Subgroups — C₃×C₂₃⋊(Dic₁₃⋊C₃) #24924507

Order 10764.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂₃×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₂₉₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂₃⋊(Dic₁₃⋊C₃)	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₂₃×C₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₃×C₂₃	C₂×C₃	1	1	yes	characteristic
6	C₂×C₂₃×C₁₃⋊C₃	C₂×C₃	1	3	yes	—
7	Dic₂₉₉	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₃×C₂₃	C₃×C₄	1	1	yes	characteristic, complemented
9	C₂₃×C₁₃⋊C₃	C₃×C₄	1	3	yes	complemented
10	C₃²×Dic₂₃	—	13	1	no	maximal, Hall
11	C₂×C₁₃×C₂₃	C₂×C₃²	1	1	yes	characteristic
12	C₃×Dic₁₃⋊C₃	—	23	1	no	maximal, Hall
13	C₂×C₃²×C₂₃	—	13	1	no	—
14	C₁₃×C₂₃	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
15	C₃×Dic₂₃	—	13	3	no	—
16	C₃×Dic₂₃	—	13	1	no	—
17	C₂×C₃×C₁₃⋊C₃	D₂₃	1	1	yes	characteristic
18	C₃²×C₂₃	—	13	1	no	Hall
19	C₃×Dic₁₃	—	23	1	no	—
20	Dic₁₃⋊C₃	—	23	3	no	—
21	C₂×C₃×C₂₃	—	13	3	no	—
22	C₂×C₃×C₂₃	D₁₃⋊C₃	1	1	yes	characteristic
23	C₃×C₁₃⋊C₃	Dic₂₃	1	1	yes	characteristic, complemented, Hall
24	Dic₂₃	—	13	1	no	Hall
25	C₂×C₃×C₁₃	C₃×D₂₃	1	1	yes	characteristic
26	C₂×C₁₃⋊C₃	C₃×D₂₃	1	3	yes	—
27	C₃×C₂₃	—	13	3	no	—
28	C₃×C₂₃	Dic₁₃⋊C₃	1	1	yes	characteristic, complemented
29	Dic₁₃	—	23	1	no	Hall
30	C₂×C₂₃	C₃×D₁₃⋊C₃	1	1	yes	characteristic
31	C₃×C₁₃	C₃×Dic₂₃	1	1	yes	characteristic, complemented
32	C₁₃⋊C₃	C₃×Dic₂₃	1	3	yes	complemented
33	C₃²×C₄	—	299	1	no	Hall
34	C₂×C₁₃	C₃²×D₂₃	1	1	yes	characteristic
35	C₂₃	C₃×Dic₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃²	—	13	1	no	—
37	C₁₃	C₃²×Dic₂₃	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₄	—	299	3	no	—
39	C₃×C₄	—	299	1	no	—
40	C₃²	—	13	1	no	Sylow
41	C₂×C₃	—	13	3	no	—
42	C₂×C₃	C₂₃⋊(D₁₃⋊C₃)	1	1	yes	characteristic
43	C₄	—	299	1	no	Sylow
44	C₃	—	13	3	no	—
45	C₃	C₂₃⋊(Dic₁₃⋊C₃)	1	1	yes	characteristic, direct product factor
46	C₂	C₃×C₂₃⋊(D₁₃⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	C₂₃⋊(D₁₃⋊C₃)
commutator, hypocenter	C₁₃×C₂₃	C₃²×C₄
Frattini	C₂	C₃×C₂₃⋊(D₁₃⋊C₃)
Fitting, socle	C₂×C₃×C₁₃×C₂₃	C₂×C₃
prime radical	C₂×C₃×C₂₃×C₁₃⋊C₃	C₂
cosocle	C₂×C₁₃×C₂₃	C₂×C₃²
LCS	G ▷ C₁₃×C₂₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
2. C₃×Dic₂₉₉	C₃	semidirect
3. C₂₃⋊(Dic₁₃⋊C₃)	C₃	direct (N × H)
4. C₃×C₂₃×C₁₃⋊C₃	C₄	semidirect
7. Dic₂₉₉	C₃²	semidirect
8. C₃×C₁₃×C₂₃	C₃×C₄	semidirect
9. C₂₃×C₁₃⋊C₃	C₃×C₄	semidirect
14. C₁₃×C₂₃	C₃²×C₄	semidirect
23. C₃×C₁₃⋊C₃	Dic₂₃	semidirect
28. C₃×C₂₃	Dic₁₃⋊C₃	semidirect
31. C₃×C₁₃	C₃×Dic₂₃	semidirect
32. C₁₃⋊C₃	C₃×Dic₂₃	semidirect
35. C₂₃	C₃×Dic₁₃⋊C₃	semidirect
37. C₁₃	C₃²×Dic₂₃	semidirect
45. C₃	C₂₃⋊(Dic₁₃⋊C₃)	direct (N × H)

Subgroups — C3×C23⋊(Dic13⋊C3) #24924507

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₂₃⋊(Dic₁₃⋊C₃) #24924507