Finite Group Databasebeta

← C₃⁴×C₁₃⋊C₃ #15691699

Subgroups — C₃⁴×C₁₃⋊C₃ #15691699

Order 3159.

5328 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₁₃⋊C₃	C₃	1	120	yes	maximal, direct product factor
2	C₃⁴×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃³×C₁₃	C₃²	1	40	yes	complemented
4	C₃²×C₁₃⋊C₃	C₃²	1	1170	yes	direct product factor
5	C₃⁵	—	13	1	no	maximal, Sylow
6	C₃²×C₁₃	C₃³	1	130	yes	complemented
7	C₃×C₁₃⋊C₃	C₃³	1	1080	yes	direct product factor
8	C₃⁴	—	13	120	no	—
9	C₃⁴	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
10	C₃×C₁₃	C₃⁴	1	40	yes	complemented
11	C₁₃⋊C₃	C₃⁴	1	81	yes	direct product factor
12	C₃³	—	13	1170	no	—
13	C₃³	C₃×C₁₃⋊C₃	1	40	yes	direct product factor
14	C₁₃	C₃⁵	1	1	yes	characteristic, complemented, Sylow
15	C₃²	—	13	1080	no	—
16	C₃²	C₃²×C₁₃⋊C₃	1	130	yes	direct product factor
17	C₃	—	13	81	no	—
18	C₃	C₃³×C₁₃⋊C₃	1	40	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₃⁴	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₃⁵
Frattini	C₁	G
Fitting, socle	C₃⁴×C₁₃	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃⁴

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃³×C₁₃⋊C₃	C₃	direct (N × H)
2. C₃⁴×C₁₃	C₃	semidirect
3. C₃³×C₁₃	C₃²	semidirect
4. C₃²×C₁₃⋊C₃	C₃²	direct (N × H)
6. C₃²×C₁₃	C₃³	semidirect
7. C₃×C₁₃⋊C₃	C₃³	direct (N × H)
9. C₃⁴	C₁₃⋊C₃	direct (N × H)
10. C₃×C₁₃	C₃⁴	semidirect
11. C₁₃⋊C₃	C₃⁴	direct (N × H)
13. C₃³	C₃×C₁₃⋊C₃	direct (N × H)
14. C₁₃	C₃⁵	semidirect
16. C₃²	C₃²×C₁₃⋊C₃	direct (N × H)
18. C₃	C₃³×C₁₃⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×C₁₃⋊C₃	3
C₃⁴×C₁₃	3
C₃⁵	13