Subgroups — C₂₃×#261⋊C₉ #24924478

Order 10764.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×D₁₃⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₂₃×#261	C₃	1	1	yes	maximal, characteristic
3	C₂₃×C₁₃⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₂₃×D₁₃	C₂×C₃	1	1	yes	characteristic
5	C₂₃×#261	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₃×C₂₃	C₃×C₄	1	1	yes	characteristic
7	C₄×C₉×C₂₃	—	13	1	no	maximal, Hall
8	C₂₃×D₁₃	C₂×C₉	1	1	yes	characteristic
9	#261⋊C₉	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₉×C₂₃	—	13	1	no	—
11	C₁₃×C₂₃	C₄×C₉	1	1	yes	characteristic, complemented, Hall
12	C₃×C₄×C₂₃	—	13	1	no	—
13	D₁₃⋊C₉	C₂×C₂₃	1	1	yes	characteristic
14	C₉×C₂₃	—	13	1	no	Hall
15	C₃×#261	C₃×C₂₃	1	1	yes	characteristic
16	C₂×C₃×C₂₃	—	13	1	no	—
17	C₁₃⋊C₉	C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
18	C₄×C₂₃	—	13	1	no	Hall
19	C₃×D₁₃	C₂×C₃×C₂₃	1	1	yes	characteristic
20	C₃×C₂₃	AGL(1,𝔽₁₃)	1	1	yes	characteristic
21	#261	C₉×C₂₃	1	1	yes	characteristic, complemented, Hall
22	C₂×C₂₃	—	13	1	no	—
23	C₃×C₁₃	C₃×C₄×C₂₃	1	1	yes	characteristic
24	C₄×C₉	—	13	1	no	Hall
25	D₁₃	C₂×C₉×C₂₃	1	1	yes	characteristic
26	C₂₃	#261⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₉	—	13	1	no	—
28	C₁₃	C₄×C₉×C₂₃	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₄	—	13	1	no	—
30	C₉	—	13	1	no	Sylow
31	C₂×C₃	—	13	1	no	—
32	C₄	—	13	1	no	Sylow
33	C₃	C₂₃×AGL(1,𝔽₁₃)	1	1	yes	characteristic
34	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₂₃	AGL(1,𝔽₁₃)
commutator, hypocenter	C₁₃	C₄×C₉×C₂₃
Frattini	C₃	C₂₃×AGL(1,𝔽₁₃)
Fitting, socle	C₃×C₁₃×C₂₃	C₃×C₄
prime radical	C₃×C₂₃×D₁₃	C₂×C₃
cosocle	C₃×D₁₃	C₂×C₃×C₂₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₂₃

Complements

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

N	H ≅ G/N	type
3. C₂₃×C₁₃⋊C₉	C₄	semidirect
5. C₂₃×#261	C₉	semidirect
9. #261⋊C₉	C₂₃	direct (N × H)
11. C₁₃×C₂₃	C₄×C₉	semidirect
17. C₁₃⋊C₉	C₄×C₂₃	semidirect
21. #261	C₉×C₂₃	semidirect
26. C₂₃	#261⋊C₉	direct (N × H)
28. C₁₃	C₄×C₉×C₂₃	semidirect

Subgroups — C23×#261⋊C9 #24924478

Conjugacy classes of subgroups

Complements

Subgroups — C₂₃×#261⋊C₉ #24924478