Subgroups — AGL(1,𝔽₅)×C₃₀₇⋊C₃ #32914101

Order 18420.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₃₀₇⋊C₃	C₂	1	1	yes	maximal, characteristic
2	AGL(1,𝔽₅)×C₃₀₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₃₀₇⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₄×C₃₀₇⋊C₃	—	5	1	no	maximal, Hall
5	D₅×C₃₀₇	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃₀₇⋊C₃	—	5	1	no	—
7	C₅×C₃₀₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₄×C₃₀₇	—	5	1	no	Hall
9	C₃₀₇⋊C₃	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃₀₇	—	5	1	no	—
11	C₃₀₇	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
12	C₃×AGL(1,𝔽₅)	—	307	1	no	maximal, Hall
13	C₃×D₅	—	307	1	no	—
14	AGL(1,𝔽₅)	C₃₀₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₅	—	307	1	no	Hall
16	C₃×C₄	—	1535	1	no	Hall
17	D₅	C₂×C₃₀₇⋊C₃	1	1	yes	characteristic
18	C₂×C₃	—	1535	1	no	—
19	C₅	C₄×C₃₀₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
20	C₄	—	5	1	no	Sylow
21	C₃	—	307	1	no	Sylow
22	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₃₀₇	C₃×C₄
prime radical	D₅×C₃₀₇⋊C₃	C₂
cosocle	D₅×C₃₀₇	C₂×C₃
LCS	G ▷ C₅×C₃₀₇
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.