Subgroups — C₁₀₉×C₃⋊(D₁₃⋊C₃) #38784121

Order 25506.

36 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, complemented, Hall
2	D₁₃⋊C₃×C₁₀₉	—	3	1	no	maximal
3	D₃₉×C₁₀₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₃×C₁₀₉	C₂×C₃	1	1	yes	characteristic, complemented
5	C₁₃⋊C₃×C₁₀₉	—	2	1	no	—
6	C₁₃⋊C₃×C₁₀₉	D₃	1	1	yes	characteristic, complemented
7	D₁₃×C₁₀₉	—	3	1	no	Hall
8	C₃×D₃×C₁₀₉	—	13	1	no	maximal, Hall
9	C₁₃×C₁₀₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
10	C₃²×C₁₀₉	—	13	1	no	Hall
11	C₂×C₃×C₁₀₉	—	39	1	no	—
12	D₃×C₁₀₉	—	13	1	no	—
13	C₃×C₁₀₉	—	13	1	no	—
14	C₃×C₁₀₉	—	26	1	no	—
15	C₃×C₁₀₉	D₁₃⋊C₃	1	1	yes	characteristic, complemented
16	C₃⋊(D₁₃⋊C₃)	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₁₀₉	—	39	1	no	Hall
18	C₃×C₁₃⋊C₃	C₂×C₁₀₉	1	1	yes	characteristic, complemented, Hall
19	C₁₀₉	C₃⋊(D₁₃⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
20	D₃₉	C₃×C₁₀₉	1	1	yes	characteristic, complemented
21	D₁₃⋊C₃	—	3	1	no	—
22	C₃×C₁₃	C₂×C₃×C₁₀₉	1	1	yes	characteristic, complemented
23	C₁₃⋊C₃	—	2	1	no	—
24	C₁₃⋊C₃	D₃×C₁₀₉	1	1	yes	characteristic, complemented
25	D₁₃	—	3	1	no	Hall
26	C₃×D₃	—	13	1	no	Hall
27	C₁₃	C₃×D₃×C₁₀₉	1	1	yes	characteristic, complemented, Sylow
28	C₃²	—	13	1	no	Sylow
29	C₂×C₃	—	39	1	no	—
30	D₃	—	13	1	no	—
31	C₃	—	13	1	no	—
32	C₃	—	26	1	no	—
33	C₃	D₁₃⋊C₃×C₁₀₉	1	1	yes	characteristic, complemented
34	C₂	—	39	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₀₉	C₃⋊(D₁₃⋊C₃)
commutator, cosocle, hypocenter	C₃×C₁₃	C₂×C₃×C₁₀₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₁₀₉	C₂×C₃
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₁₀₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃⋊C₃×C₁₀₉	C₂	semidirect
3. D₃₉×C₁₀₉	C₃	semidirect
4. C₃×C₁₃×C₁₀₉	C₂×C₃	semidirect
6. C₁₃⋊C₃×C₁₀₉	D₃	semidirect
9. C₁₃×C₁₀₉	C₃×D₃	semidirect
15. C₃×C₁₀₉	D₁₃⋊C₃	semidirect
16. C₃⋊(D₁₃⋊C₃)	C₁₀₉	direct (N × H)
18. C₃×C₁₃⋊C₃	C₂×C₁₀₉	semidirect
19. C₁₀₉	C₃⋊(D₁₃⋊C₃)	direct (N × H)
20. D₃₉	C₃×C₁₀₉	semidirect
22. C₃×C₁₃	C₂×C₃×C₁₀₉	semidirect
24. C₁₃⋊C₃	D₃×C₁₀₉	semidirect
27. C₁₃	C₃×D₃×C₁₀₉	semidirect
33. C₃	D₁₃⋊C₃×C₁₀₉	semidirect

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
D₁₃⋊C₃×C₁₀₉	3
D₃₉×C₁₀₉	3
C₃×D₃×C₁₀₉	13
C₃⋊(D₁₃⋊C₃)	109

Subgroups — C109×C3⋊(D13⋊C3) #38784121

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₉×C₃⋊(D₁₃⋊C₃) #38784121