Subgroups — C₁₉×D₁₁×D₃₇ #44525822

Order 30932.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×D₄₀₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×D₁₁×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×C₁₉×D₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×C₁₉×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₉×D₃₇	—	11	1	no	maximal, Hall
6	D₁₁×D₃₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₉×C₃₇	—	11	1	no	—
8	C₁₉×D₃₇	—	11	1	no	—
9	C₁₉×D₃₇	D₁₁	1	1	yes	characteristic, direct product factor
10	C₂×C₁₉×D₁₁	—	37	1	no	maximal, Hall
11	D₄₀₇	C₂×C₁₉	1	1	yes	characteristic, complemented
12	C₁₁×D₃₇	C₂×C₁₉	1	1	yes	characteristic, complemented
13	D₁₁×C₃₇	C₂×C₁₉	1	1	yes	characteristic, complemented
14	C₁₉×C₃₇	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
15	C₂×C₁₁×C₁₉	—	37	1	no	—
16	C₁₉×D₁₁	—	37	1	no	—
17	C₁₉×D₁₁	D₃₇	1	1	yes	characteristic, direct product factor
18	C₁₁×C₃₇	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
19	C₁₁×C₁₉	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
20	C₂×D₃₇	—	11	1	no	Hall
21	C₂²×C₁₉	—	407	1	no	Hall
22	C₂×C₃₇	—	11	1	no	—
23	D₃₇	—	11	1	no	—
24	D₃₇	C₁₉×D₁₁	1	1	yes	characteristic, direct product factor
25	C₂×D₁₁	—	37	1	no	Hall
26	C₂×C₁₉	—	11	1	no	—
27	C₂×C₁₉	—	37	1	no	—
28	C₂×C₁₉	—	407	1	no	—
29	C₃₇	C₂×C₁₉×D₁₁	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₁₁	—	37	1	no	—
31	D₁₁	—	37	1	no	—
32	D₁₁	C₁₉×D₃₇	1	1	yes	characteristic, direct product factor
33	C₁₉	D₁₁×D₃₇	1	1	yes	characteristic, direct product factor, Sylow
34	C₁₁	C₂×C₁₉×D₃₇	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	407	1	no	Sylow
36	C₂	—	11	1	no	—
37	C₂	—	37	1	no	—
38	C₂	—	407	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	D₁₁×D₃₇
commutator, cosocle, hypocenter	C₁₁×C₃₇	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₉×C₃₇	C₂²
LCS	G ▷ C₁₁×C₃₇
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×D₄₀₇	C₂	semidirect
2. C₁₉×D₁₁×C₃₇	C₂	semidirect
3. C₁₁×C₁₉×D₃₇	C₂	semidirect
4. C₁₁×C₁₉×C₃₇	C₂²	semidirect
6. D₁₁×D₃₇	C₁₉	direct (N × H)
9. C₁₉×D₃₇	D₁₁	direct (N × H)
11. D₄₀₇	C₂×C₁₉	semidirect
12. C₁₁×D₃₇	C₂×C₁₉	semidirect
13. D₁₁×C₃₇	C₂×C₁₉	semidirect
14. C₁₉×C₃₇	C₂×D₁₁	semidirect
17. C₁₉×D₁₁	D₃₇	direct (N × H)
18. C₁₁×C₃₇	C₂²×C₁₉	semidirect
19. C₁₁×C₁₉	C₂×D₃₇	semidirect
24. D₃₇	C₁₉×D₁₁	direct (N × H)
29. C₃₇	C₂×C₁₉×D₁₁	semidirect
32. D₁₁	C₁₉×D₃₇	direct (N × H)
33. C₁₉	D₁₁×D₃₇	direct (N × H)
34. C₁₁	C₂×C₁₉×D₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×D₄₀₇	2
C₁₉×D₁₁×C₃₇	2
C₁₁×C₁₉×D₃₇	2
C₂×C₁₉×D₃₇	11
D₁₁×D₃₇	19
C₂×C₁₉×D₁₁	37

Subgroups — C19×D11×D37 #44525822

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×D₁₁×D₃₇ #44525822