Subgroups — C₂²×C₃×C₂₃×C₁₃⋊C₃ #24924582

Order 10764.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂₃×C₁₃⋊C₃	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₂₃×C₁₃⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₂²×C₃×C₁₃×C₂₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₂₃×C₁₃⋊C₃	C₂²	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₃×C₁₃×C₂₃	C₂×C₃	1	3	yes	complemented
6	C₂×C₂₃×C₁₃⋊C₃	C₂×C₃	1	9	yes	direct product factor
7	C₂²×C₁₃×C₂₃	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₃×C₂₃	C₂²×C₃	1	1	yes	characteristic, complemented
9	C₂₃×C₁₃⋊C₃	C₂²×C₃	1	3	yes	direct product factor
10	C₂²×C₃²×C₂₃	—	13	1	no	maximal, Hall
11	C₂×C₁₃×C₂₃	C₂×C₃²	1	3	yes	complemented
12	C₂²×C₃×C₁₃⋊C₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃²×C₂₃	—	13	3	no	—
14	C₁₃×C₂₃	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
15	C₂²×C₃×C₂₃	—	13	3	no	—
16	C₂²×C₃×C₂₃	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
17	C₂×C₃×C₁₃⋊C₃	C₂×C₂₃	1	3	yes	direct product factor
18	C₃²×C₂₃	—	13	1	no	Hall
19	C₂²×C₃×C₁₃	C₃×C₂₃	1	1	yes	characteristic, complemented
20	C₂²×C₁₃⋊C₃	C₃×C₂₃	1	3	yes	direct product factor
21	C₂×C₃×C₂₃	—	13	9	no	—
22	C₂×C₃×C₂₃	C₂×C₁₃⋊C₃	1	3	yes	direct product factor
23	C₃×C₁₃⋊C₃	C₂²×C₂₃	1	1	yes	characteristic, direct product factor, Hall
24	C₂²×C₂₃	C₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₃×C₁₃	C₂×C₃×C₂₃	1	3	yes	complemented
26	C₂×C₁₃⋊C₃	C₂×C₃×C₂₃	1	9	yes	direct product factor
27	C₃×C₂₃	—	13	3	no	—
28	C₃×C₂₃	C₂²×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
29	C₂²×C₁₃	C₃²×C₂₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₂₃	C₂×C₃×C₁₃⋊C₃	1	3	yes	direct product factor
31	C₃×C₁₃	C₂²×C₃×C₂₃	1	1	yes	characteristic, complemented
32	C₁₃⋊C₃	C₂²×C₃×C₂₃	1	3	yes	direct product factor
33	C₂²×C₃²	—	13	1	no	Hall
34	C₂×C₁₃	C₂×C₃²×C₂₃	1	3	yes	complemented
35	C₂₃	C₂²×C₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₃²	—	13	3	no	—
37	C₁₃	C₂²×C₃²×C₂₃	1	1	yes	characteristic, complemented, Sylow
38	C₂²×C₃	—	13	3	no	—
39	C₂²×C₃	C₂₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
40	C₃²	—	13	1	no	Sylow
41	C₂×C₃	—	13	9	no	—
42	C₂×C₃	C₂×C₂₃×C₁₃⋊C₃	1	3	yes	direct product factor
43	C₂²	C₃×C₂₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
44	C₃	—	13	3	no	—
45	C₃	C₂²×C₂₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
46	C₂	C₂×C₃×C₂₃×C₁₃⋊C₃	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₃×C₂₃	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₂²×C₃²×C₂₃
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₁₃×C₂₃	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂²×C₃×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₂₃×C₁₃⋊C₃	C₂	direct (N × H)
2. C₂²×C₂₃×C₁₃⋊C₃	C₃	direct (N × H)
3. C₂²×C₃×C₁₃×C₂₃	C₃	semidirect
4. C₃×C₂₃×C₁₃⋊C₃	C₂²	direct (N × H)
5. C₂×C₃×C₁₃×C₂₃	C₂×C₃	semidirect
6. C₂×C₂₃×C₁₃⋊C₃	C₂×C₃	direct (N × H)
7. C₂²×C₁₃×C₂₃	C₃²	semidirect
8. C₃×C₁₃×C₂₃	C₂²×C₃	semidirect
9. C₂₃×C₁₃⋊C₃	C₂²×C₃	direct (N × H)
11. C₂×C₁₃×C₂₃	C₂×C₃²	semidirect
12. C₂²×C₃×C₁₃⋊C₃	C₂₃	direct (N × H)
14. C₁₃×C₂₃	C₂²×C₃²	semidirect
16. C₂²×C₃×C₂₃	C₁₃⋊C₃	direct (N × H)
17. C₂×C₃×C₁₃⋊C₃	C₂×C₂₃	direct (N × H)
19. C₂²×C₃×C₁₃	C₃×C₂₃	semidirect
20. C₂²×C₁₃⋊C₃	C₃×C₂₃	direct (N × H)
22. C₂×C₃×C₂₃	C₂×C₁₃⋊C₃	direct (N × H)
23. C₃×C₁₃⋊C₃	C₂²×C₂₃	direct (N × H)
24. C₂²×C₂₃	C₃×C₁₃⋊C₃	direct (N × H)
25. C₂×C₃×C₁₃	C₂×C₃×C₂₃	semidirect
26. C₂×C₁₃⋊C₃	C₂×C₃×C₂₃	direct (N × H)
28. C₃×C₂₃	C₂²×C₁₃⋊C₃	direct (N × H)
29. C₂²×C₁₃	C₃²×C₂₃	semidirect
30. C₂×C₂₃	C₂×C₃×C₁₃⋊C₃	direct (N × H)
31. C₃×C₁₃	C₂²×C₃×C₂₃	semidirect
32. C₁₃⋊C₃	C₂²×C₃×C₂₃	direct (N × H)
34. C₂×C₁₃	C₂×C₃²×C₂₃	semidirect
35. C₂₃	C₂²×C₃×C₁₃⋊C₃	direct (N × H)
37. C₁₃	C₂²×C₃²×C₂₃	semidirect
39. C₂²×C₃	C₂₃×C₁₃⋊C₃	direct (N × H)
42. C₂×C₃	C₂×C₂₃×C₁₃⋊C₃	direct (N × H)
43. C₂²	C₃×C₂₃×C₁₃⋊C₃	direct (N × H)
45. C₃	C₂²×C₂₃×C₁₃⋊C₃	direct (N × H)
46. C₂	C₂×C₃×C₂₃×C₁₃⋊C₃	direct (N × H)

Subgroups — C22×C3×C23×C13⋊C3 #24924582

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×C₃×C₂₃×C₁₃⋊C₃ #24924582