Finite Group Databasebeta

← C₂²×C₃×C₁₃² #14523142

Subgroups — C₂²×C₃×C₁₃² #14523142

Order 2028.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₃²	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₁₃²	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₃²	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₁₃²	C₂×C₃	1	3	yes	direct product factor
5	C₁₃²	C₂²×C₃	1	1	yes	characteristic, direct product factor, Sylow
6	C₂²×C₃×C₁₃	C₁₃	1	14	yes	maximal, direct product factor
7	C₂×C₃×C₁₃	C₂×C₁₃	1	42	yes	direct product factor
8	C₂²×C₁₃	C₃×C₁₃	1	14	yes	direct product factor
9	C₃×C₁₃	C₂²×C₁₃	1	14	yes	direct product factor
10	C₂×C₁₃	C₂×C₃×C₁₃	1	42	yes	direct product factor
11	C₁₃	C₂²×C₃×C₁₃	1	14	yes	direct product factor
12	C₂²×C₃	C₁₃²	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃	C₂×C₁₃²	1	3	yes	direct product factor
14	C₂²	C₃×C₁₃²	1	1	yes	characteristic, direct product factor, Sylow
15	C₃	C₂²×C₁₃²	1	1	yes	characteristic, direct product factor, Sylow
16	C₂	C₂×C₃×C₁₃²	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
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×C₁₃²	C₂	direct (N × H)
2. C₂²×C₁₃²	C₃	direct (N × H)
3. C₃×C₁₃²	C₂²	direct (N × H)
4. C₂×C₁₃²	C₂×C₃	direct (N × H)
5. C₁₃²	C₂²×C₃	direct (N × H)
6. C₂²×C₃×C₁₃	C₁₃	direct (N × H)
7. C₂×C₃×C₁₃	C₂×C₁₃	direct (N × H)
8. C₂²×C₁₃	C₃×C₁₃	direct (N × H)
9. C₃×C₁₃	C₂²×C₁₃	direct (N × H)
10. C₂×C₁₃	C₂×C₃×C₁₃	direct (N × H)
11. C₁₃	C₂²×C₃×C₁₃	direct (N × H)
12. C₂²×C₃	C₁₃²	direct (N × H)
13. C₂×C₃	C₂×C₁₃²	direct (N × H)
14. C₂²	C₃×C₁₃²	direct (N × H)
15. C₃	C₂²×C₁₃²	direct (N × H)
16. C₂	C₂×C₃×C₁₃²	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×C₁₃²	2
C₂²×C₁₃²	3
C₂²×C₃×C₁₃	13