Finite Group Databasebeta

← C₇×C₁₁×C₁₃×C₃₁ #44526739

Subgroups — C₇×C₁₁×C₁₃×C₃₁ #44526739

Order 31031.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₃×C₃₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₇×C₁₃×C₃₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₁₁×C₃₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×C₁₁×C₁₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₃×C₃₁	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
6	C₁₁×C₃₁	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
7	C₇×C₃₁	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
8	C₁₁×C₁₃	C₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
9	C₇×C₁₃	C₁₁×C₃₁	1	1	yes	characteristic, direct product factor, Hall
10	C₇×C₁₁	C₁₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
11	C₃₁	C₇×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₁₃	C₇×C₁₁×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
13	C₁₁	C₇×C₁₃×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
14	C₇	C₁₁×C₁₃×C₃₁	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. C₁₁×C₁₃×C₃₁	C₇	direct (N × H)
2. C₇×C₁₃×C₃₁	C₁₁	direct (N × H)
3. C₇×C₁₁×C₃₁	C₁₃	direct (N × H)
4. C₇×C₁₁×C₁₃	C₃₁	direct (N × H)
5. C₁₃×C₃₁	C₇×C₁₁	direct (N × H)
6. C₁₁×C₃₁	C₇×C₁₃	direct (N × H)
7. C₇×C₃₁	C₁₁×C₁₃	direct (N × H)
8. C₁₁×C₁₃	C₇×C₃₁	direct (N × H)
9. C₇×C₁₃	C₁₁×C₃₁	direct (N × H)
10. C₇×C₁₁	C₁₃×C₃₁	direct (N × H)
11. C₃₁	C₇×C₁₁×C₁₃	direct (N × H)
12. C₁₃	C₇×C₁₁×C₃₁	direct (N × H)
13. C₁₁	C₇×C₁₃×C₃₁	direct (N × H)
14. C₇	C₁₁×C₁₃×C₃₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×C₁₃×C₃₁	7
C₇×C₁₃×C₃₁	11
C₇×C₁₁×C₃₁	13
C₇×C₁₁×C₁₃	31