Finite Group Databasebeta

← C₂×C₅×C₁₉×C₁₆₇ #44540595

Subgroups — C₂×C₅×C₁₉×C₁₆₇ #44540595

Order 31730.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₉×C₁₆₇	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₉×C₁₆₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₉×C₁₆₇	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₅×C₁₆₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₁₆₇	C₂×C₁₉	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₁₆₇	C₅×C₁₉	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₅×C₁₉	C₁₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₆₇	C₂×C₅×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
9	C₅×C₁₉	C₂×C₁₆₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₉	C₅×C₁₆₇	1	1	yes	characteristic, direct product factor, Hall
11	C₁₉	C₂×C₅×C₁₆₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₅	C₁₉×C₁₆₇	1	1	yes	characteristic, direct product factor, Hall
13	C₅	C₂×C₁₉×C₁₆₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	C₅×C₁₉×C₁₆₇	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. C₅×C₁₉×C₁₆₇	C₂	direct (N × H)
2. C₂×C₁₉×C₁₆₇	C₅	direct (N × H)
3. C₁₉×C₁₆₇	C₂×C₅	direct (N × H)
4. C₂×C₅×C₁₆₇	C₁₉	direct (N × H)
5. C₅×C₁₆₇	C₂×C₁₉	direct (N × H)
6. C₂×C₁₆₇	C₅×C₁₉	direct (N × H)
7. C₂×C₅×C₁₉	C₁₆₇	direct (N × H)
8. C₁₆₇	C₂×C₅×C₁₉	direct (N × H)
9. C₅×C₁₉	C₂×C₁₆₇	direct (N × H)
10. C₂×C₁₉	C₅×C₁₆₇	direct (N × H)
11. C₁₉	C₂×C₅×C₁₆₇	direct (N × H)
12. C₂×C₅	C₁₉×C₁₆₇	direct (N × H)
13. C₅	C₂×C₁₉×C₁₆₇	direct (N × H)
14. C₂	C₅×C₁₉×C₁₆₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₁₉×C₁₆₇	2
C₂×C₁₉×C₁₆₇	5
C₂×C₅×C₁₆₇	19
C₂×C₅×C₁₉	167