Subgroups — C₂×C₃×C₁₃⋊C₃×C₁₀₉ #38784136

Order 25506.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃⋊C₃×C₁₀₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₃⋊C₃×C₁₀₉	C₃	1	3	yes	maximal, direct product factor
3	C₂×C₃×C₁₃×C₁₀₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₃×C₁₀₉	C₂×C₃	1	1	yes	characteristic, complemented
5	C₁₃⋊C₃×C₁₀₉	C₂×C₃	1	3	yes	direct product factor
6	C₂×C₁₃×C₁₀₉	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃²×C₁₀₉	—	13	1	no	maximal, Hall
8	C₁₃×C₁₀₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃²×C₁₀₉	—	13	1	no	Hall
10	C₂×C₃×C₁₀₉	—	13	3	no	—
11	C₂×C₃×C₁₀₉	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
12	C₃×C₁₀₉	—	13	3	no	—
13	C₃×C₁₀₉	C₂×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
14	C₂×C₃×C₁₃⋊C₃	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₁₀₉	C₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₁₃⋊C₃	C₂×C₁₀₉	1	1	yes	characteristic, direct product factor, Hall
17	C₁₀₉	C₂×C₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₃×C₁₃	C₃×C₁₀₉	1	1	yes	characteristic, complemented
19	C₂×C₁₃⋊C₃	C₃×C₁₀₉	1	3	yes	direct product factor
20	C₃×C₁₃	C₂×C₃×C₁₀₉	1	1	yes	characteristic, complemented
21	C₁₃⋊C₃	C₂×C₃×C₁₀₉	1	3	yes	direct product factor
22	C₂×C₁₃	C₃²×C₁₀₉	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃²	—	13	1	no	Hall
24	C₁₃	C₂×C₃²×C₁₀₉	1	1	yes	characteristic, complemented, Sylow
25	C₃²	—	13	1	no	Sylow
26	C₂×C₃	—	13	3	no	—
27	C₂×C₃	C₁₃⋊C₃×C₁₀₉	1	1	yes	characteristic, direct product factor
28	C₃	—	13	3	no	—
29	C₃	C₂×C₁₃⋊C₃×C₁₀₉	1	1	yes	characteristic, direct product factor
30	C₂	C₃×C₁₃⋊C₃×C₁₀₉	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₀₉	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₃²×C₁₀₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃×C₁₀₉	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₁₀₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃⋊C₃×C₁₀₉	C₂	direct (N × H)
2. C₂×C₁₃⋊C₃×C₁₀₉	C₃	direct (N × H)
3. C₂×C₃×C₁₃×C₁₀₉	C₃	semidirect
4. C₃×C₁₃×C₁₀₉	C₂×C₃	semidirect
5. C₁₃⋊C₃×C₁₀₉	C₂×C₃	direct (N × H)
6. C₂×C₁₃×C₁₀₉	C₃²	semidirect
8. C₁₃×C₁₀₉	C₂×C₃²	semidirect
11. C₂×C₃×C₁₀₉	C₁₃⋊C₃	direct (N × H)
13. C₃×C₁₀₉	C₂×C₁₃⋊C₃	direct (N × H)
14. C₂×C₃×C₁₃⋊C₃	C₁₀₉	direct (N × H)
15. C₂×C₁₀₉	C₃×C₁₃⋊C₃	direct (N × H)
16. C₃×C₁₃⋊C₃	C₂×C₁₀₉	direct (N × H)
17. C₁₀₉	C₂×C₃×C₁₃⋊C₃	direct (N × H)
18. C₂×C₃×C₁₃	C₃×C₁₀₉	semidirect
19. C₂×C₁₃⋊C₃	C₃×C₁₀₉	direct (N × H)
20. C₃×C₁₃	C₂×C₃×C₁₀₉	semidirect
21. C₁₃⋊C₃	C₂×C₃×C₁₀₉	direct (N × H)
22. C₂×C₁₃	C₃²×C₁₀₉	semidirect
24. C₁₃	C₂×C₃²×C₁₀₉	semidirect
27. C₂×C₃	C₁₃⋊C₃×C₁₀₉	direct (N × H)
29. C₃	C₂×C₁₃⋊C₃×C₁₀₉	direct (N × H)
30. C₂	C₃×C₁₃⋊C₃×C₁₀₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₁₃⋊C₃×C₁₀₉	2
C₂×C₁₃⋊C₃×C₁₀₉	3
C₂×C₃×C₁₃×C₁₀₉	3
C₂×C₃²×C₁₀₉	13
C₂×C₃×C₁₃⋊C₃	109

Subgroups — C2×C3×C13⋊C3×C109 #38784136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₁₃⋊C₃×C₁₀₉ #38784136