Subgroups — C₅₃×D₂₈₉ #44499587

Order 30634.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×C₂₈₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₇×C₅₃	—	17	1	no	maximal
3	C₁₇×C₅₃	D₁₇	1	1	yes	characteristic
4	D₂₈₉	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂₈₉	C₂×C₅₃	1	1	yes	characteristic, complemented, Sylow
6	C₂×C₅₃	—	289	1	no	Hall
7	C₅₃	D₂₈₉	1	1	yes	characteristic, direct product factor, Sylow
8	D₁₇	—	17	1	no	—
9	C₁₇	D₁₇×C₅₃	1	1	yes	characteristic
10	C₂	—	289	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅₃	D₂₈₉
commutator, cosocle, hypocenter	C₂₈₉	C₂×C₅₃
Frattini	C₁₇	D₁₇×C₅₃
Fitting	C₅₃×C₂₈₉	C₂
socle	C₁₇×C₅₃	D₁₇
LCS	G ▷ C₂₈₉
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.