Subgroups — C₂×D₂₃×C₁₃⋊C₉ #24924483

Order 10764.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×C₁₃⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₂₃×C₁₃⋊C₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₁₃×D₂₃	C₃	1	1	yes	maximal, characteristic
4	C₂₃×C₁₃⋊C₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₃×C₂₃	C₂×C₃	1	1	yes	characteristic
6	C₃×C₁₃×D₂₃	C₂×C₃	1	2	yes	—
7	C₂×C₁₃×D₂₃	C₉	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₃×C₂₃	C₂²×C₃	1	1	yes	characteristic
9	C₂×C₉×D₂₃	—	13	1	no	maximal, Hall
10	C₂×C₁₃×C₂₃	C₂×C₉	1	1	yes	characteristic, complemented
11	C₁₃×D₂₃	C₂×C₉	1	2	yes	complemented
12	C₂²×C₁₃⋊C₉	—	23	1	no	maximal, Hall
13	C₂×C₉×C₂₃	—	13	1	no	—
14	C₉×D₂₃	—	13	2	no	—
15	C₁₃×C₂₃	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×D₂₃	C₁₃⋊C₃	1	1	yes	characteristic
17	C₂×C₁₃⋊C₉	—	23	2	no	—
18	C₂×C₁₃⋊C₉	D₂₃	1	1	yes	characteristic, direct product factor
19	C₉×C₂₃	—	13	1	no	Hall
20	C₂²×C₃×C₁₃	—	23	1	no	—
21	C₂×C₃×C₂₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic
22	C₃×D₂₃	C₂×C₁₃⋊C₃	1	2	yes	—
23	C₁₃⋊C₉	C₂×D₂₃	1	1	yes	characteristic, direct product factor, Hall
24	C₂×D₂₃	C₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₃×C₁₃	—	23	2	no	—
26	C₂×C₃×C₁₃	C₃×D₂₃	1	1	yes	characteristic
27	C₃×C₂₃	C₂²×C₁₃⋊C₃	1	1	yes	characteristic
28	C₂²×C₁₃	—	23	1	no	Hall
29	C₂×C₂₃	C₂×C₁₃⋊C₉	1	1	yes	characteristic, complemented
30	D₂₃	C₂×C₁₃⋊C₉	1	2	yes	direct product factor
31	C₃×C₁₃	C₂×C₃×D₂₃	1	1	yes	characteristic
32	C₂²×C₉	—	299	1	no	Hall
33	C₂×C₁₃	—	23	2	no	—
34	C₂×C₁₃	C₉×D₂₃	1	1	yes	characteristic, complemented
35	C₂₃	C₂²×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₉	—	13	1	no	—
37	C₂×C₉	—	299	2	no	—
38	C₁₃	C₂×C₉×D₂₃	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₃	—	23	1	no	—
40	C₉	—	13	1	no	Sylow
41	C₂×C₃	—	23	2	no	—
42	C₂×C₃	C₁₃⋊C₃×D₂₃	1	1	yes	characteristic
43	C₂²	—	23	1	no	Sylow
44	C₃	C₂×C₁₃⋊C₃×D₂₃	1	1	yes	characteristic
45	C₂	—	23	2	no	—
46	C₂	D₂₃×C₁₃⋊C₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	C₁₃⋊C₃×D₂₃
commutator, hypocenter	C₁₃×C₂₃	C₂²×C₉
Frattini	C₃	C₂×C₁₃⋊C₃×D₂₃
Fitting, socle	C₂×C₃×C₁₃×C₂₃	C₂×C₃
prime radical	C₂×C₃×C₁₃×D₂₃	C₃
cosocle	C₃×C₁₃×C₂₃	C₂²×C₃
LCS	G ▷ C₁₃×C₂₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×C₁₃⋊C₉	C₂	semidirect
2. D₂₃×C₁₃⋊C₉	C₂	direct (N × H)
4. C₂₃×C₁₃⋊C₉	C₂²	semidirect
7. C₂×C₁₃×D₂₃	C₉	semidirect
10. C₂×C₁₃×C₂₃	C₂×C₉	semidirect
11. C₁₃×D₂₃	C₂×C₉	semidirect
15. C₁₃×C₂₃	C₂²×C₉	semidirect
18. C₂×C₁₃⋊C₉	D₂₃	direct (N × H)
23. C₁₃⋊C₉	C₂×D₂₃	direct (N × H)
24. C₂×D₂₃	C₁₃⋊C₉	direct (N × H)
29. C₂×C₂₃	C₂×C₁₃⋊C₉	semidirect
30. D₂₃	C₂×C₁₃⋊C₉	direct (N × H)
34. C₂×C₁₃	C₉×D₂₃	semidirect
35. C₂₃	C₂²×C₁₃⋊C₉	semidirect
38. C₁₃	C₂×C₉×D₂₃	semidirect
46. C₂	D₂₃×C₁₃⋊C₉	direct (N × H)

Subgroups — C2×D23×C13⋊C9 #24924483

Conjugacy classes of subgroups

Complements

Subgroups — C₂×D₂₃×C₁₃⋊C₉ #24924483