Subgroups — C₁₃×D₉×C₄₉ #26039378

Order 11466.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₃×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₁₃×C₄₉	—	3	1	no	maximal
3	C₃×C₁₃×C₄₉	D₃	1	1	yes	characteristic
4	C₇×C₁₃×D₉	C₇	1	1	yes	maximal, characteristic
5	C₂×C₁₃×C₄₉	—	9	1	no	Hall
6	D₉×C₄₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₇×C₉×C₁₃	C₂×C₇	1	1	yes	characteristic
8	C₁₃×C₄₉	D₉	1	1	yes	characteristic, direct product factor, Hall
9	D₃×C₇×C₁₃	—	3	1	no	—
10	C₉×C₄₉	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
11	D₃×C₄₉	—	3	1	no	—
12	C₃×C₇×C₁₃	D₃×C₇	1	1	yes	characteristic
13	C₁₃×D₉	C₄₉	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₇×C₁₃	—	9	1	no	—
15	C₃×C₄₉	D₃×C₁₃	1	1	yes	characteristic
16	C₇×D₉	C₇×C₁₃	1	1	yes	characteristic
17	C₉×C₁₃	C₂×C₄₉	1	1	yes	characteristic, complemented, Hall
18	C₂×C₄₉	—	9	1	no	Hall
19	C₇×C₁₃	C₇×D₉	1	1	yes	characteristic
20	D₃×C₁₃	—	3	1	no	—
21	C₇×C₉	C₂×C₇×C₁₃	1	1	yes	characteristic
22	C₄₉	C₁₃×D₉	1	1	yes	characteristic, direct product factor, Sylow
23	D₃×C₇	—	3	1	no	—
24	C₃×C₁₃	D₃×C₄₉	1	1	yes	characteristic
25	C₂×C₁₃	—	9	1	no	Hall
26	C₃×C₇	D₃×C₇×C₁₃	1	1	yes	characteristic
27	D₉	C₁₃×C₄₉	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₇	—	9	1	no	—
29	C₁₃	D₉×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₉	C₂×C₁₃×C₄₉	1	1	yes	characteristic, complemented, Sylow
31	C₇	C₇×C₁₃×D₉	1	1	yes	characteristic
32	D₃	—	3	1	no	—
33	C₃	D₃×C₁₃×C₄₉	1	1	yes	characteristic
34	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃×C₄₉	D₉
commutator, hypocenter	C₉	C₂×C₁₃×C₄₉
Frattini	C₃×C₇	D₃×C₇×C₁₃
Fitting	C₉×C₁₃×C₄₉	C₂
socle	C₃×C₇×C₁₃	D₃×C₇
prime radical	C₇×C₁₃×D₉	C₇
cosocle	C₇×C₉	C₂×C₇×C₁₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₁₃×C₄₉

Complements

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

N	H ≅ G/N	type
1. C₉×C₁₃×C₄₉	C₂	semidirect
6. D₉×C₄₉	C₁₃	direct (N × H)
8. C₁₃×C₄₉	D₉	direct (N × H)
10. C₉×C₄₉	C₂×C₁₃	semidirect
13. C₁₃×D₉	C₄₉	direct (N × H)
17. C₉×C₁₃	C₂×C₄₉	semidirect
22. C₄₉	C₁₃×D₉	direct (N × H)
27. D₉	C₁₃×C₄₉	direct (N × H)
29. C₁₃	D₉×C₄₉	direct (N × H)
30. C₉	C₂×C₁₃×C₄₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₉×C₁₃×C₄₉	2
D₃×C₁₃×C₄₉	3
C₇×C₁₃×D₉	7
D₉×C₄₉	13

Subgroups — C13×D9×C49 #26039378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×D₉×C₄₉ #26039378