Subgroups — C₉⋊#15668530 #39907959

Order 26100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂₉×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#15668530	—	3	1	no	maximal
3	C₅²×C₉×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₉⋊#10596816	—	5	2	no	maximal
5	C₃×C₂₉×C₅⋊D₅	D₃	1	1	yes	characteristic
6	#15668530	—	9	1	no	Hall
7	C₉×D₅×C₂₉	—	5	2	no	—
8	C₉×D₅×C₂₉	—	10	2	no	—
9	C₃×C₅²×C₂₉	Dic₃	1	1	yes	characteristic
10	C₃⋊#10596816	—	15	2	no	—
11	C₂₉×C₅⋊D₅	D₉	1	1	yes	characteristic
12	C₅×C₉×C₂₉	—	2	2	no	—
13	C₅×C₉×C₂₉	AGL(1,𝔽₅)	1	2	yes	complemented
14	Dic₂₆₁	—	25	1	no	Hall
15	C₉⋊#1044	—	29	1	no	maximal, Hall
16	C₃×D₅×C₂₉	—	5	2	no	—
17	C₃×D₅×C₂₉	—	10	2	no	—
18	C₅²×C₂₉	Dic₉	1	1	yes	characteristic, complemented, Hall
19	#10596816	—	45	2	no	—
20	C₂×C₉×C₂₉	—	25	1	no	—
21	C₉×C₅⋊D₅	D₂₉	1	1	yes	characteristic
22	C₃×C₅×C₂₉	—	2	2	no	—
23	C₃×C₅×C₂₉	ΓL(1,𝔽₁₆)	1	2	yes	—
24	Dic₈₇	—	75	1	no	—
25	C₃⋊#1044	—	87	1	no	—
26	D₅×C₂₉	—	5	2	no	—
27	D₅×C₂₉	—	10	2	no	—
28	C₉×C₂₉	#1044	1	1	yes	characteristic, complemented, Hall
29	C₅²×C₉	Dic₂₉	1	1	yes	characteristic, complemented, Hall
30	C₉⋊AGL(1,𝔽₅)	—	145	2	no	—
31	C₂×C₃×C₂₉	—	25	1	no	—
32	C₃×C₅⋊D₅	D₈₇	1	1	yes	characteristic
33	C₅×C₂₉	—	2	2	no	—
34	C₅×C₂₉	C₉⋊AGL(1,𝔽₅)	1	2	yes	complemented
35	Dic₂₉	—	225	1	no	Hall
36	#1044	—	261	1	no	Hall
37	C₉×D₅	—	5	2	no	—
38	C₉×D₅	—	10	2	no	—
39	C₃×C₂₉	C₃⋊#1044	1	1	yes	characteristic
40	C₃×C₅²	Dic₈₇	1	1	yes	characteristic
41	ΓL(1,𝔽₁₆)	—	435	2	no	—
42	C₂×C₂₉	—	25	1	no	—
43	C₅⋊D₅	D₂₆₁	1	1	yes	characteristic
44	C₅×C₉	—	2	2	no	—
45	C₅×C₉	#10596816	1	2	yes	complemented
46	Dic₉	—	725	1	no	Hall
47	C₃×D₅	—	5	2	no	—
48	C₃×D₅	—	10	2	no	—
49	C₂₉	C₉⋊#1044	1	1	yes	characteristic, complemented, Sylow
50	C₅²	Dic₂₆₁	1	1	yes	characteristic, complemented, Sylow
51	AGL(1,𝔽₅)	—	1305	2	no	—
52	C₂×C₉	—	25	1	no	—
53	C₃×C₅	—	2	2	no	—
54	C₃×C₅	C₃⋊#10596816	1	2	yes	—
55	Dic₃	—	2175	1	no	—
56	D₅	—	5	2	no	—
57	D₅	—	10	2	no	—
58	C₉	#15668530	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₃	—	25	1	no	—
60	C₅	—	2	2	no	—
61	C₅	C₉⋊#10596816	1	2	yes	complemented
62	C₄	—	6525	1	no	Sylow
63	C₃	C₃⋊#15668530	1	1	yes	characteristic
64	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₅²×C₉×C₂₉	C₄
Frattini	C₃	C₃⋊#15668530
socle	C₃×C₅²×C₂₉	Dic₃
prime radical	C₃×C₂₉×C₅⋊D₅	D₃
cosocle	C₉×C₂₉×C₅⋊D₅	C₂
LCS	G ▷ C₅²×C₉×C₂₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₅²×C₉×C₂₉	C₄	semidirect
13. C₅×C₉×C₂₉	AGL(1,𝔽₅)	semidirect
18. C₅²×C₂₉	Dic₉	semidirect
28. C₉×C₂₉	#1044	semidirect
29. C₅²×C₉	Dic₂₉	semidirect
34. C₅×C₂₉	C₉⋊AGL(1,𝔽₅)	semidirect
45. C₅×C₉	#10596816	semidirect
49. C₂₉	C₉⋊#1044	semidirect
50. C₅²	Dic₂₆₁	semidirect
58. C₉	#15668530	semidirect
61. C₅	C₉⋊#10596816	semidirect

Maximal subgroups

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

subgroup	index
C₉×C₂₉×C₅⋊D₅	2
C₃⋊#15668530	3
C₉⋊#10596816	5
C₉⋊#1044	29

Subgroups — C9⋊#15668530 #39907959

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉⋊#15668530 #39907959