Subgroups — C₁₉×D₁₁×D₂₉ #37564613

Order 24244.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×D₃₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×D₁₁×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×C₁₉×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×C₁₉×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₉×D₂₉	—	11	1	no	maximal, Hall
6	D₁₁×D₂₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₉×C₂₉	—	11	1	no	—
8	C₁₉×D₂₉	—	11	1	no	—
9	C₁₉×D₂₉	D₁₁	1	1	yes	characteristic, direct product factor
10	C₂×C₁₉×D₁₁	—	29	1	no	maximal, Hall
11	D₃₁₉	C₂×C₁₉	1	1	yes	characteristic, complemented
12	C₁₁×D₂₉	C₂×C₁₉	1	1	yes	characteristic, complemented
13	D₁₁×C₂₉	C₂×C₁₉	1	1	yes	characteristic, complemented
14	C₁₉×C₂₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
15	C₂×C₁₁×C₁₉	—	29	1	no	—
16	C₁₉×D₁₁	—	29	1	no	—
17	C₁₉×D₁₁	D₂₉	1	1	yes	characteristic, direct product factor
18	C₁₁×C₂₉	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
19	C₁₁×C₁₉	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
20	C₂×D₂₉	—	11	1	no	Hall
21	C₂²×C₁₉	—	319	1	no	Hall
22	C₂×C₂₉	—	11	1	no	—
23	D₂₉	—	11	1	no	—
24	D₂₉	C₁₉×D₁₁	1	1	yes	characteristic, direct product factor
25	C₂×D₁₁	—	29	1	no	Hall
26	C₂×C₁₉	—	11	1	no	—
27	C₂×C₁₉	—	29	1	no	—
28	C₂×C₁₉	—	319	1	no	—
29	C₂₉	C₂×C₁₉×D₁₁	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₁₁	—	29	1	no	—
31	D₁₁	—	29	1	no	—
32	D₁₁	C₁₉×D₂₉	1	1	yes	characteristic, direct product factor
33	C₁₉	D₁₁×D₂₉	1	1	yes	characteristic, direct product factor, Sylow
34	C₁₁	C₂×C₁₉×D₂₉	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	319	1	no	Sylow
36	C₂	—	11	1	no	—
37	C₂	—	29	1	no	—
38	C₂	—	319	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	D₁₁×D₂₉
commutator, cosocle, hypocenter	C₁₁×C₂₉	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₉×C₂₉	C₂²
LCS	G ▷ C₁₁×C₂₉
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×D₃₁₉	C₂	semidirect
2. C₁₉×D₁₁×C₂₉	C₂	semidirect
3. C₁₁×C₁₉×D₂₉	C₂	semidirect
4. C₁₁×C₁₉×C₂₉	C₂²	semidirect
6. D₁₁×D₂₉	C₁₉	direct (N × H)
9. C₁₉×D₂₉	D₁₁	direct (N × H)
11. D₃₁₉	C₂×C₁₉	semidirect
12. C₁₁×D₂₉	C₂×C₁₉	semidirect
13. D₁₁×C₂₉	C₂×C₁₉	semidirect
14. C₁₉×C₂₉	C₂×D₁₁	semidirect
17. C₁₉×D₁₁	D₂₉	direct (N × H)
18. C₁₁×C₂₉	C₂²×C₁₉	semidirect
19. C₁₁×C₁₉	C₂×D₂₉	semidirect
24. D₂₉	C₁₉×D₁₁	direct (N × H)
29. C₂₉	C₂×C₁₉×D₁₁	semidirect
32. D₁₁	C₁₉×D₂₉	direct (N × H)
33. C₁₉	D₁₁×D₂₉	direct (N × H)
34. C₁₁	C₂×C₁₉×D₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×D₃₁₉	2
C₁₉×D₁₁×C₂₉	2
C₁₁×C₁₉×D₂₉	2
C₂×C₁₉×D₂₉	11
D₁₁×D₂₉	19
C₂×C₁₉×D₁₁	29

Subgroups — C19×D11×D29 #37564613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×D₁₁×D₂₉ #37564613