Finite Group Databasebeta

← C₂×C₁₃×C₁₇×C₆₇ #44444142

Subgroups — C₂×C₁₃×C₁₇×C₆₇ #44444142

Order 29614.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₇×C₆₇	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₇×C₆₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₁₃×C₆₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₇×C₆₇	C₂×C₁₃	1	1	yes	characteristic, direct product factor, Hall
5	C₁₃×C₆₇	C₂×C₁₇	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₁₃×C₁₇	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₃×C₁₇	C₂×C₆₇	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₆₇	C₁₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
9	C₆₇	C₂×C₁₃×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
10	C₂×C₁₇	C₁₃×C₆₇	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₁₃	C₁₇×C₆₇	1	1	yes	characteristic, direct product factor, Hall
12	C₁₇	C₂×C₁₃×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
13	C₁₃	C₂×C₁₇×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	C₁₃×C₁₇×C₆₇	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×C₁₇×C₆₇	C₂	direct (N × H)
2. C₂×C₁₇×C₆₇	C₁₃	direct (N × H)
3. C₂×C₁₃×C₆₇	C₁₇	direct (N × H)
4. C₁₇×C₆₇	C₂×C₁₃	direct (N × H)
5. C₁₃×C₆₇	C₂×C₁₇	direct (N × H)
6. C₂×C₁₃×C₁₇	C₆₇	direct (N × H)
7. C₁₃×C₁₇	C₂×C₆₇	direct (N × H)
8. C₂×C₆₇	C₁₃×C₁₇	direct (N × H)
9. C₆₇	C₂×C₁₃×C₁₇	direct (N × H)
10. C₂×C₁₇	C₁₃×C₆₇	direct (N × H)
11. C₂×C₁₃	C₁₇×C₆₇	direct (N × H)
12. C₁₇	C₂×C₁₃×C₆₇	direct (N × H)
13. C₁₃	C₂×C₁₇×C₆₇	direct (N × H)
14. C₂	C₁₃×C₁₇×C₆₇	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×C₁₇×C₆₇	2
C₂×C₁₇×C₆₇	13
C₂×C₁₃×C₆₇	17
C₂×C₁₃×C₁₇	67