Finite Group Databasebeta

← C₃×C₁₁×C₁₃×C₇₃ #44531185

Subgroups — C₃×C₁₁×C₁₃×C₇₃ #44531185

Order 31317.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₃×C₇₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₁₃×C₇₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₁×C₇₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₃×C₇₃	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
5	C₁₁×C₇₃	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₁₁×C₁₃	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₇₃	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
8	C₁₁×C₁₃	C₃×C₇₃	1	1	yes	characteristic, direct product factor, Hall
9	C₇₃	C₃×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
10	C₃×C₁₃	C₁₁×C₇₃	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₁₁	C₁₃×C₇₃	1	1	yes	characteristic, direct product factor, Hall
12	C₁₃	C₃×C₁₁×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₁₁	C₃×C₁₃×C₇₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₃	C₁₁×C₁₃×C₇₃	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×C₇₃	C₃	direct (N × H)
2. C₃×C₁₃×C₇₃	C₁₁	direct (N × H)
3. C₃×C₁₁×C₇₃	C₁₃	direct (N × H)
4. C₁₃×C₇₃	C₃×C₁₁	direct (N × H)
5. C₁₁×C₇₃	C₃×C₁₃	direct (N × H)
6. C₃×C₁₁×C₁₃	C₇₃	direct (N × H)
7. C₃×C₇₃	C₁₁×C₁₃	direct (N × H)
8. C₁₁×C₁₃	C₃×C₇₃	direct (N × H)
9. C₇₃	C₃×C₁₁×C₁₃	direct (N × H)
10. C₃×C₁₃	C₁₁×C₇₃	direct (N × H)
11. C₃×C₁₁	C₁₃×C₇₃	direct (N × H)
12. C₁₃	C₃×C₁₁×C₇₃	direct (N × H)
13. C₁₁	C₃×C₁₃×C₇₃	direct (N × H)
14. C₃	C₁₁×C₁₃×C₇₃	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×C₇₃	3
C₃×C₁₃×C₇₃	11
C₃×C₁₁×C₇₃	13
C₃×C₁₁×C₁₃	73