Subgroups — C₂×C₁₁×C₁₉×C₅²⋊C₃ #44535518

Order 31350.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₉×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅²×C₁₁×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₁₁×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₉×C₅²⋊C₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₁₁×C₁₉	—	3	2	no	—
6	C₂×C₁₁×C₅²⋊C₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₉×C₅²⋊C₃	C₂×C₁₁	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₃×C₁₁×C₁₉	—	25	1	no	maximal, Hall
9	C₅×C₁₁×C₁₉	—	3	2	no	—
10	C₂×C₅²×C₁₉	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
11	C₁₁×C₅²⋊C₃	C₂×C₁₉	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₁₁×C₁₉	—	25	1	no	Hall
13	C₂×C₅²×C₁₁	C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
14	C₅²×C₁₉	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
15	C₂×C₁₁×C₁₉	C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
16	C₅²×C₁₁	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
17	C₁₁×C₁₉	C₂×C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₅×C₁₉	—	3	2	no	—
19	C₂×C₅²⋊C₃	C₁₁×C₁₉	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₃×C₁₉	—	25	1	no	Hall
21	C₂×C₅×C₁₁	—	3	2	no	—
22	C₅×C₁₉	—	3	2	no	—
23	C₅²⋊C₃	C₂×C₁₁×C₁₉	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₃×C₁₁	—	25	1	no	Hall
25	C₃×C₁₉	—	25	1	no	Hall
26	C₅×C₁₁	—	3	2	no	—
27	C₂×C₅²	C₃×C₁₁×C₁₉	1	1	yes	characteristic, complemented, Hall
28	C₂×C₁₉	C₁₁×C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
29	C₃×C₁₁	—	25	1	no	Hall
30	C₅²	C₂×C₃×C₁₁×C₁₉	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₁₁	C₁₉×C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
32	C₁₉	C₂×C₁₁×C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
33	C₁₁	C₂×C₁₉×C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₅	—	3	2	no	—
35	C₂×C₃	—	25	1	no	Hall
36	C₅	—	3	2	no	—
37	C₃	—	25	1	no	Sylow
38	C₂	C₁₁×C₁₉×C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₁₁×C₁₉	C₅²⋊C₃
commutator, cosocle, hypocenter	C₅²	C₂×C₃×C₁₁×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₁₁×C₁₉	C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₁₁×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₉×C₅²⋊C₃	C₂	direct (N × H)
2. C₂×C₅²×C₁₁×C₁₉	C₃	semidirect
3. C₅²×C₁₁×C₁₉	C₂×C₃	semidirect
4. C₂×C₁₉×C₅²⋊C₃	C₁₁	direct (N × H)
6. C₂×C₁₁×C₅²⋊C₃	C₁₉	direct (N × H)
7. C₁₉×C₅²⋊C₃	C₂×C₁₁	direct (N × H)
10. C₂×C₅²×C₁₉	C₃×C₁₁	semidirect
11. C₁₁×C₅²⋊C₃	C₂×C₁₉	direct (N × H)
13. C₂×C₅²×C₁₁	C₃×C₁₉	semidirect
14. C₅²×C₁₉	C₂×C₃×C₁₁	semidirect
15. C₂×C₁₁×C₁₉	C₅²⋊C₃	direct (N × H)
16. C₅²×C₁₁	C₂×C₃×C₁₉	semidirect
17. C₁₁×C₁₉	C₂×C₅²⋊C₃	direct (N × H)
19. C₂×C₅²⋊C₃	C₁₁×C₁₉	direct (N × H)
23. C₅²⋊C₃	C₂×C₁₁×C₁₉	direct (N × H)
27. C₂×C₅²	C₃×C₁₁×C₁₉	semidirect
28. C₂×C₁₉	C₁₁×C₅²⋊C₃	direct (N × H)
30. C₅²	C₂×C₃×C₁₁×C₁₉	semidirect
31. C₂×C₁₁	C₁₉×C₅²⋊C₃	direct (N × H)
32. C₁₉	C₂×C₁₁×C₅²⋊C₃	direct (N × H)
33. C₁₁	C₂×C₁₉×C₅²⋊C₃	direct (N × H)
38. C₂	C₁₁×C₁₉×C₅²⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×C₁₉×C₅²⋊C₃	2
C₂×C₅²×C₁₁×C₁₉	3
C₂×C₁₉×C₅²⋊C₃	11
C₂×C₁₁×C₅²⋊C₃	19
C₂×C₃×C₁₁×C₁₉	25

Subgroups — C2×C11×C19×C52⋊C3 #44535518

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×C₁₉×C₅²⋊C₃ #44535518