Subgroups — C₅₃×#10597243 #44545462

Order 32065.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁²×C₅₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅₃×C₁₁⋊C₅	—	11	12	no	maximal
3	#10597243	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₁×C₅₃	C₁₁⋊C₅	1	12	yes	complemented
5	C₅×C₅₃	—	121	1	no	Hall
6	C₁₁²	C₅×C₅₃	1	1	yes	characteristic, complemented, Sylow
7	C₁₁⋊C₅	—	11	12	no	—
8	C₅₃	#10597243	1	1	yes	characteristic, direct product factor, Sylow
9	C₁₁	C₅₃×C₁₁⋊C₅	1	12	yes	complemented
10	C₅	—	121	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅₃	#10597243
commutator, cosocle, hypocenter	C₁₁²	C₅×C₅₃
Frattini	C₁	G
Fitting, socle	C₁₁²×C₅₃	C₅
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₅₃

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.