Subgroups — C₂²×C₂₃×C₁₃⋊C₉ #24924495

Order 10764.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂²×C₃×C₂₃	C₁₃⋊C₃
commutator, hypocenter	C₁₃	C₂²×C₉×C₂₃
Frattini	C₃	C₂²×C₂₃×C₁₃⋊C₃
Fitting, socle, prime radical	C₂²×C₃×C₁₃×C₂₃	C₃
cosocle	C₃×C₁₃	C₂²×C₃×C₂₃
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×C₂₃×C₁₃⋊C₉	C₂	direct (N × H)
3. C₂₃×C₁₃⋊C₉	C₂²	direct (N × H)
5. C₂²×C₁₃×C₂₃	C₉	semidirect
8. C₂×C₁₃×C₂₃	C₂×C₉	semidirect
9. C₂²×C₁₃⋊C₉	C₂₃	direct (N × H)
11. C₁₃×C₂₃	C₂²×C₉	semidirect
13. C₂×C₁₃⋊C₉	C₂×C₂₃	direct (N × H)
17. C₁₃⋊C₉	C₂²×C₂₃	direct (N × H)
18. C₂²×C₂₃	C₁₃⋊C₉	direct (N × H)
21. C₂²×C₁₃	C₉×C₂₃	semidirect
22. C₂×C₂₃	C₂×C₁₃⋊C₉	direct (N × H)
25. C₂×C₁₃	C₂×C₉×C₂₃	semidirect
26. C₂₃	C₂²×C₁₃⋊C₉	direct (N × H)
28. C₁₃	C₂²×C₉×C₂₃	semidirect
32. C₂²	C₂₃×C₁₃⋊C₉	direct (N × H)
34. C₂	C₂×C₂₃×C₁₃⋊C₉	direct (N × H)

Subgroups — C22×C23×C13⋊C9 #24924495

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×C₂₃×C₁₃⋊C₉ #24924495