Subgroups — C₁₃⋊C₃×C₁₁⋊C₂₅ #24924330

Order 10725.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₁⋊C₂₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₁×C₁₃⋊C₃	C₅	1	1	yes	maximal, characteristic
3	C₂₅×C₁₃⋊C₃	—	11	1	no	maximal, Hall
4	C₃×C₁₁⋊C₂₅	—	13	1	no	maximal, Hall
5	C₅×C₁₁×C₁₃	C₃×C₅	1	1	yes	characteristic
6	C₁₁×C₁₃⋊C₃	C₂₅	1	1	yes	characteristic, complemented, Hall
7	C₁₃×C₂₅	—	11	1	no	Hall
8	C₁₁⋊C₂₅	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
9	C₅×C₁₃⋊C₃	C₁₁⋊C₅	1	1	yes	characteristic
10	C₃×C₅×C₁₁	—	13	1	no	—
11	C₁₁×C₁₃	C₃×C₂₅	1	1	yes	characteristic, complemented, Hall
12	C₃×C₂₅	—	143	1	no	Hall
13	C₅×C₁₃	C₃×C₁₁⋊C₅	1	1	yes	characteristic
14	C₅×C₁₁	C₅×C₁₃⋊C₃	1	1	yes	characteristic
15	C₁₃⋊C₃	C₁₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₁₁	—	13	1	no	Hall
17	C₂₅	—	11	1	no	Sylow
18	C₃×C₅	—	13	1	no	—
19	C₁₃	C₃×C₁₁⋊C₂₅	1	1	yes	characteristic, complemented, Sylow
20	C₁₁	C₂₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
21	C₅	C₁₃⋊C₃×C₁₁⋊C₅	1	1	yes	characteristic
22	C₃	—	13	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₅	C₁₃⋊C₃×C₁₁⋊C₅
commutator, hypocenter	C₁₁×C₁₃	C₃×C₂₅
Fitting, socle, cosocle	C₅×C₁₁×C₁₃	C₃×C₅
prime radical	C₅×C₁₁×C₁₃⋊C₃	C₅
LCS	G ▷ C₁₁×C₁₃
UCS	C₁ ◁ C₅

Splittings G = N ⋊ H with N normal; H ≅ G/N.