Finite Group Databasebeta

← C₂×C₁₃×C₁₇² #21418926

Subgroups — C₂×C₁₃×C₁₇² #21418926

Order 7514.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₇²	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₇²	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₁₃×C₁₇	C₁₇	1	18	yes	maximal, direct product factor
4	C₁₇²	C₂×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
5	C₁₃×C₁₇	C₂×C₁₇	1	18	yes	direct product factor
6	C₂×C₁₇	C₁₃×C₁₇	1	18	yes	direct product factor
7	C₂×C₁₃	C₁₇²	1	1	yes	characteristic, direct product factor, Hall
8	C₁₇	C₂×C₁₃×C₁₇	1	18	yes	direct product factor
9	C₁₃	C₂×C₁₇²	1	1	yes	characteristic, direct product factor, Sylow
10	C₂	C₁₃×C₁₇²	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. C₁₃×C₁₇²	C₂	direct (N × H)
2. C₂×C₁₇²	C₁₃	direct (N × H)
3. C₂×C₁₃×C₁₇	C₁₇	direct (N × H)
4. C₁₇²	C₂×C₁₃	direct (N × H)
5. C₁₃×C₁₇	C₂×C₁₇	direct (N × H)
6. C₂×C₁₇	C₁₃×C₁₇	direct (N × H)
7. C₂×C₁₃	C₁₇²	direct (N × H)
8. C₁₇	C₂×C₁₃×C₁₇	direct (N × H)
9. C₁₃	C₂×C₁₇²	direct (N × H)
10. C₂	C₁₃×C₁₇²	direct (N × H)