Subgroups — C₂₉×C₃⋊(C₃⋊#1039) #39908005

Order 26100.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₅²×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂₉×C₃⋊#1039	—	3	4	no	maximal
3	C₃²×C₅²×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂₉×C₃⋊Dic₁₅	—	5	6	no	maximal
5	C₂×C₃×C₅²×C₂₉	D₃	1	4	yes	—
6	C₂₉×#1039	—	9	1	no	Hall
7	C₂×C₃²×C₅×C₂₉	D₅	1	6	yes	—
8	C₃×C₅²×C₂₉	Dic₃	1	4	yes	complemented
9	C₂₉×Dic₁₅	—	15	24	no	—
10	C₂×C₅²×C₂₉	C₃⋊D₃	1	1	yes	characteristic
11	C₃²×C₅×C₂₉	Dic₅	1	6	yes	complemented
12	C₂₉×C₃⋊Dic₃	—	25	1	no	Hall
13	C₃⋊(C₃⋊#1039)	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₃×C₅×C₂₉	D₁₅	1	24	yes	—
15	C₅²×C₂₉	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
16	Dic₅×C₂₉	—	45	6	no	—
17	C₂×C₃²×C₂₉	C₅⋊D₅	1	1	yes	characteristic
18	C₂×C₃²×C₅²	C₂×C₂₉	1	1	yes	characteristic
19	C₃×C₅×C₂₉	Dic₁₅	1	24	yes	complemented
20	Dic₃×C₂₉	—	75	4	no	—
21	C₃⋊#1039	—	3	4	no	—
22	C₂×C₅×C₂₉	C₃⋊D₁₅	1	6	yes	—
23	C₃²×C₂₉	#1039	1	1	yes	characteristic, complemented, Hall
24	C₃²×C₅²	C₄×C₂₉	1	1	yes	characteristic, complemented, Hall
25	C₃⋊Dic₁₅	—	5	6	no	—
26	C₂×C₃×C₂₉	C₃⋊(C₅⋊D₅)	1	4	yes	—
27	C₂×C₃×C₅²	D₃×C₂₉	1	4	yes	—
28	C₅×C₂₉	C₃⋊Dic₁₅	1	6	yes	complemented
29	C₄×C₂₉	—	225	1	no	Hall
30	#1039	—	9	1	no	Hall
31	C₂×C₃²×C₅	D₅×C₂₉	1	6	yes	—
32	C₃×C₂₉	C₃⋊#1039	1	4	yes	complemented
33	C₃×C₅²	Dic₃×C₂₉	1	4	yes	complemented
34	Dic₁₅	—	15	24	no	—
35	C₂×C₂₉	C₃⋊(C₃⋊(C₅⋊D₅))	1	1	yes	characteristic
36	C₂×C₅²	C₃⋊D₃×C₂₉	1	1	yes	characteristic
37	C₃²×C₅	Dic₅×C₂₉	1	6	yes	complemented
38	C₃⋊Dic₃	—	25	1	no	Hall
39	C₂×C₃×C₅	C₂₉×D₁₅	1	24	yes	—
40	C₂₉	C₃⋊(C₃⋊#1039)	1	1	yes	characteristic, direct product factor, Sylow
41	C₅²	C₂₉×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
42	Dic₅	—	45	6	no	—
43	C₂×C₃²	C₂₉×C₅⋊D₅	1	1	yes	characteristic
44	C₃×C₅	C₂₉×Dic₁₅	1	24	yes	complemented
45	Dic₃	—	75	4	no	—
46	C₂×C₅	C₂₉×C₃⋊D₁₅	1	6	yes	—
47	C₃²	C₂₉×#1039	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃	C₂₉×C₃⋊(C₅⋊D₅)	1	4	yes	—
49	C₅	C₂₉×C₃⋊Dic₁₅	1	6	yes	complemented
50	C₄	—	225	1	no	Sylow
51	C₃	C₂₉×C₃⋊#1039	1	4	yes	complemented
52	C₂	C₂₉×C₃⋊(C₃⋊(C₅⋊D₅))	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₂₉	C₃⋊(C₃⋊(C₅⋊D₅))
commutator, hypocenter	C₃²×C₅²	C₄×C₂₉
Frattini	C₂	C₂₉×C₃⋊(C₃⋊(C₅⋊D₅))
Fitting, socle, prime radical	C₂×C₃²×C₅²×C₂₉	C₂
cosocle	C₂×C₃²×C₅²	C₂×C₂₉
LCS	G ▷ C₃²×C₅²
UCS	C₁ ◁ C₂×C₂₉

Complements

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

N	H ≅ G/N	type
3. C₃²×C₅²×C₂₉	C₄	semidirect
8. C₃×C₅²×C₂₉	Dic₃	semidirect
11. C₃²×C₅×C₂₉	Dic₅	semidirect
13. C₃⋊(C₃⋊#1039)	C₂₉	direct (N × H)
15. C₅²×C₂₉	C₃⋊Dic₃	semidirect
19. C₃×C₅×C₂₉	Dic₁₅	semidirect
23. C₃²×C₂₉	#1039	semidirect
24. C₃²×C₅²	C₄×C₂₉	semidirect
28. C₅×C₂₉	C₃⋊Dic₁₅	semidirect
32. C₃×C₂₉	C₃⋊#1039	semidirect
33. C₃×C₅²	Dic₃×C₂₉	semidirect
37. C₃²×C₅	Dic₅×C₂₉	semidirect
40. C₂₉	C₃⋊(C₃⋊#1039)	direct (N × H)
41. C₅²	C₂₉×C₃⋊Dic₃	semidirect
44. C₃×C₅	C₂₉×Dic₁₅	semidirect
47. C₃²	C₂₉×#1039	semidirect
49. C₅	C₂₉×C₃⋊Dic₁₅	semidirect
51. C₃	C₂₉×C₃⋊#1039	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₅²×C₂₉	2
C₂₉×C₃⋊#1039	3
C₂₉×C₃⋊Dic₁₅	5
C₃⋊(C₃⋊#1039)	29

Subgroups — C29×C3⋊(C3⋊#1039) #39908005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×C₃⋊(C₃⋊#1039) #39908005