Subgroups — C₂×C₉×C₂₃×D₁₃ #24924499

Order 10764.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂₃×D₁₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₉×C₁₃×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₂₃×D₁₃	C₃	1	1	yes	maximal, characteristic
4	C₉×C₁₃×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₃×C₂₃	C₂×C₃	1	1	yes	characteristic
6	C₃×C₂₃×D₁₃	C₂×C₃	1	2	yes	—
7	C₂×C₂₃×D₁₃	C₉	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₁₃×C₂₃	C₂²×C₃	1	1	yes	characteristic
9	C₂²×C₉×C₂₃	—	13	1	no	maximal, Hall
10	C₂×C₁₃×C₂₃	C₂×C₉	1	1	yes	characteristic, complemented
11	C₂₃×D₁₃	C₂×C₉	1	2	yes	direct product factor
12	C₂×C₉×D₁₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₉×C₂₃	—	13	2	no	—
14	C₂×C₉×C₂₃	D₁₃	1	1	yes	characteristic, direct product factor
15	C₁₃×C₂₃	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
16	C₂²×C₃×C₂₃	—	13	1	no	—
17	C₂×C₉×C₁₃	C₂×C₂₃	1	1	yes	characteristic, complemented
18	C₉×D₁₃	C₂×C₂₃	1	2	yes	direct product factor
19	C₉×C₂₃	C₂×D₁₃	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₃×D₁₃	C₃×C₂₃	1	1	yes	characteristic
21	C₂×C₃×C₂₃	—	13	2	no	—
22	C₂×C₃×C₂₃	C₃×D₁₃	1	1	yes	characteristic
23	C₉×C₁₃	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
24	C₂²×C₂₃	—	13	1	no	Hall
25	C₂×C₃×C₁₃	C₂×C₃×C₂₃	1	1	yes	characteristic
26	C₃×D₁₃	C₂×C₃×C₂₃	1	2	yes	—
27	C₃×C₂₃	C₂×C₃×D₁₃	1	1	yes	characteristic
28	C₂×D₁₃	C₉×C₂₃	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₂₃	—	13	2	no	—
30	C₂×C₂₃	C₉×D₁₃	1	1	yes	characteristic, direct product factor
31	C₃×C₁₃	C₂²×C₃×C₂₃	1	1	yes	characteristic
32	C₂²×C₉	—	13	1	no	Hall
33	C₂×C₁₃	C₂×C₉×C₂₃	1	1	yes	characteristic, complemented
34	D₁₃	C₂×C₉×C₂₃	1	2	yes	direct product factor
35	C₂₃	C₂×C₉×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₉	—	13	2	no	—
37	C₂×C₉	C₂₃×D₁₃	1	1	yes	characteristic, direct product factor
38	C₁₃	C₂²×C₉×C₂₃	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₃	—	13	1	no	—
40	C₉	C₂×C₂₃×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₃	—	13	2	no	—
42	C₂×C₃	C₃×C₂₃×D₁₃	1	1	yes	characteristic
43	C₂²	—	13	1	no	Sylow
44	C₃	C₂×C₃×C₂₃×D₁₃	1	1	yes	characteristic
45	C₂	—	13	2	no	—
46	C₂	C₉×C₂₃×D₁₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₉×C₂₃	D₁₃
commutator, hypocenter	C₁₃	C₂²×C₉×C₂₃
Frattini	C₃	C₂×C₃×C₂₃×D₁₃
Fitting	C₂×C₉×C₁₃×C₂₃	C₂
socle	C₂×C₃×C₁₃×C₂₃	C₂×C₃
prime radical	C₂×C₃×C₂₃×D₁₃	C₃
cosocle	C₃×C₁₃	C₂²×C₃×C₂₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₉×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₉×C₂₃×D₁₃	C₂	direct (N × H)
2. C₂×C₉×C₁₃×C₂₃	C₂	semidirect
4. C₉×C₁₃×C₂₃	C₂²	semidirect
7. C₂×C₂₃×D₁₃	C₉	direct (N × H)
10. C₂×C₁₃×C₂₃	C₂×C₉	semidirect
11. C₂₃×D₁₃	C₂×C₉	direct (N × H)
12. C₂×C₉×D₁₃	C₂₃	direct (N × H)
14. C₂×C₉×C₂₃	D₁₃	direct (N × H)
15. C₁₃×C₂₃	C₂²×C₉	semidirect
17. C₂×C₉×C₁₃	C₂×C₂₃	semidirect
18. C₉×D₁₃	C₂×C₂₃	direct (N × H)
19. C₉×C₂₃	C₂×D₁₃	direct (N × H)
23. C₉×C₁₃	C₂²×C₂₃	semidirect
28. C₂×D₁₃	C₉×C₂₃	direct (N × H)
30. C₂×C₂₃	C₉×D₁₃	direct (N × H)
33. C₂×C₁₃	C₂×C₉×C₂₃	semidirect
34. D₁₃	C₂×C₉×C₂₃	direct (N × H)
35. C₂₃	C₂×C₉×D₁₃	direct (N × H)
37. C₂×C₉	C₂₃×D₁₃	direct (N × H)
38. C₁₃	C₂²×C₉×C₂₃	semidirect
40. C₉	C₂×C₂₃×D₁₃	direct (N × H)
46. C₂	C₉×C₂₃×D₁₃	direct (N × H)

Subgroups — C2×C9×C23×D13 #24924499

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₉×C₂₃×D₁₃ #24924499