Subgroups — C₂×C₁₉×D₁₄₃ #24925889

Order 10868.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×D₁₄₃	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×C₁₉×D₁₃	—	11	1	no	maximal, Hall
5	C₂×C₁₉×D₁₁	—	13	1	no	maximal, Hall
6	C₂×D₁₄₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₃×C₁₉	D₁₁	1	1	yes	characteristic, complemented
8	C₁₉×D₁₃	—	11	2	no	—
9	C₂×C₁₁×C₁₉	D₁₃	1	1	yes	characteristic, complemented
10	C₁₉×D₁₁	—	13	2	no	—
11	C₂×C₁₁×C₁₃	C₂×C₁₉	1	1	yes	characteristic, complemented
12	D₁₄₃	C₂×C₁₉	1	2	yes	direct product factor
13	C₁₃×C₁₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
14	C₁₁×C₁₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
15	C₁₁×C₁₃	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
16	C₂²×C₁₉	—	143	1	no	Hall
17	C₂×D₁₃	—	11	1	no	Hall
18	C₂×D₁₁	—	13	1	no	Hall
19	C₂×C₁₉	—	143	2	no	—
20	C₂×C₁₉	D₁₄₃	1	1	yes	characteristic, direct product factor
21	C₂×C₁₃	C₁₉×D₁₁	1	1	yes	characteristic, complemented
22	D₁₃	—	11	2	no	—
23	C₂×C₁₁	C₁₉×D₁₃	1	1	yes	characteristic, complemented
24	D₁₁	—	13	2	no	—
25	C₁₉	C₂×D₁₄₃	1	1	yes	characteristic, direct product factor, Sylow
26	C₁₃	C₂×C₁₉×D₁₁	1	1	yes	characteristic, complemented, Sylow
27	C₁₁	C₂×C₁₉×D₁₃	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	143	1	no	Sylow
29	C₂	—	143	2	no	—
30	C₂	C₁₉×D₁₄₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₉	D₁₄₃
commutator, cosocle, hypocenter	C₁₁×C₁₃	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₁₁×C₁₃×C₁₉	C₂
LCS	G ▷ C₁₁×C₁₃
UCS	C₁ ◁ C₂×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×D₁₄₃	C₂	direct (N × H)
2. C₂×C₁₁×C₁₃×C₁₉	C₂	semidirect
3. C₁₁×C₁₃×C₁₉	C₂²	semidirect
6. C₂×D₁₄₃	C₁₉	direct (N × H)
7. C₂×C₁₃×C₁₉	D₁₁	semidirect
9. C₂×C₁₁×C₁₉	D₁₃	semidirect
11. C₂×C₁₁×C₁₃	C₂×C₁₉	semidirect
12. D₁₄₃	C₂×C₁₉	direct (N × H)
13. C₁₃×C₁₉	C₂×D₁₁	semidirect
14. C₁₁×C₁₉	C₂×D₁₃	semidirect
15. C₁₁×C₁₃	C₂²×C₁₉	semidirect
20. C₂×C₁₉	D₁₄₃	direct (N × H)
21. C₂×C₁₃	C₁₉×D₁₁	semidirect
23. C₂×C₁₁	C₁₉×D₁₃	semidirect
25. C₁₉	C₂×D₁₄₃	direct (N × H)
26. C₁₃	C₂×C₁₉×D₁₁	semidirect
27. C₁₁	C₂×C₁₉×D₁₃	semidirect
30. C₂	C₁₉×D₁₄₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×D₁₄₃	2
C₂×C₁₁×C₁₃×C₁₉	2
C₂×C₁₉×D₁₃	11
C₂×C₁₉×D₁₁	13
C₂×D₁₄₃	19

Subgroups — C2×C19×D143 #24925889

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×D₁₄₃ #24925889