Subgroups — C₇⋊(C₂₆₃⋊AGL(1,𝔽₅)) #49145607

Order 36820.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₅×C₂₆₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇×C₂₆₃	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₈₄₁	—	5	1	no	maximal, Hall
4	C₂₆₃⋊AGL(1,𝔽₅)	—	7	1	no	maximal, Hall
5	C₂×C₇×C₂₆₃	—	5	1	no	—
6	D₅×C₂₆₃	D₇	1	1	yes	characteristic
7	C₇×C₂₆₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
8	C₅×C₂₆₃	Dic₇	1	1	yes	characteristic, complemented, Hall
9	Dic₂₆₃	—	35	1	no	Hall
10	C₂×C₂₆₃	—	5	1	no	—
11	C₂₆₃	C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
12	C₇⋊AGL(1,𝔽₅)	—	263	1	no	maximal, Hall
13	C₇×D₅	D₂₆₃	1	1	yes	characteristic
14	C₅×C₇	Dic₂₆₃	1	1	yes	characteristic, complemented, Hall
15	Dic₇	—	1315	1	no	Hall
16	AGL(1,𝔽₅)	—	1841	1	no	Hall
17	C₂×C₇	—	5	1	no	—
18	D₅	D₁₈₄₁	1	1	yes	characteristic
19	C₇	C₂₆₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
20	C₅	Dic₁₈₄₁	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	9205	1	no	Sylow
22	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₇×C₂₆₃	C₄
prime radical, cosocle	C₇×D₅×C₂₆₃	C₂
LCS	G ▷ C₅×C₇×C₂₆₃
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.