Finite Group Databasebeta

← C₂×C₁₃×C₂₉×C₄₁ #44525639

Subgroups — C₂×C₁₃×C₂₉×C₄₁ #44525639

Order 30914.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₂₉×C₄₁	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₂₉×C₄₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂₉×C₄₁	C₂×C₁₃	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₁₃×C₄₁	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₃×C₂₉	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₃×C₄₁	C₂×C₂₉	1	1	yes	characteristic, direct product factor, Hall
7	C₁₃×C₂₉	C₂×C₄₁	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₄₁	C₁₃×C₂₉	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₂₉	C₁₃×C₄₁	1	1	yes	characteristic, direct product factor, Hall
10	C₄₁	C₂×C₁₃×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
11	C₂₉	C₂×C₁₃×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₁₃	C₂₉×C₄₁	1	1	yes	characteristic, direct product factor, Hall
13	C₁₃	C₂×C₂₉×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	C₁₃×C₂₉×C₄₁	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×C₂₉×C₄₁	C₂	direct (N × H)
2. C₂×C₂₉×C₄₁	C₁₃	direct (N × H)
3. C₂₉×C₄₁	C₂×C₁₃	direct (N × H)
4. C₂×C₁₃×C₄₁	C₂₉	direct (N × H)
5. C₂×C₁₃×C₂₉	C₄₁	direct (N × H)
6. C₁₃×C₄₁	C₂×C₂₉	direct (N × H)
7. C₁₃×C₂₉	C₂×C₄₁	direct (N × H)
8. C₂×C₄₁	C₁₃×C₂₉	direct (N × H)
9. C₂×C₂₉	C₁₃×C₄₁	direct (N × H)
10. C₄₁	C₂×C₁₃×C₂₉	direct (N × H)
11. C₂₉	C₂×C₁₃×C₄₁	direct (N × H)
12. C₂×C₁₃	C₂₉×C₄₁	direct (N × H)
13. C₁₃	C₂×C₂₉×C₄₁	direct (N × H)
14. C₂	C₁₃×C₂₉×C₄₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×C₂₉×C₄₁	2
C₂×C₂₉×C₄₁	13
C₂×C₁₃×C₄₁	29
C₂×C₁₃×C₂₉	41