Finite Group Databasebeta

← C₃²×C₁₉×C₁₃₉ #37557750

Subgroups — C₃²×C₁₉×C₁₃₉ #37557750

Order 23769.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×C₁₃₉	C₃	1	4	yes	maximal, direct product factor
2	C₁₉×C₁₃₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
3	C₃²×C₁₃₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₁₃₉	C₃×C₁₉	1	4	yes	direct product factor
5	C₃²×C₁₉	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₃₉	C₃²×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
7	C₃×C₁₉	C₃×C₁₃₉	1	4	yes	direct product factor
8	C₁₉	C₃²×C₁₃₉	1	1	yes	characteristic, direct product factor, Sylow
9	C₃²	C₁₉×C₁₃₉	1	1	yes	characteristic, direct product factor, Sylow
10	C₃	C₃×C₁₉×C₁₃₉	1	4	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. C₃×C₁₉×C₁₃₉	C₃	direct (N × H)
2. C₁₉×C₁₃₉	C₃²	direct (N × H)
3. C₃²×C₁₃₉	C₁₉	direct (N × H)
4. C₃×C₁₃₉	C₃×C₁₉	direct (N × H)
5. C₃²×C₁₉	C₁₃₉	direct (N × H)
6. C₁₃₉	C₃²×C₁₉	direct (N × H)
7. C₃×C₁₉	C₃×C₁₃₉	direct (N × H)
8. C₁₉	C₃²×C₁₃₉	direct (N × H)
9. C₃²	C₁₉×C₁₃₉	direct (N × H)
10. C₃	C₃×C₁₉×C₁₃₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₁₉×C₁₃₉	3
C₃²×C₁₃₉	19
C₃²×C₁₉	139