Subgroups — C₁₃×Dic₂₀₇ #24924474

Order 10764.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₁₃×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₁₃×Dic₆₉	—	3	1	no	maximal
3	C₉×C₁₃×C₂₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₃×C₂₃	D₃	1	1	yes	characteristic
5	C₁₃×Dic₂₃	—	9	1	no	Hall
6	C₃×C₁₃×C₂₃	Dic₃	1	1	yes	characteristic
7	Dic₂₀₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₁₃×C₂₃	D₉	1	1	yes	characteristic
9	C₁₃×Dic₉	—	23	1	no	maximal, Hall
10	C₂×C₉×C₂₃	C₂×C₁₃	1	1	yes	characteristic
11	C₁₃×C₂₃	Dic₉	1	1	yes	characteristic, complemented, Hall
12	Dic₆₉	—	3	1	no	—
13	C₂×C₉×C₁₃	D₂₃	1	1	yes	characteristic
14	C₉×C₂₃	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
15	Dic₃×C₁₃	—	69	1	no	—
16	C₂×C₃×C₂₃	D₃×C₁₃	1	1	yes	characteristic
17	C₉×C₁₃	Dic₂₃	1	1	yes	characteristic, complemented, Hall
18	Dic₂₃	—	9	1	no	Hall
19	C₂×C₃×C₁₃	D₆₉	1	1	yes	characteristic
20	C₃×C₂₃	Dic₃×C₁₃	1	1	yes	characteristic
21	C₄×C₁₃	—	207	1	no	Hall
22	C₂×C₂₃	C₁₃×D₉	1	1	yes	characteristic
23	C₃×C₁₃	Dic₆₉	1	1	yes	characteristic
24	Dic₉	—	23	1	no	Hall
25	C₂×C₁₃	D₂₀₇	1	1	yes	characteristic
26	C₂₃	C₁₃×Dic₉	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₉	C₁₃×D₂₃	1	1	yes	characteristic
28	C₁₃	Dic₂₀₇	1	1	yes	characteristic, direct product factor, Sylow
29	Dic₃	—	69	1	no	—
30	C₉	C₁₃×Dic₂₃	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	C₁₃×D₆₉	1	1	yes	characteristic
32	C₄	—	207	1	no	Sylow
33	C₃	C₁₃×Dic₆₉	1	1	yes	characteristic
34	C₂	C₁₃×D₂₀₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₃	D₂₀₇
commutator, hypocenter	C₉×C₂₃	C₄×C₁₃
Frattini	C₂×C₃	C₁₃×D₆₉
Fitting	C₂×C₉×C₁₃×C₂₃	C₂
socle, prime radical	C₂×C₃×C₁₃×C₂₃	D₃
cosocle	C₂×C₉×C₂₃	C₂×C₁₃
LCS	G ▷ C₉×C₂₃
UCS	C₁ ◁ C₂×C₁₃

Complements

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

N	H ≅ G/N	type
3. C₉×C₁₃×C₂₃	C₄	semidirect
7. Dic₂₀₇	C₁₃	direct (N × H)
11. C₁₃×C₂₃	Dic₉	semidirect
14. C₉×C₂₃	C₄×C₁₃	semidirect
17. C₉×C₁₃	Dic₂₃	semidirect
26. C₂₃	C₁₃×Dic₉	semidirect
28. C₁₃	Dic₂₀₇	direct (N × H)
30. C₉	C₁₃×Dic₂₃	semidirect

Subgroups — C13×Dic207 #24924474

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×Dic₂₀₇ #24924474