Subgroups — C₅×C₁₁×C₂²⋊(C₁₉⋊C₃) #27160091

Order 12540.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₁₁×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₁×C₁₉⋊C₃	—	4	1	no	maximal, Hall
3	C₁₁×C₂²⋊(C₁₉⋊C₃)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₅×C₁₁×C₁₉	—	3	1	no	—
5	C₅×C₂²⋊(C₁₉⋊C₃)	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₁₁×C₁₉	A₄	1	1	yes	characteristic, complemented, Hall
7	C₂²×C₁₁×C₁₉	C₃×C₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₁₁×A₄	—	19	1	no	maximal, Hall
9	C₁₁×C₁₉⋊C₃	—	4	1	no	Hall
10	C₂×C₁₁×C₁₉	—	3	1	no	—
11	C₂²×C₅×C₁₉	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₅×C₁₉⋊C₃	—	4	1	no	Hall
13	C₂²⋊(C₁₉⋊C₃)	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
14	C₂²×C₅×C₁₁	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
15	C₁₁×C₁₉	C₅×A₄	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅×C₁₉	—	3	1	no	—
17	C₃×C₅×C₁₁	—	76	1	no	Hall
18	C₁₁×A₄	—	19	1	no	Hall
19	C₂×C₅×C₁₁	—	3	1	no	—
20	C₅×C₁₉	C₁₁×A₄	1	1	yes	characteristic, complemented, Hall
21	C₂²×C₁₉	C₃×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
22	C₅×A₄	—	19	1	no	Hall
23	C₁₉⋊C₃	—	4	1	no	Hall
24	C₅×C₁₁	C₂²⋊(C₁₉⋊C₃)	1	1	yes	characteristic, direct product factor, Hall
25	C₂²×C₁₁	C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₉	—	3	1	no	—
27	C₃×C₁₁	—	76	1	no	Hall
28	C₂×C₁₁	—	3	1	no	—
29	C₂²×C₅	C₁₁×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
30	C₁₉	C₅×C₁₁×A₄	1	1	yes	characteristic, complemented, Sylow
31	C₃×C₅	—	76	1	no	Hall
32	A₄	—	19	1	no	Hall
33	C₁₁	C₅×C₂²⋊(C₁₉⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₅	—	3	1	no	—
35	C₅	C₁₁×C₂²⋊(C₁₉⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
36	C₂²	C₅×C₁₁×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
37	C₃	—	76	1	no	Sylow
38	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₁₁	C₂²⋊(C₁₉⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₁₉	C₃×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₁₁×C₁₉	C₃
LCS	G ▷ C₂²×C₁₉
UCS	C₁ ◁ C₅×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×C₁₁×C₁₉	C₃	semidirect
3. C₁₁×C₂²⋊(C₁₉⋊C₃)	C₅	direct (N × H)
5. C₅×C₂²⋊(C₁₉⋊C₃)	C₁₁	direct (N × H)
6. C₅×C₁₁×C₁₉	A₄	semidirect
7. C₂²×C₁₁×C₁₉	C₃×C₅	semidirect
11. C₂²×C₅×C₁₉	C₃×C₁₁	semidirect
13. C₂²⋊(C₁₉⋊C₃)	C₅×C₁₁	direct (N × H)
14. C₂²×C₅×C₁₁	C₁₉⋊C₃	semidirect
15. C₁₁×C₁₉	C₅×A₄	semidirect
20. C₅×C₁₉	C₁₁×A₄	semidirect
21. C₂²×C₁₉	C₃×C₅×C₁₁	semidirect
24. C₅×C₁₁	C₂²⋊(C₁₉⋊C₃)	direct (N × H)
25. C₂²×C₁₁	C₅×C₁₉⋊C₃	semidirect
29. C₂²×C₅	C₁₁×C₁₉⋊C₃	semidirect
30. C₁₉	C₅×C₁₁×A₄	semidirect
33. C₁₁	C₅×C₂²⋊(C₁₉⋊C₃)	direct (N × H)
35. C₅	C₁₁×C₂²⋊(C₁₉⋊C₃)	direct (N × H)
36. C₂²	C₅×C₁₁×C₁₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×C₁₁×C₁₉	3
C₅×C₁₁×C₁₉⋊C₃	4
C₁₁×C₂²⋊(C₁₉⋊C₃)	5
C₅×C₂²⋊(C₁₉⋊C₃)	11
C₅×C₁₁×A₄	19

Subgroups — C5×C11×C22⋊(C19⋊C3) #27160091

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁×C₂²⋊(C₁₉⋊C₃) #27160091