	no	—
12	C₃×C₈	—	10	1	no	—
13	C₃⋊C₈	—	10	1	no	—
14	C₂×D₅	—	6	1	no	—
15	AGL(1,𝔽₅)	—	6	4	no	—
16	C₄×C₅	—	6	1	no	—
17	Dic₅	—	6	1	no	—
18	#41	—	5	1	no	—
19	M₁₆	—	15	1	no	—
20	C₄²	—	15	1	no	—
21	C₂×D₃	—	10	1	no	—
22	C₃×C₄	—	10	1	no	—
23	Dic₃	—	10	1	no	—
24	C₂×C₅	—	6	1	no	—
25	D₅	—	6	2	no	—
26	Q₈	—	5	1	no	—
27	D₄	—	15	1	no	—
28	C₂×C₄	—	15	1	no	—
29	C₂×C₄	—	30	1	no	—
30	C₈	—	10	1	no	—
31	C₂×C₃	—	10	1	no	—
32	D₃	—	20	1	no	—
33	C₅	—	6	1	no	Sylow
34	C₂²	—	15	1	no	—
35	C₄	—	15	1	no	—
36	C₄	—	30	2	no	—
37	C₄	S₅	1	1	yes	characteristic
38	C₃	—	10	1	no	Sylow
39	C₂	—	30	1	no	—
40	C₂	A₅⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, Fitting, hypercenter	C₄	S₅
commutator, hypocenter	SL(2,𝔽₅)	C₄
socle	C₂	A₅⋊C₄
prime radical, cosocle	#6732	C₂
LCS	G ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₄

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

N	H ≅ G/N	type
2. SL(2,𝔽₅)	C₄	semidirect

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