Finite Group Databasebeta

← C₂×C₁₇×C₁₉×C₂₉ #34035481

Subgroups — C₂×C₁₇×C₁₉×C₂₉ #34035481

Order 18734.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₁₉×C₂₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₉×C₂₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₁₇×C₂₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₁₇×C₁₉	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₉×C₂₉	C₂×C₁₇	1	1	yes	characteristic, direct product factor, Hall
6	C₁₇×C₂₉	C₂×C₁₉	1	1	yes	characteristic, direct product factor, Hall
7	C₁₇×C₁₉	C₂×C₂₉	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₂₉	C₁₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₁₉	C₁₇×C₂₉	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₇	C₁₉×C₂₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂₉	C₂×C₁₇×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
12	C₁₉	C₂×C₁₇×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
13	C₁₇	C₂×C₁₉×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	C₁₇×C₁₉×C₂₉	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. C₁₇×C₁₉×C₂₉	C₂	direct (N × H)
2. C₂×C₁₉×C₂₉	C₁₇	direct (N × H)
3. C₂×C₁₇×C₂₉	C₁₉	direct (N × H)
4. C₂×C₁₇×C₁₉	C₂₉	direct (N × H)
5. C₁₉×C₂₉	C₂×C₁₇	direct (N × H)
6. C₁₇×C₂₉	C₂×C₁₉	direct (N × H)
7. C₁₇×C₁₉	C₂×C₂₉	direct (N × H)
8. C₂×C₂₉	C₁₇×C₁₉	direct (N × H)
9. C₂×C₁₉	C₁₇×C₂₉	direct (N × H)
10. C₂×C₁₇	C₁₉×C₂₉	direct (N × H)
11. C₂₉	C₂×C₁₇×C₁₉	direct (N × H)
12. C₁₉	C₂×C₁₇×C₂₉	direct (N × H)
13. C₁₇	C₂×C₁₉×C₂₉	direct (N × H)
14. C₂	C₁₇×C₁₉×C₂₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×C₁₉×C₂₉	2
C₂×C₁₉×C₂₉	17
C₂×C₁₇×C₂₉	19
C₂×C₁₇×C₁₉	29