Subgroups — C₅⋊(#41⋊C₃) #6747

Order 240.

30 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	#713	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₃×Dic₅	—	4	1	no	maximal
4	#41⋊C₃	—	5	1	no	maximal, Hall
5	C₅×Q₈	C₂×C₃	1	1	yes	characteristic
6	D₂₀	—	3	1	no	—
7	C₄×D₅	—	3	1	no	—
8	C₂×C₃×C₅	—	4	1	no	—
9	SL(2,𝔽₃)	D₅	1	1	yes	characteristic, complemented
10	C₂×D₅	—	3	1	no	—
11	C₄×C₅	—	3	1	no	—
12	Dic₅	A₄	1	1	yes	characteristic
13	#41	—	5	1	no	Sylow
14	C₃×C₅	—	4	1	no	Hall
15	C₃×C₄	—	20	1	no	—
16	C₂×C₅	C₂×A₄	1	1	yes	characteristic
17	D₅	—	6	1	no	—
18	Q₈	C₃×D₅	1	1	yes	characteristic
19	D₄	—	15	1	no	—
20	C₂×C₄	—	15	1	no	—
21	C₂×C₃	—	4	1	no	—
22	C₅	#41⋊C₃	1	1	yes	characteristic, complemented, Sylow
23	C₂²	—	15	1	no	—
24	C₄	—	3	1	no	—
25	C₄	—	5	1	no	—
26	C₃	—	4	1	no	Sylow
27	C₂	—	30	1	no	—
28	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.