Subgroups — ΓL(1,𝔽₈)×C₆₁⋊C₂₅ #44545052

Order 32025.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₆₁⋊C₂₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×ΓL(1,𝔽₈)×C₆₁	C₅	1	1	yes	maximal, characteristic
3	C₃×C₆₁⋊C₂₅	—	7	1	no	maximal, Hall
4	C₅×C₇×C₆₁	C₃×C₅	1	1	yes	characteristic
5	C₆₁⋊C₂₅	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor, Hall
6	ΓL(1,𝔽₈)×C₆₁	C₂₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×C₆₁	—	7	1	no	—
8	ΓL(1,𝔽₈)×C₂₅	—	61	1	no	maximal, Hall
9	C₇×C₆₁	C₃×C₂₅	1	1	yes	characteristic, complemented, Hall
10	C₅×C₆₁	C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
11	C₃×C₆₁	—	7	1	no	Hall
12	C₇×C₂₅	—	61	1	no	Hall
13	C₅×ΓL(1,𝔽₈)	C₆₁⋊C₅	1	1	yes	characteristic
14	C₃×C₂₅	—	427	1	no	Hall
15	C₆₁	ΓL(1,𝔽₈)×C₂₅	1	1	yes	characteristic, complemented, Sylow
16	C₅×C₇	C₃×C₆₁⋊C₅	1	1	yes	characteristic
17	C₂₅	—	61	1	no	Sylow
18	ΓL(1,𝔽₈)	C₆₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₅	—	7	1	no	—
20	C₇	C₃×C₆₁⋊C₂₅	1	1	yes	characteristic, complemented, Sylow
21	C₅	ΓL(1,𝔽₈)×C₆₁⋊C₅	1	1	yes	characteristic
22	C₃	—	7	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₅	ΓL(1,𝔽₈)×C₆₁⋊C₅
commutator, hypocenter	C₇×C₆₁	C₃×C₂₅
Fitting, socle, cosocle	C₅×C₇×C₆₁	C₃×C₅
prime radical	C₅×ΓL(1,𝔽₈)×C₆₁	C₅
LCS	G ▷ C₇×C₆₁
UCS	C₁ ◁ C₅

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.