Finite Group Databasebeta

← C₃³×C₁₃×C₇₁ #72202159

Subgroups — C₃³×C₁₃×C₇₁ #72202159

Order 24921.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×C₇₁	C₃	1	13	yes	maximal, direct product factor
2	C₃×C₁₃×C₇₁	C₃²	1	13	yes	direct product factor
3	C₃³×C₇₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₃×C₇₁	C₃³	1	1	yes	characteristic, direct product factor, Hall
5	C₃²×C₇₁	C₃×C₁₃	1	13	yes	direct product factor
6	C₃³×C₁₃	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₇₁	C₃²×C₁₃	1	13	yes	direct product factor
8	C₃²×C₁₃	C₃×C₇₁	1	13	yes	direct product factor
9	C₇₁	C₃³×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
10	C₃×C₁₃	C₃²×C₇₁	1	13	yes	direct product factor
11	C₃³	C₁₃×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
12	C₁₃	C₃³×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
13	C₃²	C₃×C₁₃×C₇₁	1	13	yes	direct product factor
14	C₃	C₃²×C₁₃×C₇₁	1	13	yes	direct product factor

	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. C₃²×C₁₃×C₇₁	C₃	direct (N × H)
2. C₃×C₁₃×C₇₁	C₃²	direct (N × H)
3. C₃³×C₇₁	C₁₃	direct (N × H)
4. C₁₃×C₇₁	C₃³	direct (N × H)
5. C₃²×C₇₁	C₃×C₁₃	direct (N × H)
6. C₃³×C₁₃	C₇₁	direct (N × H)
7. C₃×C₇₁	C₃²×C₁₃	direct (N × H)
8. C₃²×C₁₃	C₃×C₇₁	direct (N × H)
9. C₇₁	C₃³×C₁₃	direct (N × H)
10. C₃×C₁₃	C₃²×C₇₁	direct (N × H)
11. C₃³	C₁₃×C₇₁	direct (N × H)
12. C₁₃	C₃³×C₇₁	direct (N × H)
13. C₃²	C₃×C₁₃×C₇₁	direct (N × H)
14. C₃	C₃²×C₁₃×C₇₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₁₃×C₇₁	3
C₃³×C₇₁	13
C₃³×C₁₃	71