Subgroups — C₅₉×D₂₀₇ #37567664

Order 24426.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂₃×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅₉×D₆₉	—	3	1	no	maximal
3	C₃×C₂₃×C₅₉	D₃	1	1	yes	characteristic
4	D₂₃×C₅₉	—	9	1	no	Hall
5	C₂₃×C₅₉	D₉	1	1	yes	characteristic, complemented, Hall
6	D₉×C₅₉	—	23	1	no	maximal, Hall
7	C₉×C₅₉	D₂₃	1	1	yes	characteristic, complemented, Hall
8	D₂₀₇	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	D₃×C₅₉	—	69	1	no	—
10	C₉×C₂₃	C₂×C₅₉	1	1	yes	characteristic, complemented, Hall
11	C₃×C₅₉	D₆₉	1	1	yes	characteristic
12	D₆₉	—	3	1	no	—
13	C₂×C₅₉	—	207	1	no	Hall
14	C₃×C₂₃	D₃×C₅₉	1	1	yes	characteristic
15	C₅₉	D₂₀₇	1	1	yes	characteristic, direct product factor, Sylow
16	D₂₃	—	9	1	no	Hall
17	C₂₃	D₉×C₅₉	1	1	yes	characteristic, complemented, Sylow
18	D₉	—	23	1	no	Hall
19	C₉	D₂₃×C₅₉	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	69	1	no	—
21	C₃	C₅₉×D₆₉	1	1	yes	characteristic
22	C₂	—	207	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅₉	D₂₀₇
commutator, cosocle, hypocenter	C₉×C₂₃	C₂×C₅₉
Frattini	C₃	C₅₉×D₆₉
Fitting	C₉×C₂₃×C₅₉	C₂
socle	C₃×C₂₃×C₅₉	D₃
LCS	G ▷ C₉×C₂₃
UCS	C₁ ◁ C₅₉

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.