Subgroups — C₂×C₁₃×D₂₀₉ #24925890

Order 10868.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₂₀₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₁×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₃×D₁₉	—	11	1	no	maximal, Hall
5	C₂×D₂₀₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₁₃×D₁₁	—	19	1	no	maximal, Hall
7	C₂×C₁₃×C₁₉	D₁₁	1	1	yes	characteristic, complemented
8	C₁₃×D₁₉	—	11	2	no	—
9	C₂×C₁₁×C₁₉	C₂×C₁₃	1	1	yes	characteristic, complemented
10	D₂₀₉	C₂×C₁₃	1	2	yes	direct product factor
11	C₂×C₁₁×C₁₃	D₁₉	1	1	yes	characteristic, complemented
12	C₁₃×D₁₁	—	19	2	no	—
13	C₁₃×C₁₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
14	C₁₁×C₁₉	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
15	C₁₁×C₁₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
16	C₂×D₁₉	—	11	1	no	Hall
17	C₂²×C₁₃	—	209	1	no	Hall
18	C₂×D₁₁	—	19	1	no	Hall
19	C₂×C₁₉	C₁₃×D₁₁	1	1	yes	characteristic, complemented
20	D₁₉	—	11	2	no	—
21	C₂×C₁₃	—	209	2	no	—
22	C₂×C₁₃	D₂₀₉	1	1	yes	characteristic, direct product factor
23	C₂×C₁₁	C₁₃×D₁₉	1	1	yes	characteristic, complemented
24	D₁₁	—	19	2	no	—
25	C₁₉	C₂×C₁₃×D₁₁	1	1	yes	characteristic, complemented, Sylow
26	C₁₃	C₂×D₂₀₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₁₁	C₂×C₁₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	209	1	no	Sylow
29	C₂	—	209	2	no	—
30	C₂	C₁₃×D₂₀₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃	D₂₀₉
commutator, cosocle, hypocenter	C₁₁×C₁₉	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₁×C₁₃×C₁₉	C₂
LCS	G ▷ C₁₁×C₁₉
UCS	C₁ ◁ C₂×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×D₂₀₉	C₂	direct (N × H)
2. C₂×C₁₁×C₁₃×C₁₉	C₂	semidirect
3. C₁₁×C₁₃×C₁₉	C₂²	semidirect
5. C₂×D₂₀₉	C₁₃	direct (N × H)
7. C₂×C₁₃×C₁₉	D₁₁	semidirect
9. C₂×C₁₁×C₁₉	C₂×C₁₃	semidirect
10. D₂₀₉	C₂×C₁₃	direct (N × H)
11. C₂×C₁₁×C₁₃	D₁₉	semidirect
13. C₁₃×C₁₉	C₂×D₁₁	semidirect
14. C₁₁×C₁₉	C₂²×C₁₃	semidirect
15. C₁₁×C₁₃	C₂×D₁₉	semidirect
19. C₂×C₁₉	C₁₃×D₁₁	semidirect
22. C₂×C₁₃	D₂₀₉	direct (N × H)
23. C₂×C₁₁	C₁₃×D₁₉	semidirect
25. C₁₉	C₂×C₁₃×D₁₁	semidirect
26. C₁₃	C₂×D₂₀₉	direct (N × H)
27. C₁₁	C₂×C₁₃×D₁₉	semidirect
30. C₂	C₁₃×D₂₀₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×D₂₀₉	2
C₂×C₁₁×C₁₃×C₁₉	2
C₂×C₁₃×D₁₉	11
C₂×D₂₀₉	13
C₂×C₁₃×D₁₁	19

Subgroups — C2×C13×D209 #24925890

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×D₂₀₉ #24925890