Subgroups — C₅²×C₁₁×C₁₃⋊C₃ #24924336

Order 10725.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₁×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₁×C₁₃⋊C₃	C₅	1	6	yes	maximal, direct product factor
3	C₅²×C₁₃⋊C₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅²×C₁₁	—	13	1	no	maximal, Hall
5	C₅×C₁₁×C₁₃	C₃×C₅	1	6	yes	complemented
6	C₁₁×C₁₃⋊C₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
7	C₅²×C₁₃	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
8	C₅²×C₁₁	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
9	C₅×C₁₃⋊C₃	C₅×C₁₁	1	6	yes	direct product factor
10	C₃×C₅×C₁₁	—	13	6	no	—
11	C₁₁×C₁₃	C₃×C₅²	1	1	yes	characteristic, complemented, Hall
12	C₃×C₅²	—	13	1	no	Hall
13	C₅×C₁₃	C₃×C₅×C₁₁	1	6	yes	complemented
14	C₅×C₁₁	C₅×C₁₃⋊C₃	1	6	yes	direct product factor
15	C₁₃⋊C₃	C₅²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₁₁	—	13	1	no	Hall
17	C₅²	C₁₁×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×C₅	—	13	6	no	—
19	C₁₃	C₃×C₅²×C₁₁	1	1	yes	characteristic, complemented, Sylow
20	C₁₁	C₅²×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₅	C₅×C₁₁×C₁₃⋊C₃	1	6	yes	direct product factor
22	C₃	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²×C₁₁	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₃×C₅²×C₁₁
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₁₃	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₅²×C₁₁

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