Subgroups — C₁₃⋊C₃×D₂₀₉ #30654452

Order 16302.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₉×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₂₀₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	D₁₉×C₁₃⋊C₃	—	11	1	no	maximal, Hall
5	C₃×D₂₀₉	—	13	1	no	maximal, Hall
6	D₁₁×C₁₃⋊C₃	—	19	1	no	maximal, Hall
7	C₁₉×C₁₃⋊C₃	D₁₁	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₁×C₁₉	—	13	1	no	Hall
9	C₁₃×D₁₉	—	11	1	no	Hall
10	C₁₁×C₁₃⋊C₃	D₁₉	1	1	yes	characteristic, complemented, Hall
11	D₂₀₉	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
12	C₁₃×D₁₁	—	19	1	no	Hall
13	C₁₃×C₁₉	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
14	C₁₁×C₁₉	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
15	C₁₁×C₁₃	C₃×D₁₉	1	1	yes	characteristic, complemented, Hall
16	C₃×D₁₉	—	143	1	no	Hall
17	C₂×C₁₃⋊C₃	—	209	1	no	Hall
18	C₃×D₁₁	—	247	1	no	Hall
19	C₃×C₁₉	—	13	1	no	Hall
20	C₁₃⋊C₃	D₂₀₉	1	1	yes	characteristic, direct product factor, Hall
21	D₁₉	—	11	1	no	Hall
22	C₃×C₁₁	—	13	1	no	Hall
23	C₂×C₁₃	—	209	1	no	Hall
24	D₁₁	—	19	1	no	Hall
25	C₁₉	D₁₁×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	C₁₃	C₃×D₂₀₉	1	1	yes	characteristic, complemented, Sylow
27	C₁₁	D₁₉×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	2717	1	no	Hall
29	C₃	—	13	1	no	Sylow
30	C₂	—	209	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₁₁×C₁₃×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₉×C₁₃⋊C₃	C₂	semidirect
2. C₁₃×D₂₀₉	C₃	semidirect
3. C₁₁×C₁₃×C₁₉	C₂×C₃	semidirect
7. C₁₉×C₁₃⋊C₃	D₁₁	semidirect
10. C₁₁×C₁₃⋊C₃	D₁₉	semidirect
11. D₂₀₉	C₁₃⋊C₃	direct (N × H)
13. C₁₃×C₁₉	C₃×D₁₁	semidirect
14. C₁₁×C₁₉	C₂×C₁₃⋊C₃	semidirect
15. C₁₁×C₁₃	C₃×D₁₉	semidirect
20. C₁₃⋊C₃	D₂₀₉	direct (N × H)
25. C₁₉	D₁₁×C₁₃⋊C₃	semidirect
26. C₁₃	C₃×D₂₀₉	semidirect
27. C₁₁	D₁₉×C₁₃⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×C₁₉×C₁₃⋊C₃	2
C₁₃×D₂₀₉	3
D₁₉×C₁₃⋊C₃	11
C₃×D₂₀₉	13
D₁₁×C₁₃⋊C₃	19

Subgroups — C13⋊C3×D209 #30654452

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃⋊C₃×D₂₀₉ #30654452