Subgroups — C₃×C₂₃×C₂²⋊(C₁₃⋊C₃) #24924580

Order 10764.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×C₂²⋊(C₁₃⋊C₃)	C₃	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₁₃×C₂₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₂₃×C₁₃⋊C₃	—	4	1	no	maximal, Hall
4	C₂×C₃×C₁₃×C₂₃	—	3	1	no	—
5	C₂²×C₁₃×C₂₃	C₃²	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₃×C₂₃	A₄	1	1	yes	characteristic, complemented
7	C₂₃×C₁₃⋊C₃	—	4	3	no	—
8	C₃×A₄×C₂₃	—	13	1	no	maximal, Hall
9	C₂×C₁₃×C₂₃	—	3	1	no	—
10	C₃×C₂²⋊(C₁₃⋊C₃)	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₁₃×C₂₃	C₃×A₄	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₃×C₂₃	C₁₃⋊C₃	1	1	yes	characteristic, complemented
13	A₄×C₂₃	—	13	3	no	—
14	C₃²×C₂₃	—	52	1	no	Hall
15	C₂²×C₃×C₁₃	C₃×C₂₃	1	1	yes	characteristic, complemented
16	C₂²⋊(C₁₃⋊C₃)	C₃×C₂₃	1	3	yes	direct product factor
17	C₂×C₃×C₂₃	—	3	1	no	—
18	C₃×C₁₃⋊C₃	—	4	1	no	Hall
19	C₂²×C₂₃	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₁₃	—	3	1	no	—
21	C₃×C₂₃	—	52	3	no	—
22	C₃×C₂₃	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor
23	C₂²×C₁₃	C₃²×C₂₃	1	1	yes	characteristic, complemented, Hall
24	C₂×C₂₃	—	3	1	no	—
25	C₃×C₁₃	A₄×C₂₃	1	1	yes	characteristic, complemented
26	C₁₃⋊C₃	—	4	3	no	—
27	C₃×A₄	—	13	1	no	Hall
28	C₂×C₁₃	—	3	1	no	—
29	C₂₃	C₃×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
30	C₁₃	C₃×A₄×C₂₃	1	1	yes	characteristic, complemented, Sylow
31	C₂²×C₃	C₂₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented
32	A₄	—	13	3	no	—
33	C₃²	—	52	1	no	Sylow
34	C₂×C₃	—	3	1	no	—
35	C₂²	C₃×C₂₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
36	C₃	—	52	3	no	—
37	C₃	C₂₃×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor
38	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₂₃	C₂²⋊(C₁₃⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₁₃	C₃²×C₂₃
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₁₃×C₂₃	C₃
LCS	G ▷ C₂²×C₁₃
UCS	C₁ ◁ C₃×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₂₃×C₂²⋊(C₁₃⋊C₃)	C₃	direct (N × H)
2. C₂²×C₃×C₁₃×C₂₃	C₃	semidirect
5. C₂²×C₁₃×C₂₃	C₃²	semidirect
6. C₃×C₁₃×C₂₃	A₄	semidirect
10. C₃×C₂²⋊(C₁₃⋊C₃)	C₂₃	direct (N × H)
11. C₁₃×C₂₃	C₃×A₄	semidirect
12. C₂²×C₃×C₂₃	C₁₃⋊C₃	semidirect
15. C₂²×C₃×C₁₃	C₃×C₂₃	semidirect
16. C₂²⋊(C₁₃⋊C₃)	C₃×C₂₃	direct (N × H)
19. C₂²×C₂₃	C₃×C₁₃⋊C₃	semidirect
22. C₃×C₂₃	C₂²⋊(C₁₃⋊C₃)	direct (N × H)
23. C₂²×C₁₃	C₃²×C₂₃	semidirect
25. C₃×C₁₃	A₄×C₂₃	semidirect
29. C₂₃	C₃×C₂²⋊(C₁₃⋊C₃)	direct (N × H)
30. C₁₃	C₃×A₄×C₂₃	semidirect
31. C₂²×C₃	C₂₃×C₁₃⋊C₃	semidirect
35. C₂²	C₃×C₂₃×C₁₃⋊C₃	semidirect
37. C₃	C₂₃×C₂²⋊(C₁₃⋊C₃)	direct (N × H)

Subgroups — C3×C23×C22⋊(C13⋊C3) #24924580

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₂₃×C₂²⋊(C₁₃⋊C₃) #24924580