Subgroups — C₉×C₅⋊(C₁₃⋊D₁₃) #29503597

Order 15210.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₁₃²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅⋊(C₁₃⋊D₁₃)	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₃⋊D₁₃	—	5	1	no	maximal, Hall
4	C₃×C₅×C₁₃²	C₂×C₃	1	1	yes	characteristic
5	C₅⋊(C₁₃⋊D₁₃)	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₉×C₁₃²	D₅	1	1	yes	characteristic, complemented, Hall
7	C₉×D₆₅	—	13	14	no	maximal
8	C₃×C₁₃⋊D₁₃	—	5	1	no	—
9	C₅×C₁₃²	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	C₅×C₉×C₁₃	D₁₃	1	14	yes	complemented
11	C₃×C₁₃²	C₃×D₅	1	1	yes	characteristic
12	C₃×D₆₅	—	13	14	no	—
13	C₁₃⋊D₁₃	—	5	1	no	Hall
14	C₉×D₁₃	—	65	14	no	—
15	C₃×C₅×C₁₃	C₃×D₁₃	1	14	yes	—
16	C₁₃²	C₉×D₅	1	1	yes	characteristic, complemented, Sylow
17	D₆₅	—	13	14	no	—
18	C₉×C₁₃	D₆₅	1	14	yes	complemented
19	C₉×D₅	—	169	1	no	Hall
20	C₃×D₁₃	—	65	14	no	—
21	C₅×C₁₃	C₉×D₁₃	1	14	yes	complemented
22	C₅×C₉	C₁₃⋊D₁₃	1	1	yes	characteristic, complemented, Hall
23	C₃×C₁₃	C₃×D₆₅	1	14	yes	—
24	C₃×D₅	—	169	1	no	—
25	D₁₃	—	65	14	no	—
26	C₂×C₉	—	845	1	no	Hall
27	C₃×C₅	C₃×C₁₃⋊D₁₃	1	1	yes	characteristic
28	C₁₃	C₉×D₆₅	1	14	yes	complemented
29	D₅	—	169	1	no	Hall
30	C₉	C₅⋊(C₁₃⋊D₁₃)	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	845	1	no	—
32	C₅	C₉×C₁₃⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
33	C₃	C₃×C₅⋊(C₁₃⋊D₁₃)	1	1	yes	characteristic
34	C₂	—	845	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₉	C₅⋊(C₁₃⋊D₁₃)
commutator, hypocenter	C₅×C₁₃²	C₂×C₉
Frattini	C₃	C₃×C₅⋊(C₁₃⋊D₁₃)
Fitting	C₅×C₉×C₁₃²	C₂
socle, cosocle	C₃×C₅×C₁₃²	C₂×C₃
prime radical	C₃×C₅⋊(C₁₃⋊D₁₃)	C₃
LCS	G ▷ C₅×C₁₃²
UCS	C₁ ◁ C₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₉×C₁₃²	C₂	semidirect
5. C₅⋊(C₁₃⋊D₁₃)	C₉	direct (N × H)
6. C₉×C₁₃²	D₅	semidirect
9. C₅×C₁₃²	C₂×C₉	semidirect
10. C₅×C₉×C₁₃	D₁₃	semidirect
16. C₁₃²	C₉×D₅	semidirect
18. C₉×C₁₃	D₆₅	semidirect
21. C₅×C₁₃	C₉×D₁₃	semidirect
22. C₅×C₉	C₁₃⋊D₁₃	semidirect
28. C₁₃	C₉×D₆₅	semidirect
30. C₉	C₅⋊(C₁₃⋊D₁₃)	direct (N × H)
32. C₅	C₉×C₁₃⋊D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₉×C₁₃²	2
C₃×C₅⋊(C₁₃⋊D₁₃)	3
C₉×C₁₃⋊D₁₃	5
C₉×D₆₅	13

Subgroups — C9×C5⋊(C13⋊D13) #29503597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₅⋊(C₁₃⋊D₁₃) #29503597