Subgroups — #15668527⋊C₉ #39907906

Order 26100.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×(C₅⋊D₅)⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×#15668527	C₃	1	1	yes	maximal, characteristic
3	C₂₉×C₅²⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₂₉×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
5	#15668527	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅²×C₂₉	C₃×C₄	1	1	yes	characteristic
7	C₃×#10596816	—	15	2	no	—
8	C₂₉×C₅⋊D₅	C₂×C₉	1	1	yes	characteristic
9	C₉×Dic₂₉	—	25	1	no	maximal, Hall
10	#1043⋊C₉	—	29	1	no	maximal, Hall
11	C₃×D₅×C₂₉	—	15	2	no	—
12	C₅²×C₂₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
13	#10596816	—	15	2	no	—
14	C₂×C₉×C₂₉	—	25	1	no	—
15	(C₅⋊D₅)⋊C₉	D₂₉	1	1	yes	characteristic
16	C₃×C₅×C₂₉	—	3	2	no	—
17	C₃×Dic₂₉	—	75	1	no	—
18	C₃×#1043	—	29	1	no	—
19	D₅×C₂₉	—	15	2	no	—
20	C₉×C₂₉	—	25	1	no	Hall
21	C₅²⋊C₉	Dic₂₉	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₂₉	—	75	1	no	—
23	C₃×C₅⋊D₅	C₃×D₂₉	1	1	yes	characteristic
24	C₅×C₂₉	—	3	2	no	—
25	Dic₂₉	—	75	1	no	Hall
26	#1043	—	29	1	no	Hall
27	C₃×C₂₉	#1043⋊C₃	1	1	yes	characteristic
28	C₃×C₅²	C₃×Dic₂₉	1	1	yes	characteristic
29	C₃×AGL(1,𝔽₅)	—	435	2	no	—
30	C₂×C₂₉	—	75	1	no	—
31	C₅⋊D₅	C₉×D₂₉	1	1	yes	characteristic
32	C₄×C₉	—	725	1	no	Hall
33	C₃×D₅	—	15	2	no	—
34	C₂₉	#1043⋊C₉	1	1	yes	characteristic, complemented, Sylow
35	C₅²	C₉×Dic₂₉	1	1	yes	characteristic, complemented, Sylow
36	AGL(1,𝔽₅)	—	435	2	no	—
37	C₂×C₉	—	25	1	no	—
38	C₃×C₅	—	3	2	no	—
39	C₃×C₄	—	2175	1	no	—
40	D₅	—	15	2	no	—
41	C₉	—	25	1	no	Sylow
42	C₂×C₃	—	75	1	no	—
43	C₅	—	3	2	no	—
44	C₄	—	2175	1	no	Sylow
45	C₃	#15668527⋊C₃	1	1	yes	characteristic
46	C₂	—	75	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	#15668527⋊C₃
commutator, hypocenter	C₅²×C₂₉	C₄×C₉
Fitting, socle	C₃×C₅²×C₂₉	C₃×C₄
prime radical, cosocle	C₃×C₂₉×C₅⋊D₅	C₂×C₃
LCS	G ▷ C₅²×C₂₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
3. C₂₉×C₅²⋊C₉	C₄	semidirect
5. #15668527	C₉	semidirect
12. C₅²×C₂₉	C₄×C₉	semidirect
21. C₅²⋊C₉	Dic₂₉	semidirect
34. C₂₉	#1043⋊C₉	semidirect
35. C₅²	C₉×Dic₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×(C₅⋊D₅)⋊C₉	2
C₃×#15668527	3
C₉×Dic₂₉	25
#1043⋊C₉	29

Subgroups — #15668527⋊C9 #39907906

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #15668527⋊C₉ #39907906