Subgroups — C₉⋊#15668504 #39907786

Order 26100.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂₉×D₂₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#15668504	—	3	1	no	maximal
3	C₉×C₂₅×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₉⋊#10596816	—	5	1	no	maximal
5	C₃×C₂₉×D₂₅	D₃	1	1	yes	characteristic
6	#15668504	—	9	1	no	Hall
7	C₉×D₅×C₂₉	—	5	1	no	—
8	C₃×C₂₅×C₂₉	Dic₃	1	1	yes	characteristic
9	C₃⋊#10596816	—	15	1	no	—
10	C₂₉×D₂₅	D₉	1	1	yes	characteristic
11	C₅×C₉×C₂₉	AGL(1,𝔽₅)	1	1	yes	characteristic
12	Dic₂₆₁	—	25	1	no	Hall
13	C₉⋊#1035	—	29	1	no	maximal, Hall
14	C₃×D₅×C₂₉	—	5	1	no	—
15	C₂₅×C₂₉	Dic₉	1	1	yes	characteristic, complemented, Hall
16	#10596816	—	45	1	no	—
17	C₂×C₉×C₂₉	—	25	1	no	—
18	C₉×D₂₅	D₂₉	1	1	yes	characteristic
19	C₃×C₅×C₂₉	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
20	Dic₈₇	—	75	1	no	—
21	C₃⋊#1035	—	87	1	no	—
22	D₅×C₂₉	—	5	1	no	—
23	C₉×C₂₉	#1035	1	1	yes	characteristic, complemented, Hall
24	C₉×C₂₅	Dic₂₉	1	1	yes	characteristic, complemented, Hall
25	C₉⋊AGL(1,𝔽₅)	—	145	1	no	—
26	C₂×C₃×C₂₉	—	25	1	no	—
27	C₃×D₂₅	D₈₇	1	1	yes	characteristic
28	C₅×C₂₉	C₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic
29	Dic₂₉	—	225	1	no	Hall
30	#1035	—	261	1	no	Hall
31	C₉×D₅	—	5	1	no	—
32	C₃×C₂₉	C₃⋊#1035	1	1	yes	characteristic
33	C₃×C₂₅	Dic₈₇	1	1	yes	characteristic
34	ΓL(1,𝔽₁₆)	—	435	1	no	—
35	C₂×C₂₉	—	25	1	no	—
36	D₂₅	D₂₆₁	1	1	yes	characteristic
37	C₅×C₉	#10596816	1	1	yes	characteristic
38	Dic₉	—	725	1	no	Hall
39	C₃×D₅	—	5	1	no	—
40	C₂₉	C₉⋊#1035	1	1	yes	characteristic, complemented, Sylow
41	C₂₅	Dic₂₆₁	1	1	yes	characteristic, complemented, Sylow
42	AGL(1,𝔽₅)	—	1305	1	no	—
43	C₂×C₉	—	25	1	no	—
44	C₃×C₅	C₃⋊#10596816	1	1	yes	characteristic
45	Dic₃	—	2175	1	no	—
46	D₅	—	5	1	no	—
47	C₉	#15668504	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃	—	25	1	no	—
49	C₅	C₉⋊#10596816	1	1	yes	characteristic
50	C₄	—	6525	1	no	Sylow
51	C₃	C₃⋊#15668504	1	1	yes	characteristic
52	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₉×C₂₅×C₂₉	C₄
Frattini	C₃×C₅	C₃⋊#10596816
socle	C₃×C₅×C₂₉	ΓL(1,𝔽₁₆)
prime radical	C₃×C₂₉×D₂₅	D₃
cosocle	C₉×C₂₉×D₂₅	C₂
LCS	G ▷ C₉×C₂₅×C₂₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₉×C₂₅×C₂₉	C₄	semidirect
15. C₂₅×C₂₉	Dic₉	semidirect
23. C₉×C₂₉	#1035	semidirect
24. C₉×C₂₅	Dic₂₉	semidirect
40. C₂₉	C₉⋊#1035	semidirect
41. C₂₅	Dic₂₆₁	semidirect
47. C₉	#15668504	semidirect

Maximal subgroups

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

subgroup	index
C₉×C₂₉×D₂₅	2
C₃⋊#15668504	3
C₉⋊#10596816	5
C₉⋊#1035	29

Subgroups — C9⋊#15668504 #39907786

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉⋊#15668504 #39907786