Subgroups — C₂₃×(C₃⋊D₃)⋊D₁₃ #24924571

Order 10764.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃⋊D₃×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₂₃×D₃₉	C₂	1	2	yes	maximal, complemented
3	D₃×C₂₃×D₁₃	—	3	2	no	maximal
4	C₃²×C₁₃×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂₃×D₃₉	D₃	1	2	yes	complemented
6	D₃×C₁₃×C₂₃	—	3	2	no	—
7	D₃×C₁₃×C₂₃	—	6	1	no	—
8	C₃×C₂₃×D₁₃	—	3	2	no	—
9	C₂×C₂₃×D₁₃	—	9	1	no	Hall
10	C₃×C₁₃×C₂₃	—	2	1	no	—
11	C₃×C₁₃×C₂₃	C₂×D₃	1	2	yes	complemented
12	D₃²×C₂₃	—	13	1	no	maximal, Hall
13	C₂×C₁₃×C₂₃	—	9	1	no	—
14	C₂₃×D₁₃	—	3	2	no	—
15	(C₃⋊D₃)⋊D₁₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₃⋊D₃×C₂₃	D₁₃	1	1	yes	characteristic, complemented
17	C₃×D₃×C₂₃	—	13	2	no	—
18	C₁₃×C₂₃	D₃²	1	1	yes	characteristic, complemented, Hall
19	C₂×D₃×C₂₃	—	39	2	no	—
20	C₁₃×C₃⋊D₃	C₂×C₂₃	1	1	yes	characteristic, complemented
21	C₃×D₃₉	C₂×C₂₃	1	2	yes	complemented
22	C₃²×C₂₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
23	D₃×D₁₃	—	3	2	no	—
24	C₂×C₃×C₂₃	—	39	2	no	—
25	D₃×C₂₃	—	3	2	no	—
26	D₃×C₂₃	—	6	1	no	—
27	D₃×C₂₃	—	13	2	no	—
28	C₃²×C₁₃	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
29	C₂²×C₂₃	—	117	1	no	Hall
30	D₃₉	D₃×C₂₃	1	2	yes	complemented
31	C₃×D₁₃	—	3	2	no	—
32	D₃×C₁₃	—	3	2	no	—
33	D₃×C₁₃	—	6	1	no	—
34	C₃×C₂₃	—	2	1	no	—
35	C₃×C₂₃	D₃×D₁₃	1	2	yes	complemented
36	C₂×D₁₃	—	9	1	no	Hall
37	C₂×C₂₃	—	9	1	no	—
38	C₂×C₂₃	—	39	2	no	—
39	C₃×C₁₃	—	2	1	no	—
40	C₃×C₁₃	C₂×D₃×C₂₃	1	2	yes	complemented
41	D₃²	—	13	1	no	Hall
42	C₂×C₁₃	—	9	1	no	—
43	D₁₃	—	3	2	no	—
44	C₂₃	(C₃⋊D₃)⋊D₁₃	1	1	yes	characteristic, direct product factor, Sylow
45	C₃⋊D₃	C₂₃×D₁₃	1	1	yes	characteristic, complemented
46	C₃×D₃	—	13	2	no	—
47	C₁₃	D₃²×C₂₃	1	1	yes	characteristic, complemented, Sylow
48	C₂×D₃	—	39	2	no	—
49	C₃²	C₂×C₂₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	39	2	no	—
51	D₃	—	3	2	no	—
52	D₃	—	6	1	no	—
53	D₃	—	13	2	no	—
54	C₂²	—	117	1	no	Sylow
55	C₃	—	2	1	no	—
56	C₃	D₃×C₂₃×D₁₃	1	2	yes	complemented
57	C₂	—	9	1	no	—
58	C₂	—	39	2	no	—

	subgroup	G/H
center, hypercenter	C₂₃	(C₃⋊D₃)⋊D₁₃
commutator, cosocle, hypocenter	C₃²×C₁₃	C₂²×C₂₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₂₃	C₂²
LCS	G ▷ C₃²×C₁₃
UCS	C₁ ◁ C₂₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₃⋊D₃×C₂₃	C₂	semidirect
2. C₃×C₂₃×D₃₉	C₂	semidirect
4. C₃²×C₁₃×C₂₃	C₂²	semidirect
5. C₂₃×D₃₉	D₃	semidirect
11. C₃×C₁₃×C₂₃	C₂×D₃	semidirect
15. (C₃⋊D₃)⋊D₁₃	C₂₃	direct (N × H)
16. C₃⋊D₃×C₂₃	D₁₃	semidirect
18. C₁₃×C₂₃	D₃²	semidirect
20. C₁₃×C₃⋊D₃	C₂×C₂₃	semidirect
21. C₃×D₃₉	C₂×C₂₃	semidirect
22. C₃²×C₂₃	C₂×D₁₃	semidirect
28. C₃²×C₁₃	C₂²×C₂₃	semidirect
30. D₃₉	D₃×C₂₃	semidirect
35. C₃×C₂₃	D₃×D₁₃	semidirect
40. C₃×C₁₃	C₂×D₃×C₂₃	semidirect
44. C₂₃	(C₃⋊D₃)⋊D₁₃	direct (N × H)
45. C₃⋊D₃	C₂₃×D₁₃	semidirect
47. C₁₃	D₃²×C₂₃	semidirect
49. C₃²	C₂×C₂₃×D₁₃	semidirect
56. C₃	D₃×C₂₃×D₁₃	semidirect

Subgroups — C23×(C3⋊D3)⋊D13 #24924571

Conjugacy classes of subgroups

Complements

Subgroups — C₂₃×(C₃⋊D₃)⋊D₁₃ #24924571