Subgroups — C₃×C₂₃×D₁₆₉ #37552213

Order 23322.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₃×C₁₆₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₃×D₁₆₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂₃×C₁₆₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×C₂₃×D₁₃	—	13	1	no	maximal
5	C₃×D₁₆₉	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₁₃×C₂₃	D₁₃	1	1	yes	characteristic
7	C₂₃×D₁₃	—	13	1	no	—
8	C₃×C₁₆₉	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
9	D₁₆₉	C₃×C₂₃	1	1	yes	characteristic, direct product factor, Hall
10	C₁₃×C₂₃	C₃×D₁₃	1	1	yes	characteristic
11	C₁₆₉	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃×C₂₃	—	169	1	no	Hall
13	C₃×D₁₃	—	13	1	no	—
14	C₃×C₂₃	D₁₆₉	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₂₃	—	169	1	no	Hall
16	C₃×C₁₃	C₂₃×D₁₃	1	1	yes	characteristic
17	D₁₃	—	13	1	no	—
18	C₂₃	C₃×D₁₆₉	1	1	yes	characteristic, direct product factor, Sylow
19	C₁₃	C₃×C₂₃×D₁₃	1	1	yes	characteristic
20	C₂×C₃	—	169	1	no	Hall
21	C₃	C₂₃×D₁₆₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	169	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₂₃	D₁₆₉
commutator, cosocle, hypocenter	C₁₆₉	C₂×C₃×C₂₃
Frattini	C₁₃	C₃×C₂₃×D₁₃
Fitting	C₃×C₂₃×C₁₆₉	C₂
socle	C₃×C₁₃×C₂₃	D₁₃
LCS	G ▷ C₁₆₉
UCS	C₁ ◁ C₃×C₂₃

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.