Subgroups — C₉⋊#16810003 #44477756

Order 30420.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₅⋊(C₁₃⋊D₁₃)	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#16810003	—	3	1	no	maximal
3	C₅×C₉×C₁₃²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₉⋊#10621728	—	5	1	no	maximal, Hall
5	C₃×C₅⋊(C₁₃⋊D₁₃)	D₃	1	1	yes	characteristic
6	#16810003	—	9	1	no	Hall
7	C₉×C₁₃⋊D₁₃	—	5	1	no	—
8	C₃×C₅×C₁₃²	Dic₃	1	1	yes	characteristic
9	C₉⋊#63121	—	13	14	no	maximal
10	C₃⋊#10621728	—	15	1	no	—
11	C₅⋊(C₁₃⋊D₁₃)	D₉	1	1	yes	characteristic
12	C₉×C₁₃²	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
13	C₉×D₆₅	—	13	14	no	—
14	C₃×C₁₃⋊D₁₃	—	5	1	no	—
15	C₅×C₁₃²	Dic₉	1	1	yes	characteristic, complemented, Hall
16	C₃⋊#63121	—	39	14	no	—
17	#10621728	—	45	1	no	Hall
18	C₅×C₉×C₁₃	#261	1	14	yes	complemented
19	C₃×C₁₃²	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
20	C₉⋊#261	—	65	14	no	—
21	C₃×D₆₅	—	13	14	no	—
22	C₁₃⋊D₁₃	—	5	1	no	—
23	#63121	—	117	14	no	—
24	C₉×D₁₃	—	65	14	no	—
25	C₃×C₅×C₁₃	C₃⋊#261	1	14	yes	—
26	C₉⋊AGL(1,𝔽₅)	—	169	1	no	Hall
27	C₁₃²	C₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
28	C₃⋊#261	—	195	14	no	—
29	D₆₅	—	13	14	no	—
30	C₉×C₁₃	#63121	1	14	yes	complemented
31	C₉×D₅	—	169	1	no	—
32	C₃×D₁₃	—	65	14	no	—
33	C₅×C₁₃	C₉⋊#261	1	14	yes	complemented
34	ΓL(1,𝔽₁₆)	—	507	1	no	—
35	#261	—	585	14	no	—
36	C₅×C₉	#10621728	1	1	yes	characteristic, complemented, Hall
37	C₃×C₁₃	C₃⋊#63121	1	14	yes	—
38	Dic₉	—	845	1	no	Hall
39	C₃×D₅	—	169	1	no	—
40	D₁₃	—	65	14	no	—
41	AGL(1,𝔽₅)	—	1521	1	no	Hall
42	C₂×C₉	—	845	1	no	—
43	C₃×C₅	C₃⋊#10621728	1	1	yes	characteristic
44	C₁₃	C₉⋊#63121	1	14	yes	complemented
45	Dic₃	—	2535	1	no	—
46	D₅	—	169	1	no	—
47	C₉	#16810003	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃	—	845	1	no	—
49	C₅	C₉⋊#10621728	1	1	yes	characteristic, complemented, Sylow
50	C₄	—	7605	1	no	Sylow
51	C₃	C₃⋊#16810003	1	1	yes	characteristic
52	C₂	—	845	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₅×C₉×C₁₃²	C₄
Frattini	C₃	C₃⋊#16810003
socle	C₃×C₅×C₁₃²	Dic₃
prime radical	C₃×C₅⋊(C₁₃⋊D₁₃)	D₃
cosocle	C₉×C₅⋊(C₁₃⋊D₁₃)	C₂
LCS	G ▷ C₅×C₉×C₁₃²
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₅×C₉×C₁₃²	C₄	semidirect
12. C₉×C₁₃²	AGL(1,𝔽₅)	semidirect
15. C₅×C₁₃²	Dic₉	semidirect
18. C₅×C₉×C₁₃	#261	semidirect
27. C₁₃²	C₉⋊AGL(1,𝔽₅)	semidirect
30. C₉×C₁₃	#63121	semidirect
33. C₅×C₁₃	C₉⋊#261	semidirect
36. C₅×C₉	#10621728	semidirect
44. C₁₃	C₉⋊#63121	semidirect
47. C₉	#16810003	semidirect
49. C₅	C₉⋊#10621728	semidirect

Maximal subgroups

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

subgroup	index
C₉×C₅⋊(C₁₃⋊D₁₃)	2
C₃⋊#16810003	3
C₉⋊#10621728	5
C₉⋊#63121	13

Subgroups — C9⋊#16810003 #44477756

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉⋊#16810003 #44477756