Subgroups — C₃⋊(C₇⋊AGL(1,𝔽₅)) #88298

Order 420.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×D₅	C₂	1	1	yes	maximal, characteristic
2	C₇⋊AGL(1,𝔽₅)	—	3	1	no	maximal, Hall
3	C₃×C₅×C₇	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₂₁	—	5	1	no	maximal, Hall
5	C₇×D₅	D₃	1	1	yes	characteristic
6	ΓL(1,𝔽₁₆)	—	7	1	no	maximal, Hall
7	C₂×C₃×C₇	—	5	1	no	—
8	C₅×C₇	Dic₃	1	1	yes	characteristic, complemented, Hall
9	C₃×D₅	D₇	1	1	yes	characteristic
10	Dic₇	—	15	1	no	Hall
11	C₃×C₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	AGL(1,𝔽₅)	—	21	1	no	Hall
13	C₃×C₅	Dic₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₇	—	5	1	no	—
15	Dic₃	—	35	1	no	Hall
16	D₅	D₂₁	1	1	yes	characteristic
17	C₇	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃	—	5	1	no	—
19	C₅	Dic₂₁	1	1	yes	characteristic, complemented, Sylow
20	C₄	—	105	1	no	Sylow
21	C₃	C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅×C₇	C₄
prime radical, cosocle	C₃×C₇×D₅	C₂
LCS	G ▷ C₃×C₅×C₇
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.