Subgroups — C₂×C₁₃×D₉×C₂₃ #24924501

Order 10764.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₉×C₂₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₉×C₁₃×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃×C₁₃×C₂₃	—	3	1	no	maximal
4	C₉×C₁₃×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₃×C₂₃	D₃	1	1	yes	characteristic
6	D₃×C₁₃×C₂₃	—	3	2	no	—
7	C₂²×C₁₃×C₂₃	—	9	1	no	Hall
8	C₃×C₁₃×C₂₃	C₂×D₃	1	1	yes	characteristic
9	C₂×D₉×C₂₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₁₃×C₂₃	—	9	2	no	—
11	C₂×C₁₃×C₂₃	D₉	1	1	yes	characteristic, direct product factor
12	C₂×C₁₃×D₉	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₉×C₂₃	C₂×C₁₃	1	1	yes	characteristic, complemented
14	D₉×C₂₃	C₂×C₁₃	1	2	yes	direct product factor
15	C₁₃×C₂₃	C₂×D₉	1	1	yes	characteristic, direct product factor, Hall
16	C₂×D₃×C₂₃	—	3	1	no	—
17	C₂×C₉×C₁₃	C₂×C₂₃	1	1	yes	characteristic, complemented
18	C₁₃×D₉	C₂×C₂₃	1	2	yes	direct product factor
19	C₉×C₂₃	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
20	C₂×D₃×C₁₃	—	3	1	no	—
21	C₂×C₃×C₂₃	D₃×C₁₃	1	1	yes	characteristic
22	D₃×C₂₃	—	3	2	no	—
23	C₉×C₁₃	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
24	C₂²×C₂₃	—	9	1	no	Hall
25	C₂×C₃×C₁₃	D₃×C₂₃	1	1	yes	characteristic
26	D₃×C₁₃	—	3	2	no	—
27	C₃×C₂₃	C₂×D₃×C₁₃	1	1	yes	characteristic
28	C₂²×C₁₃	—	9	1	no	Hall
29	C₂×C₂₃	—	9	2	no	—
30	C₂×C₂₃	C₁₃×D₉	1	1	yes	characteristic, direct product factor
31	C₃×C₁₃	C₂×D₃×C₂₃	1	1	yes	characteristic
32	C₂×D₉	C₁₃×C₂₃	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₁₃	—	9	2	no	—
34	C₂×C₁₃	D₉×C₂₃	1	1	yes	characteristic, direct product factor
35	C₂₃	C₂×C₁₃×D₉	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₉	C₂×C₁₃×C₂₃	1	1	yes	characteristic, complemented
37	D₉	C₂×C₁₃×C₂₃	1	2	yes	direct product factor
38	C₁₃	C₂×D₉×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×D₃	—	3	1	no	—
40	C₉	C₂²×C₁₃×C₂₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	D₃×C₁₃×C₂₃	1	1	yes	characteristic
42	D₃	—	3	2	no	—
43	C₂²	—	9	1	no	Sylow
44	C₃	C₂×D₃×C₁₃×C₂₃	1	1	yes	characteristic
45	C₂	—	9	2	no	—
46	C₂	C₁₃×D₉×C₂₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃×C₂₃	D₉
commutator, cosocle, hypocenter	C₉	C₂²×C₁₃×C₂₃
Frattini	C₃	C₂×D₃×C₁₃×C₂₃
Fitting	C₂×C₉×C₁₃×C₂₃	C₂
socle	C₂×C₃×C₁₃×C₂₃	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₁₃×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×D₉×C₂₃	C₂	direct (N × H)
2. C₂×C₉×C₁₃×C₂₃	C₂	semidirect
4. C₉×C₁₃×C₂₃	C₂²	semidirect
9. C₂×D₉×C₂₃	C₁₃	direct (N × H)
11. C₂×C₁₃×C₂₃	D₉	direct (N × H)
12. C₂×C₁₃×D₉	C₂₃	direct (N × H)
13. C₂×C₉×C₂₃	C₂×C₁₃	semidirect
14. D₉×C₂₃	C₂×C₁₃	direct (N × H)
15. C₁₃×C₂₃	C₂×D₉	direct (N × H)
17. C₂×C₉×C₁₃	C₂×C₂₃	semidirect
18. C₁₃×D₉	C₂×C₂₃	direct (N × H)
19. C₉×C₂₃	C₂²×C₁₃	semidirect
23. C₉×C₁₃	C₂²×C₂₃	semidirect
30. C₂×C₂₃	C₁₃×D₉	direct (N × H)
32. C₂×D₉	C₁₃×C₂₃	direct (N × H)
34. C₂×C₁₃	D₉×C₂₃	direct (N × H)
35. C₂₃	C₂×C₁₃×D₉	direct (N × H)
36. C₂×C₉	C₂×C₁₃×C₂₃	semidirect
37. D₉	C₂×C₁₃×C₂₃	direct (N × H)
38. C₁₃	C₂×D₉×C₂₃	direct (N × H)
40. C₉	C₂²×C₁₃×C₂₃	semidirect
46. C₂	C₁₃×D₉×C₂₃	direct (N × H)

Subgroups — C2×C13×D9×C23 #24924501

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₁₃×D₉×C₂₃ #24924501