Subgroups — C₂×C₃²×C₂₃×D₁₃ #24924592

Order 10764.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₃×D₁₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₃×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₂₃×D₁₃	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×C₂₃×D₁₃	C₂×C₃	1	8	yes	direct product factor
7	C₂×C₂₃×D₁₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₁₃×C₂₃	C₂²×C₃	1	4	yes	complemented
9	C₂²×C₃²×C₂₃	—	13	1	no	maximal, Hall
10	C₂×C₁₃×C₂₃	C₂×C₃²	1	1	yes	characteristic, complemented
11	C₂₃×D₁₃	C₂×C₃²	1	2	yes	direct product factor
12	C₂×C₃²×D₁₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃²×C₂₃	—	13	2	no	—
14	C₂×C₃²×C₂₃	D₁₃	1	1	yes	characteristic, direct product factor
15	C₁₃×C₂₃	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
16	C₂²×C₃×C₂₃	—	13	4	no	—
17	C₂×C₃²×C₁₃	C₂×C₂₃	1	1	yes	characteristic, complemented
18	C₃²×D₁₃	C₂×C₂₃	1	2	yes	direct product factor
19	C₃²×C₂₃	C₂×D₁₃	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₃×D₁₃	C₃×C₂₃	1	4	yes	direct product factor
21	C₂×C₃×C₂₃	—	13	8	no	—
22	C₂×C₃×C₂₃	C₃×D₁₃	1	4	yes	direct product factor
23	C₃²×C₁₃	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
24	C₂²×C₂₃	—	13	1	no	Hall
25	C₂×C₃×C₁₃	C₂×C₃×C₂₃	1	4	yes	complemented
26	C₃×D₁₃	C₂×C₃×C₂₃	1	8	yes	direct product factor
27	C₃×C₂₃	C₂×C₃×D₁₃	1	4	yes	direct product factor
28	C₂×D₁₃	C₃²×C₂₃	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₂₃	—	13	2	no	—
30	C₂×C₂₃	C₃²×D₁₃	1	1	yes	characteristic, direct product factor
31	C₃×C₁₃	C₂²×C₃×C₂₃	1	4	yes	complemented
32	C₂²×C₃²	—	13	1	no	Hall
33	C₂×C₁₃	C₂×C₃²×C₂₃	1	1	yes	characteristic, complemented
34	D₁₃	C₂×C₃²×C₂₃	1	2	yes	direct product factor
35	C₂₃	C₂×C₃²×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₃²	—	13	2	no	—
37	C₂×C₃²	C₂₃×D₁₃	1	1	yes	characteristic, direct product factor
38	C₁₃	C₂²×C₃²×C₂₃	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₃	—	13	4	no	—
40	C₃²	C₂×C₂₃×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₃	—	13	8	no	—
42	C₂×C₃	C₃×C₂₃×D₁₃	1	4	yes	direct product factor
43	C₂²	—	13	1	no	Sylow
44	C₃	C₂×C₃×C₂₃×D₁₃	1	4	yes	direct product factor
45	C₂	—	13	2	no	—
46	C₂	C₃²×C₂₃×D₁₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₂₃	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂²×C₃²×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₃×C₂₃	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃²×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₂₃×D₁₃	C₂	direct (N × H)
2. C₂×C₃²×C₁₃×C₂₃	C₂	semidirect
3. C₂×C₃×C₂₃×D₁₃	C₃	direct (N × H)
4. C₃²×C₁₃×C₂₃	C₂²	semidirect
5. C₂×C₃×C₁₃×C₂₃	C₂×C₃	semidirect
6. C₃×C₂₃×D₁₃	C₂×C₃	direct (N × H)
7. C₂×C₂₃×D₁₃	C₃²	direct (N × H)
8. C₃×C₁₃×C₂₃	C₂²×C₃	semidirect
10. C₂×C₁₃×C₂₃	C₂×C₃²	semidirect
11. C₂₃×D₁₃	C₂×C₃²	direct (N × H)
12. C₂×C₃²×D₁₃	C₂₃	direct (N × H)
14. C₂×C₃²×C₂₃	D₁₃	direct (N × H)
15. C₁₃×C₂₃	C₂²×C₃²	semidirect
17. C₂×C₃²×C₁₃	C₂×C₂₃	semidirect
18. C₃²×D₁₃	C₂×C₂₃	direct (N × H)
19. C₃²×C₂₃	C₂×D₁₃	direct (N × H)
20. C₂×C₃×D₁₃	C₃×C₂₃	direct (N × H)
22. C₂×C₃×C₂₃	C₃×D₁₃	direct (N × H)
23. C₃²×C₁₃	C₂²×C₂₃	semidirect
25. C₂×C₃×C₁₃	C₂×C₃×C₂₃	semidirect
26. C₃×D₁₃	C₂×C₃×C₂₃	direct (N × H)
27. C₃×C₂₃	C₂×C₃×D₁₃	direct (N × H)
28. C₂×D₁₃	C₃²×C₂₃	direct (N × H)
30. C₂×C₂₃	C₃²×D₁₃	direct (N × H)
31. C₃×C₁₃	C₂²×C₃×C₂₃	semidirect
33. C₂×C₁₃	C₂×C₃²×C₂₃	semidirect
34. D₁₃	C₂×C₃²×C₂₃	direct (N × H)
35. C₂₃	C₂×C₃²×D₁₃	direct (N × H)
37. C₂×C₃²	C₂₃×D₁₃	direct (N × H)
38. C₁₃	C₂²×C₃²×C₂₃	semidirect
40. C₃²	C₂×C₂₃×D₁₃	direct (N × H)
42. C₂×C₃	C₃×C₂₃×D₁₃	direct (N × H)
44. C₃	C₂×C₃×C₂₃×D₁₃	direct (N × H)
46. C₂	C₃²×C₂₃×D₁₃	direct (N × H)

Subgroups — C2×C32×C23×D13 #24924592

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃²×C₂₃×D₁₃ #24924592