Finite Group Databasebeta

← C₂²×C₃×C₁₆₉ #14523113

Subgroups — C₂²×C₃×C₁₆₉ #14523113

Order 2028.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₆₉	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₁₆₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₆₉	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₁₆₉	C₂×C₃	1	3	yes	direct product factor
5	C₁₆₉	C₂²×C₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₂²×C₃×C₁₃	C₁₃	1	1	yes	maximal, characteristic
7	C₂×C₃×C₁₃	C₂×C₁₃	1	3	yes	—
8	C₂²×C₁₃	C₃×C₁₃	1	1	yes	characteristic
9	C₃×C₁₃	C₂²×C₁₃	1	1	yes	characteristic
10	C₂×C₁₃	C₂×C₃×C₁₃	1	3	yes	—
11	C₁₃	C₂²×C₃×C₁₃	1	1	yes	characteristic
12	C₂²×C₃	C₁₆₉	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃	C₂×C₁₆₉	1	3	yes	direct product factor
14	C₂²	C₃×C₁₆₉	1	1	yes	characteristic, direct product factor, Sylow
15	C₃	C₂²×C₁₆₉	1	1	yes	characteristic, direct product factor, Sylow
16	C₂	C₂×C₃×C₁₆₉	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₃	C₂²×C₃×C₁₃
socle, prime radical	C₂²×C₃×C₁₃	C₁₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₃×C₁₆₉	C₂	direct (N × H)
2. C₂²×C₁₆₉	C₃	direct (N × H)
3. C₃×C₁₆₉	C₂²	direct (N × H)
4. C₂×C₁₆₉	C₂×C₃	direct (N × H)
5. C₁₆₉	C₂²×C₃	direct (N × H)
12. C₂²×C₃	C₁₆₉	direct (N × H)
13. C₂×C₃	C₂×C₁₆₉	direct (N × H)
14. C₂²	C₃×C₁₆₉	direct (N × H)
15. C₃	C₂²×C₁₆₉	direct (N × H)
16. C₂	C₂×C₃×C₁₆₉	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₁₆₉	2
C₂²×C₁₆₉	3
C₂²×C₃×C₁₃	13