Subgroups — D₅×SL(2,𝔽₃) #6748

Order 240.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×D₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₃×D₅	—	4	1	no	maximal
4	C₂×SL(2,𝔽₃)	—	5	1	no	maximal, Hall
5	C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
6	C₄×D₅	—	3	1	no	—
7	Dic₁₀	—	3	1	no	—
8	C₂×C₃×C₅	—	4	1	no	—
9	C₃×D₅	—	4	2	no	—
10	SL(2,𝔽₃)	D₅	1	1	yes	characteristic, direct product factor
11	C₂×D₅	A₄	1	1	yes	characteristic
12	C₄×C₅	—	3	1	no	—
13	Dic₅	—	3	1	no	—
14	C₂×Q₈	—	5	1	no	Sylow
15	C₃×C₅	—	4	1	no	Hall
16	C₂²×C₃	—	20	1	no	—
17	C₂×C₅	C₂×A₄	1	1	yes	characteristic
18	D₅	SL(2,𝔽₃)	1	2	yes	direct product factor
19	Q₈	—	15	1	no	—
20	Q₈	C₃×D₅	1	1	yes	characteristic, complemented
21	C₂×C₄	—	15	1	no	—
22	C₂×C₃	—	4	1	no	—
23	C₂×C₃	—	20	2	no	—
24	C₅	C₂×SL(2,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
25	C₂²	—	5	1	no	—
26	C₄	—	3	1	no	—
27	C₄	—	15	1	no	—
28	C₃	—	4	1	no	Sylow
29	C₂	—	5	2	no	—
30	C₂	D₅×A₄	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅×A₄
commutator, Fitting, cosocle, hypocenter	C₅×Q₈	C₂×C₃
socle	C₂×C₅	C₂×A₄
LCS	G ▷ C₅×Q₈
UCS	C₁ ◁ C₂

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.