Subgroups — D₉×C₂₃×D₁₃ #24924491

Order 10764.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×D₁₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×D₉×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×C₂₃×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₂₃×D₁₃	—	3	1	no	maximal
5	C₉×C₁₃×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂₃×D₃₉	—	3	1	no	—
7	D₃×C₁₃×C₂₃	—	3	1	no	—
8	C₃×C₂₃×D₁₃	D₃	1	1	yes	characteristic
9	C₂×C₂₃×D₁₃	—	9	1	no	Hall
10	C₃×C₁₃×C₂₃	C₂×D₃	1	1	yes	characteristic
11	C₂×D₉×C₂₃	—	13	1	no	maximal, Hall
12	C₂×C₁₃×C₂₃	—	9	1	no	—
13	C₂₃×D₁₃	—	9	1	no	—
14	C₂₃×D₁₃	D₉	1	1	yes	characteristic, direct product factor
15	D₉×D₁₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₉×C₂₃	—	13	1	no	—
17	D₉×C₂₃	—	13	1	no	—
18	D₉×C₂₃	D₁₃	1	1	yes	characteristic, direct product factor
19	C₁₃×C₂₃	C₂×D₉	1	1	yes	characteristic, complemented, Hall
20	C₂×D₃×C₂₃	—	39	1	no	—
21	D₁₁₇	C₂×C₂₃	1	1	yes	characteristic, complemented
22	C₉×D₁₃	C₂×C₂₃	1	1	yes	characteristic, complemented
23	C₁₃×D₉	C₂×C₂₃	1	1	yes	characteristic, complemented
24	C₉×C₂₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
25	D₃×D₁₃	—	3	1	no	—
26	C₂×C₃×C₂₃	—	13	1	no	—
27	D₃×C₂₃	—	3	1	no	—
28	D₃×C₂₃	—	39	1	no	—
29	C₉×C₁₃	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
30	C₂²×C₂₃	—	117	1	no	Hall
31	D₃₉	—	3	1	no	—
32	C₃×D₁₃	D₃×C₂₃	1	1	yes	characteristic
33	D₃×C₁₃	—	3	1	no	—
34	C₃×C₂₃	D₃×D₁₃	1	1	yes	characteristic
35	C₂×D₁₃	—	9	1	no	Hall
36	C₂×C₂₃	—	9	1	no	—
37	C₂×C₂₃	—	13	1	no	—
38	C₂×C₂₃	—	117	1	no	—
39	C₃×C₁₃	C₂×D₃×C₂₃	1	1	yes	characteristic
40	C₂×D₉	—	13	1	no	Hall
41	C₂×C₁₃	—	9	1	no	—
42	D₁₃	—	9	1	no	—
43	D₁₃	D₉×C₂₃	1	1	yes	characteristic, direct product factor
44	C₂₃	D₉×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
45	C₂×C₉	—	13	1	no	—
46	D₉	—	13	1	no	—
47	D₉	C₂₃×D₁₃	1	1	yes	characteristic, direct product factor
48	C₁₃	C₂×D₉×C₂₃	1	1	yes	characteristic, complemented, Sylow
49	C₂×D₃	—	39	1	no	—
50	C₉	C₂×C₂₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	13	1	no	—
52	D₃	—	3	1	no	—
53	D₃	—	39	1	no	—
54	C₂²	—	117	1	no	Sylow
55	C₃	D₃×C₂₃×D₁₃	1	1	yes	characteristic
56	C₂	—	9	1	no	—
57	C₂	—	13	1	no	—
58	C₂	—	117	1	no	—

	subgroup	G/H
center, hypercenter	C₂₃	D₉×D₁₃
commutator, cosocle, hypocenter	C₉×C₁₃	C₂²×C₂₃
Frattini	C₃	D₃×C₂₃×D₁₃
Fitting	C₉×C₁₃×C₂₃	C₂²
socle	C₃×C₁₃×C₂₃	C₂×D₃
LCS	G ▷ C₉×C₁₃
UCS	C₁ ◁ C₂₃

Complements

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

N	H ≅ G/N	type
1. C₂₃×D₁₁₇	C₂	semidirect
2. C₁₃×D₉×C₂₃	C₂	semidirect
3. C₉×C₂₃×D₁₃	C₂	semidirect
5. C₉×C₁₃×C₂₃	C₂²	semidirect
14. C₂₃×D₁₃	D₉	direct (N × H)
15. D₉×D₁₃	C₂₃	direct (N × H)
18. D₉×C₂₃	D₁₃	direct (N × H)
19. C₁₃×C₂₃	C₂×D₉	semidirect
21. D₁₁₇	C₂×C₂₃	semidirect
22. C₉×D₁₃	C₂×C₂₃	semidirect
23. C₁₃×D₉	C₂×C₂₃	semidirect
24. C₉×C₂₃	C₂×D₁₃	semidirect
29. C₉×C₁₃	C₂²×C₂₃	semidirect
43. D₁₃	D₉×C₂₃	direct (N × H)
44. C₂₃	D₉×D₁₃	direct (N × H)
47. D₉	C₂₃×D₁₃	direct (N × H)
48. C₁₃	C₂×D₉×C₂₃	semidirect
50. C₉	C₂×C₂₃×D₁₃	semidirect

Subgroups — D9×C23×D13 #24924491

Conjugacy classes of subgroups

Complements

Subgroups — D₉×C₂₃×D₁₃ #24924491