Finite Group Databasebeta

← C₄×C₂₃×C₁₆₉ #29509751

Subgroups — C₄×C₂₃×C₁₆₉ #29509751

Order 15548.

18 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×C₁₆₉	C₂	1	1	yes	maximal, characteristic
2	C₂₃×C₁₆₉	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₁₃×C₂₃	C₁₃	1	1	yes	maximal, characteristic
4	C₄×C₁₆₉	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₃×C₂₃	C₂×C₁₃	1	1	yes	characteristic
6	C₂×C₁₆₉	C₂×C₂₃	1	1	yes	characteristic
7	C₁₃×C₂₃	C₄×C₁₃	1	1	yes	characteristic
8	C₁₆₉	C₄×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
9	C₄×C₂₃	C₁₆₉	1	1	yes	characteristic, direct product factor, Hall
10	C₄×C₁₃	C₁₃×C₂₃	1	1	yes	characteristic
11	C₂×C₂₃	C₂×C₁₆₉	1	1	yes	characteristic
12	C₂×C₁₃	C₂×C₁₃×C₂₃	1	1	yes	characteristic
13	C₂₃	C₄×C₁₆₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₁₃	C₄×C₁₃×C₂₃	1	1	yes	characteristic
15	C₄	C₂₃×C₁₆₉	1	1	yes	characteristic, direct product factor, Sylow
16	C₂	C₂×C₂₃×C₁₆₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₁₃	C₂×C₁₃×C₂₃
socle, prime radical	C₂×C₁₃×C₂₃	C₂×C₁₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×C₁₆₉	C₄	direct (N × H)
4. C₄×C₁₆₉	C₂₃	direct (N × H)
8. C₁₆₉	C₄×C₂₃	direct (N × H)
9. C₄×C₂₃	C₁₆₉	direct (N × H)
13. C₂₃	C₄×C₁₆₉	direct (N × H)
15. C₄	C₂₃×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×C₂₃×C₁₆₉	2
C₄×C₁₃×C₂₃	13
C₄×C₁₆₉	23