Subgroups — C₅×C₁₁×A₄×C₁₃ #22575180

Order 8580.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₁₁×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅×C₁₁×C₁₃	—	4	1	no	maximal, Hall
3	C₁₁×A₄×C₁₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₅×C₁₁×C₁₃	—	3	1	no	—
5	C₅×A₄×C₁₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₁₁×C₁₃	A₄	1	1	yes	characteristic, direct product factor, Hall
7	C₅×C₁₁×A₄	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₁₁×C₁₃	C₃×C₅	1	1	yes	characteristic, complemented, Hall
9	C₃×C₁₁×C₁₃	—	4	1	no	Hall
10	C₂×C₁₁×C₁₃	—	3	1	no	—
11	C₂²×C₅×C₁₃	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₅×C₁₁	C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
13	C₃×C₅×C₁₃	—	4	1	no	Hall
14	C₃×C₅×C₁₁	—	4	1	no	Hall
15	A₄×C₁₃	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
16	C₁₁×C₁₃	C₅×A₄	1	1	yes	characteristic, direct product factor, Hall
17	C₁₁×A₄	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₅×C₁₃	—	3	1	no	—
19	C₂×C₅×C₁₁	—	3	1	no	—
20	C₅×C₁₃	C₁₁×A₄	1	1	yes	characteristic, direct product factor, Hall
21	C₅×A₄	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
22	C₅×C₁₁	A₄×C₁₃	1	1	yes	characteristic, direct product factor, Hall
23	C₂²×C₁₃	C₃×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
24	C₂²×C₁₁	C₃×C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
25	C₃×C₁₃	—	4	1	no	Hall
26	C₃×C₁₁	—	4	1	no	Hall
27	C₂×C₁₃	—	3	1	no	—
28	C₂×C₁₁	—	3	1	no	—
29	C₂²×C₅	C₃×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Hall
30	C₃×C₅	—	4	1	no	Hall
31	C₁₃	C₅×C₁₁×A₄	1	1	yes	characteristic, direct product factor, Sylow
32	A₄	C₅×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
33	C₁₁	C₅×A₄×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₅	—	3	1	no	—
35	C₅	C₁₁×A₄×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
36	C₂²	C₃×C₅×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Sylow
37	C₃	—	4	1	no	Sylow
38	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₁₁×C₁₃	A₄
commutator, hypocenter	C₂²	C₃×C₅×C₁₁×C₁₃
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₁₁×C₁₃	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₅×C₁₁×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×C₁₁×C₁₃	C₃	semidirect
3. C₁₁×A₄×C₁₃	C₅	direct (N × H)
5. C₅×A₄×C₁₃	C₁₁	direct (N × H)
6. C₅×C₁₁×C₁₃	A₄	direct (N × H)
7. C₅×C₁₁×A₄	C₁₃	direct (N × H)
8. C₂²×C₁₁×C₁₃	C₃×C₅	semidirect
11. C₂²×C₅×C₁₃	C₃×C₁₁	semidirect
12. C₂²×C₅×C₁₁	C₃×C₁₃	semidirect
15. A₄×C₁₃	C₅×C₁₁	direct (N × H)
16. C₁₁×C₁₃	C₅×A₄	direct (N × H)
17. C₁₁×A₄	C₅×C₁₃	direct (N × H)
20. C₅×C₁₃	C₁₁×A₄	direct (N × H)
21. C₅×A₄	C₁₁×C₁₃	direct (N × H)
22. C₅×C₁₁	A₄×C₁₃	direct (N × H)
23. C₂²×C₁₃	C₃×C₅×C₁₁	semidirect
24. C₂²×C₁₁	C₃×C₅×C₁₃	semidirect
29. C₂²×C₅	C₃×C₁₁×C₁₃	semidirect
31. C₁₃	C₅×C₁₁×A₄	direct (N × H)
32. A₄	C₅×C₁₁×C₁₃	direct (N × H)
33. C₁₁	C₅×A₄×C₁₃	direct (N × H)
35. C₅	C₁₁×A₄×C₁₃	direct (N × H)
36. C₂²	C₃×C₅×C₁₁×C₁₃	semidirect

Subgroups — C5×C11×A4×C13 #22575180

Conjugacy classes of subgroups

Complements

Subgroups — C₅×C₁₁×A₄×C₁₃ #22575180