Subgroups — D₅₃×C₁₃⋊C₉ #27137151

Order 12402.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×C₁₃⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₁₃×D₅₃	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₃×C₅₃	C₂×C₃	1	1	yes	characteristic
4	C₁₃×D₅₃	C₉	1	1	yes	characteristic, complemented, Hall
5	C₉×D₅₃	—	13	1	no	maximal, Hall
6	C₁₃×C₅₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
7	C₉×C₅₃	—	13	1	no	Hall
8	C₃×D₅₃	C₁₃⋊C₃	1	1	yes	characteristic
9	C₂×C₁₃⋊C₉	—	53	1	no	maximal, Hall
10	C₃×C₅₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic
11	C₁₃⋊C₉	D₅₃	1	1	yes	characteristic, direct product factor, Hall
12	D₅₃	C₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×C₁₃	—	53	1	no	—
14	C₅₃	C₂×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
15	C₃×C₁₃	C₃×D₅₃	1	1	yes	characteristic
16	C₂×C₁₃	—	53	1	no	Hall
17	C₂×C₉	—	689	1	no	Hall
18	C₁₃	C₉×D₅₃	1	1	yes	characteristic, complemented, Sylow
19	C₉	—	13	1	no	Sylow
20	C₂×C₃	—	53	1	no	—
21	C₃	C₁₃⋊C₃×D₅₃	1	1	yes	characteristic
22	C₂	—	53	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₁₃⋊C₃×D₅₃
commutator, hypocenter	C₁₃×C₅₃	C₂×C₉
Fitting, socle, cosocle	C₃×C₁₃×C₅₃	C₂×C₃
prime radical	C₃×C₁₃×D₅₃	C₃
LCS	G ▷ C₁₃×C₅₃
UCS	C₁ ◁ C₃

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.