Finite Group Databasebeta

← C₂×C₇×C₁₇×C₁₉ #17985282

Subgroups — C₂×C₇×C₁₇×C₁₉ #17985282

Order 4522.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₇×C₁₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₇×C₁₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₇×C₁₉	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₇×C₁₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₇×C₁₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₁₉	C₂×C₁₇	1	1	yes	characteristic, direct product factor, Hall
7	C₇×C₁₇	C₂×C₁₉	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₁₉	C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₁₇	C₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
10	C₁₉	C₂×C₇×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
11	C₁₇	C₂×C₇×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₇	C₁₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
13	C₇	C₂×C₁₇×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	C₇×C₁₇×C₁₉	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. C₇×C₁₇×C₁₉	C₂	direct (N × H)
2. C₂×C₁₇×C₁₉	C₇	direct (N × H)
3. C₁₇×C₁₉	C₂×C₇	direct (N × H)
4. C₂×C₇×C₁₉	C₁₇	direct (N × H)
5. C₂×C₇×C₁₇	C₁₉	direct (N × H)
6. C₇×C₁₉	C₂×C₁₇	direct (N × H)
7. C₇×C₁₇	C₂×C₁₉	direct (N × H)
8. C₂×C₁₉	C₇×C₁₇	direct (N × H)
9. C₂×C₁₇	C₇×C₁₉	direct (N × H)
10. C₁₉	C₂×C₇×C₁₇	direct (N × H)
11. C₁₇	C₂×C₇×C₁₉	direct (N × H)
12. C₂×C₇	C₁₇×C₁₉	direct (N × H)
13. C₇	C₂×C₁₇×C₁₉	direct (N × H)
14. C₂	C₇×C₁₇×C₁₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₁₇×C₁₉	2
C₂×C₁₇×C₁₉	7
C₂×C₇×C₁₉	17
C₂×C₇×C₁₇	19