Finite Group Databasebeta

← C₂×C₁₉×C₂₃×C₄₃ #49178012

Subgroups — C₂×C₁₉×C₂₃×C₄₃ #49178012

Order 37582.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₂₃×C₄₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₂₃×C₄₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₁₉×C₄₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂₃×C₄₃	C₂×C₁₉	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₁₉×C₂₃	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₉×C₄₃	C₂×C₂₃	1	1	yes	characteristic, direct product factor, Hall
7	C₁₉×C₂₃	C₂×C₄₃	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₄₃	C₁₉×C₂₃	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₂₃	C₁₉×C₄₃	1	1	yes	characteristic, direct product factor, Hall
10	C₄₃	C₂×C₁₉×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
11	C₂×C₁₉	C₂₃×C₄₃	1	1	yes	characteristic, direct product factor, Hall
12	C₂₃	C₂×C₁₉×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₁₉	C₂×C₂₃×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	C₁₉×C₂₃×C₄₃	1	1	yes	characteristic, direct product factor, Sylow

	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. C₁₉×C₂₃×C₄₃	C₂	direct (N × H)
2. C₂×C₂₃×C₄₃	C₁₉	direct (N × H)
3. C₂×C₁₉×C₄₃	C₂₃	direct (N × H)
4. C₂₃×C₄₃	C₂×C₁₉	direct (N × H)
5. C₂×C₁₉×C₂₃	C₄₃	direct (N × H)
6. C₁₉×C₄₃	C₂×C₂₃	direct (N × H)
7. C₁₉×C₂₃	C₂×C₄₃	direct (N × H)
8. C₂×C₄₃	C₁₉×C₂₃	direct (N × H)
9. C₂×C₂₃	C₁₉×C₄₃	direct (N × H)
10. C₄₃	C₂×C₁₉×C₂₃	direct (N × H)
11. C₂×C₁₉	C₂₃×C₄₃	direct (N × H)
12. C₂₃	C₂×C₁₉×C₄₃	direct (N × H)
13. C₁₉	C₂×C₂₃×C₄₃	direct (N × H)
14. C₂	C₁₉×C₂₃×C₄₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×C₂₃×C₄₃	2
C₂×C₂₃×C₄₃	19
C₂×C₁₉×C₄₃	23
C₂×C₁₉×C₂₃	43