Subgroups — C₁₃×C₃⋊D₃×D₂₃ #24924556

Order 10764.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃⋊D₆₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×C₃⋊D₃×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₁₃×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₁₃×D₂₃	—	3	4	no	maximal
5	C₃²×C₁₃×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₃×D₆₉	—	3	4	no	—
7	D₃×C₁₃×C₂₃	—	3	4	no	—
8	C₃×C₁₃×D₂₃	D₃	1	4	yes	complemented
9	C₂×C₁₃×D₂₃	—	9	1	no	Hall
10	C₃×C₁₃×C₂₃	C₂×D₃	1	4	yes	complemented
11	C₃⋊D₃×D₂₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₁₃×C₂₃	—	9	1	no	—
13	C₁₃×D₂₃	—	9	1	no	—
14	C₁₃×D₂₃	C₃⋊D₃	1	1	yes	characteristic, direct product factor
15	C₂×C₁₃×C₃⋊D₃	—	23	1	no	maximal, Hall
16	C₃⋊D₆₉	C₂×C₁₃	1	1	yes	characteristic, complemented
17	C₃⋊D₃×C₂₃	C₂×C₁₃	1	1	yes	characteristic, complemented
18	C₃²×D₂₃	C₂×C₁₃	1	1	yes	characteristic, complemented
19	C₁₃×C₂₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
20	D₃×D₂₃	—	3	4	no	—
21	C₂×C₃²×C₁₃	—	23	1	no	—
22	C₁₃×C₃⋊D₃	—	23	1	no	—
23	C₁₃×C₃⋊D₃	D₂₃	1	1	yes	characteristic, direct product factor
24	C₃²×C₂₃	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
25	C₂×D₃×C₁₃	—	69	4	no	—
26	D₆₉	—	3	4	no	—
27	C₃×D₂₃	D₃×C₁₃	1	4	yes	complemented
28	D₃×C₂₃	—	3	4	no	—
29	C₃²×C₁₃	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
30	C₂×D₂₃	—	9	1	no	Hall
31	C₂×C₃×C₁₃	—	23	4	no	—
32	D₃×C₁₃	—	3	4	no	—
33	D₃×C₁₃	—	69	4	no	—
34	C₃×C₂₃	C₂×D₃×C₁₃	1	4	yes	complemented
35	C₂²×C₁₃	—	207	1	no	Hall
36	C₂×C₂₃	—	9	1	no	—
37	D₂₃	—	9	1	no	—
38	D₂₃	C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor
39	C₃×C₁₃	D₃×D₂₃	1	4	yes	complemented
40	C₂×C₃⋊D₃	—	23	1	no	Hall
41	C₂×C₁₃	—	9	1	no	—
42	C₂×C₁₃	—	23	1	no	—
43	C₂×C₁₃	—	207	1	no	—
44	C₂₃	C₂×C₁₃×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₃²	—	23	1	no	—
46	C₃⋊D₃	—	23	1	no	—
47	C₃⋊D₃	C₁₃×D₂₃	1	1	yes	characteristic, direct product factor
48	C₁₃	C₃⋊D₃×D₂₃	1	1	yes	characteristic, direct product factor, Sylow
49	C₂×D₃	—	69	4	no	—
50	C₃²	C₂×C₁₃×D₂₃	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	23	4	no	—
52	D₃	—	3	4	no	—
53	D₃	—	69	4	no	—
54	C₂²	—	207	1	no	Sylow
55	C₃	D₃×C₁₃×D₂₃	1	4	yes	complemented
56	C₂	—	9	1	no	—
57	C₂	—	23	1	no	—
58	C₂	—	207	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	C₃⋊D₃×D₂₃
commutator, cosocle, hypocenter	C₃²×C₂₃	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₂₃	C₂²
LCS	G ▷ C₃²×C₂₃
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₃⋊D₆₉	C₂	semidirect
2. C₁₃×C₃⋊D₃×C₂₃	C₂	semidirect
3. C₃²×C₁₃×D₂₃	C₂	semidirect
5. C₃²×C₁₃×C₂₃	C₂²	semidirect
8. C₃×C₁₃×D₂₃	D₃	semidirect
10. C₃×C₁₃×C₂₃	C₂×D₃	semidirect
11. C₃⋊D₃×D₂₃	C₁₃	direct (N × H)
14. C₁₃×D₂₃	C₃⋊D₃	direct (N × H)
16. C₃⋊D₆₉	C₂×C₁₃	semidirect
17. C₃⋊D₃×C₂₃	C₂×C₁₃	semidirect
18. C₃²×D₂₃	C₂×C₁₃	semidirect
19. C₁₃×C₂₃	C₂×C₃⋊D₃	semidirect
23. C₁₃×C₃⋊D₃	D₂₃	direct (N × H)
24. C₃²×C₂₃	C₂²×C₁₃	semidirect
27. C₃×D₂₃	D₃×C₁₃	semidirect
29. C₃²×C₁₃	C₂×D₂₃	semidirect
34. C₃×C₂₃	C₂×D₃×C₁₃	semidirect
38. D₂₃	C₁₃×C₃⋊D₃	direct (N × H)
39. C₃×C₁₃	D₃×D₂₃	semidirect
44. C₂₃	C₂×C₁₃×C₃⋊D₃	semidirect
47. C₃⋊D₃	C₁₃×D₂₃	direct (N × H)
48. C₁₃	C₃⋊D₃×D₂₃	direct (N × H)
50. C₃²	C₂×C₁₃×D₂₃	semidirect
55. C₃	D₃×C₁₃×D₂₃	semidirect

Subgroups — C13×C3⋊D3×D23 #24924556

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×C₃⋊D₃×D₂₃ #24924556