Subgroups — C₉×C₂₃×Dic₁₃ #24924471

Order 10764.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₁₃×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₂₃×Dic₁₃	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₃×C₂₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₃×C₂₃	C₂×C₃	1	1	yes	characteristic
5	C₂₃×Dic₁₃	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₁₃×C₂₃	C₃×C₄	1	1	yes	characteristic
7	C₄×C₉×C₂₃	—	13	1	no	maximal, Hall
8	C₂×C₁₃×C₂₃	C₂×C₉	1	1	yes	characteristic
9	C₉×Dic₁₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₉×C₂₃	D₁₃	1	1	yes	characteristic
11	C₁₃×C₂₃	C₄×C₉	1	1	yes	characteristic, complemented, Hall
12	C₃×C₄×C₂₃	—	13	1	no	—
13	C₂×C₉×C₁₃	C₂×C₂₃	1	1	yes	characteristic
14	C₉×C₂₃	Dic₁₃	1	1	yes	characteristic, direct product factor, Hall
15	C₃×Dic₁₃	C₃×C₂₃	1	1	yes	characteristic
16	C₂×C₃×C₂₃	C₃×D₁₃	1	1	yes	characteristic
17	C₉×C₁₃	C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
18	C₄×C₂₃	—	13	1	no	Hall
19	C₂×C₃×C₁₃	C₂×C₃×C₂₃	1	1	yes	characteristic
20	C₃×C₂₃	C₃×Dic₁₃	1	1	yes	characteristic
21	Dic₁₃	C₉×C₂₃	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₂₃	C₉×D₁₃	1	1	yes	characteristic
23	C₃×C₁₃	C₃×C₄×C₂₃	1	1	yes	characteristic
24	C₄×C₉	—	13	1	no	Hall
25	C₂×C₁₃	C₂×C₉×C₂₃	1	1	yes	characteristic
26	C₂₃	C₉×Dic₁₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₉	C₂₃×D₁₃	1	1	yes	characteristic
28	C₁₃	C₄×C₉×C₂₃	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₄	—	13	1	no	—
30	C₉	C₂₃×Dic₁₃	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₃×C₂₃×D₁₃	1	1	yes	characteristic
32	C₄	—	13	1	no	Sylow
33	C₃	C₃×C₂₃×Dic₁₃	1	1	yes	characteristic
34	C₂	C₉×C₂₃×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₉×C₂₃	D₁₃
commutator, hypocenter	C₁₃	C₄×C₉×C₂₃
Frattini	C₂×C₃	C₃×C₂₃×D₁₃
Fitting	C₂×C₉×C₁₃×C₂₃	C₂
socle, prime radical	C₂×C₃×C₁₃×C₂₃	C₂×C₃
cosocle	C₂×C₃×C₁₃	C₂×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
3. C₉×C₁₃×C₂₃	C₄	semidirect
5. C₂₃×Dic₁₃	C₉	direct (N × H)
9. C₉×Dic₁₃	C₂₃	direct (N × H)
11. C₁₃×C₂₃	C₄×C₉	semidirect
14. C₉×C₂₃	Dic₁₃	direct (N × H)
17. C₉×C₁₃	C₄×C₂₃	semidirect
21. Dic₁₃	C₉×C₂₃	direct (N × H)
26. C₂₃	C₉×Dic₁₃	direct (N × H)
28. C₁₃	C₄×C₉×C₂₃	semidirect
30. C₉	C₂₃×Dic₁₃	direct (N × H)

Subgroups — C9×C23×Dic13 #24924471

Conjugacy classes of subgroups

Complements

Subgroups — C₉×C₂₃×Dic₁₃ #24924471