Subgroups — C₂×C₃²×C₁₃×D₂₃ #24924593

Order 10764.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×D₂₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₃×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₁₃×D₂₃	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₁₃×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₃×C₂₃	C₂×C₃	1	4	yes	complemented
6	C₃×C₁₃×D₂₃	C₂×C₃	1	8	yes	direct product factor
7	C₂×C₁₃×D₂₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₁₃×C₂₃	C₂²×C₃	1	4	yes	complemented
9	C₂×C₃²×D₂₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₁₃×C₂₃	C₂×C₃²	1	1	yes	characteristic, complemented
11	C₁₃×D₂₃	C₂×C₃²	1	2	yes	direct product factor
12	C₂²×C₃²×C₁₃	—	23	1	no	maximal, Hall
13	C₂×C₃²×C₂₃	C₂×C₁₃	1	1	yes	characteristic, complemented
14	C₃²×D₂₃	C₂×C₁₃	1	2	yes	direct product factor
15	C₁₃×C₂₃	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×D₂₃	C₃×C₁₃	1	4	yes	direct product factor
17	C₂×C₃²×C₁₃	—	23	2	no	—
18	C₂×C₃²×C₁₃	D₂₃	1	1	yes	characteristic, direct product factor
19	C₃²×C₂₃	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
20	C₂²×C₃×C₁₃	—	23	4	no	—
21	C₂×C₃×C₂₃	C₂×C₃×C₁₃	1	4	yes	complemented
22	C₃×D₂₃	C₂×C₃×C₁₃	1	8	yes	direct product factor
23	C₃²×C₁₃	C₂×D₂₃	1	1	yes	characteristic, direct product factor, Hall
24	C₂×D₂₃	C₃²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₃×C₁₃	—	23	8	no	—
26	C₂×C₃×C₁₃	C₃×D₂₃	1	4	yes	direct product factor
27	C₃×C₂₃	C₂²×C₃×C₁₃	1	4	yes	complemented
28	C₂²×C₁₃	—	23	1	no	Hall
29	C₂×C₂₃	C₂×C₃²×C₁₃	1	1	yes	characteristic, complemented
30	D₂₃	C₂×C₃²×C₁₃	1	2	yes	direct product factor
31	C₃×C₁₃	C₂×C₃×D₂₃	1	4	yes	direct product factor
32	C₂²×C₃²	—	23	1	no	Hall
33	C₂×C₁₃	—	23	2	no	—
34	C₂×C₁₃	C₃²×D₂₃	1	1	yes	characteristic, direct product factor
35	C₂₃	C₂²×C₃²×C₁₃	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃²	—	23	2	no	—
37	C₂×C₃²	C₁₃×D₂₃	1	1	yes	characteristic, direct product factor
38	C₁₃	C₂×C₃²×D₂₃	1	1	yes	characteristic, direct product factor, Sylow
39	C₂²×C₃	—	23	4	no	—
40	C₃²	C₂×C₁₃×D₂₃	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₃	—	23	8	no	—
42	C₂×C₃	C₃×C₁₃×D₂₃	1	4	yes	direct product factor
43	C₂²	—	23	1	no	Sylow
44	C₃	C₂×C₃×C₁₃×D₂₃	1	4	yes	direct product factor
45	C₂	—	23	2	no	—
46	C₂	C₃²×C₁₃×D₂₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₁₃	D₂₃
commutator, cosocle, hypocenter	C₂₃	C₂²×C₃²×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₃×C₂₃	C₂
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₂×C₃²×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₃×D₂₃	C₂	direct (N × H)
2. C₂×C₃²×C₁₃×C₂₃	C₂	semidirect
3. C₂×C₃×C₁₃×D₂₃	C₃	direct (N × H)
4. C₃²×C₁₃×C₂₃	C₂²	semidirect
5. C₂×C₃×C₁₃×C₂₃	C₂×C₃	semidirect
6. C₃×C₁₃×D₂₃	C₂×C₃	direct (N × H)
7. C₂×C₁₃×D₂₃	C₃²	direct (N × H)
8. C₃×C₁₃×C₂₃	C₂²×C₃	semidirect
9. C₂×C₃²×D₂₃	C₁₃	direct (N × H)
10. C₂×C₁₃×C₂₃	C₂×C₃²	semidirect
11. C₁₃×D₂₃	C₂×C₃²	direct (N × H)
13. C₂×C₃²×C₂₃	C₂×C₁₃	semidirect
14. C₃²×D₂₃	C₂×C₁₃	direct (N × H)
15. C₁₃×C₂₃	C₂²×C₃²	semidirect
16. C₂×C₃×D₂₃	C₃×C₁₃	direct (N × H)
18. C₂×C₃²×C₁₃	D₂₃	direct (N × H)
19. C₃²×C₂₃	C₂²×C₁₃	semidirect
21. C₂×C₃×C₂₃	C₂×C₃×C₁₃	semidirect
22. C₃×D₂₃	C₂×C₃×C₁₃	direct (N × H)
23. C₃²×C₁₃	C₂×D₂₃	direct (N × H)
24. C₂×D₂₃	C₃²×C₁₃	direct (N × H)
26. C₂×C₃×C₁₃	C₃×D₂₃	direct (N × H)
27. C₃×C₂₃	C₂²×C₃×C₁₃	semidirect
29. C₂×C₂₃	C₂×C₃²×C₁₃	semidirect
30. D₂₃	C₂×C₃²×C₁₃	direct (N × H)
31. C₃×C₁₃	C₂×C₃×D₂₃	direct (N × H)
34. C₂×C₁₃	C₃²×D₂₃	direct (N × H)
35. C₂₃	C₂²×C₃²×C₁₃	semidirect
37. C₂×C₃²	C₁₃×D₂₃	direct (N × H)
38. C₁₃	C₂×C₃²×D₂₃	direct (N × H)
40. C₃²	C₂×C₁₃×D₂₃	direct (N × H)
42. C₂×C₃	C₃×C₁₃×D₂₃	direct (N × H)
44. C₃	C₂×C₃×C₁₃×D₂₃	direct (N × H)
46. C₂	C₃²×C₁₃×D₂₃	direct (N × H)

Subgroups — C2×C32×C13×D23 #24924593

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃²×C₁₃×D₂₃ #24924593