Subgroups — C₅₉⋊(D₁₁⋊C₂₅) #44570089

Order 32450.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×C₁₁⋊C₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₆₄₉	C₅	1	1	yes	maximal, characteristic
3	C₅×C₁₁×C₅₉	C₂×C₅	1	1	yes	characteristic
4	C₂₅×D₅₉	—	11	1	no	maximal, Hall
5	C₂₅×C₅₉	—	11	1	no	Hall
6	D₆₄₉	C₂₅	1	1	yes	characteristic, complemented, Hall
7	C₁₁×C₅₉	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
8	C₅×D₅₉	—	11	1	no	—
9	D₁₁⋊C₂₅	—	59	1	no	maximal, Hall
10	C₅×C₅₉	AGL(1,𝔽₁₁)	1	1	yes	characteristic
11	C₁₁⋊C₂₅	D₅₉	1	1	yes	characteristic, complemented, Hall
12	D₅₉	—	11	1	no	Hall
13	C₅×D₁₁	—	59	1	no	—
14	C₅₉	D₁₁⋊C₂₅	1	1	yes	characteristic, complemented, Sylow
15	C₅×C₁₁	C₅×D₅₉	1	1	yes	characteristic
16	C₂×C₂₅	—	649	1	no	Hall
17	C₂₅	—	11	1	no	Sylow
18	D₁₁	—	59	1	no	Hall
19	C₁₁	C₂₅×D₅₉	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₅	—	649	1	no	—
21	C₅	(C₁₁⋊C₅)⋊D₅₉	1	1	yes	characteristic
22	C₂	—	649	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₅	(C₁₁⋊C₅)⋊D₅₉
commutator, hypocenter	C₁₁×C₅₉	C₂×C₂₅
Fitting, socle, cosocle	C₅×C₁₁×C₅₉	C₂×C₅
prime radical	C₅×D₆₄₉	C₅
LCS	G ▷ C₁₁×C₅₉
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.