Subgroups — C₅×C₂₉×C₃⋊ΓL(1,𝔽₁₆) #39908192

Order 26100.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×D₅×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₂₉×ΓL(1,𝔽₁₆)	—	3	4	no	maximal
3	C₃²×C₅²×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂₉×C₃⋊ΓL(1,𝔽₁₆)	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₅×C₂₉×C₃⋊Dic₃	—	5	1	no	maximal
6	C₃×C₅×D₅×C₂₉	D₃	1	4	yes	—
7	C₅×AGL(1,𝔽₅)×C₂₉	—	9	1	no	Hall
8	C₃²×D₅×C₂₉	C₂×C₅	1	1	yes	characteristic
9	C₂×C₃²×C₅×C₂₉	—	5	1	no	—
10	C₃×C₅²×C₂₉	Dic₃	1	4	yes	complemented
11	C₂₉×ΓL(1,𝔽₁₆)	—	3	4	no	—
12	C₅×Dic₃×C₂₉	—	15	4	no	—
13	C₅×D₅×C₂₉	C₃⋊D₃	1	1	yes	characteristic
14	C₃²×C₅×C₂₉	—	4	1	no	—
15	C₃²×C₅×C₂₉	C₄×C₅	1	1	yes	characteristic, complemented
16	C₃²×C₅×C₂₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
17	C₂₉×C₃⋊Dic₃	—	5	1	no	Hall
18	C₅×C₃⋊ΓL(1,𝔽₁₆)	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₃×C₅×C₂₉	—	5	4	no	—
20	C₃×D₅×C₂₉	C₅×D₃	1	4	yes	—
21	C₅²×C₂₉	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
22	AGL(1,𝔽₅)×C₂₉	—	9	1	no	—
23	C₄×C₅×C₂₉	—	45	1	no	—
24	C₂×C₃²×C₂₉	—	5	1	no	—
25	C₃²×C₅×D₅	C₂×C₂₉	1	1	yes	characteristic
26	C₃×C₅×C₂₉	—	4	4	no	—
27	C₃×C₅×C₂₉	C₅×Dic₃	1	4	yes	complemented
28	C₃×C₅×C₂₉	ΓL(1,𝔽₁₆)	1	4	yes	complemented
29	Dic₃×C₂₉	—	15	4	no	—
30	C₅×ΓL(1,𝔽₁₆)	—	3	4	no	—
31	C₂×C₅×C₂₉	—	5	1	no	—
32	D₅×C₂₉	C₅×C₃⋊D₃	1	1	yes	characteristic
33	C₃²×C₂₉	C₅×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
34	C₃²×C₅²	C₄×C₂₉	1	1	yes	characteristic, complemented, Hall
35	C₃⋊ΓL(1,𝔽₁₆)	C₅×C₂₉	1	1	yes	characteristic, direct product factor
36	C₅×C₃⋊Dic₃	—	5	1	no	—
37	C₂×C₃×C₂₉	—	5	4	no	—
38	C₃×C₅×D₅	D₃×C₂₉	1	4	yes	—
39	C₅×C₂₉	—	4	1	no	—
40	C₅×C₂₉	C₅×C₃⋊Dic₃	1	1	yes	characteristic, complemented
41	C₅×C₂₉	C₃⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic, direct product factor
42	C₄×C₂₉	—	45	1	no	Hall
43	C₅×AGL(1,𝔽₅)	—	9	1	no	Hall
44	C₂×C₃²×C₅	—	5	1	no	—
45	C₃²×D₅	C₂×C₅×C₂₉	1	1	yes	characteristic
46	C₃×C₂₉	C₅×ΓL(1,𝔽₁₆)	1	4	yes	complemented
47	C₃×C₅²	Dic₃×C₂₉	1	4	yes	complemented
48	ΓL(1,𝔽₁₆)	—	3	4	no	—
49	C₅×Dic₃	—	15	4	no	—
50	C₂×C₂₉	—	5	1	no	—
51	C₅×D₅	C₃⋊D₃×C₂₉	1	1	yes	characteristic
52	C₃²×C₅	—	4	1	no	—
53	C₃²×C₅	C₄×C₅×C₂₉	1	1	yes	characteristic, complemented
54	C₃²×C₅	AGL(1,𝔽₅)×C₂₉	1	1	yes	characteristic, complemented
55	C₃⋊Dic₃	—	5	1	no	Hall
56	C₂×C₃×C₅	—	5	4	no	—
57	C₃×D₅	C₅×D₃×C₂₉	1	4	yes	—
58	C₂₉	C₅×C₃⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic, direct product factor, Sylow
59	C₅²	C₂₉×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
60	AGL(1,𝔽₅)	—	9	1	no	—
61	C₄×C₅	—	45	1	no	—
62	C₂×C₃²	—	5	1	no	—
63	C₃×C₅	—	4	4	no	—
64	C₃×C₅	C₅×Dic₃×C₂₉	1	4	yes	complemented
65	C₃×C₅	C₂₉×ΓL(1,𝔽₁₆)	1	4	yes	complemented
66	Dic₃	—	15	4	no	—
67	C₂×C₅	—	5	1	no	—
68	D₅	C₅×C₃⋊D₃×C₂₉	1	1	yes	characteristic
69	C₃²	C₅×AGL(1,𝔽₅)×C₂₉	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	—	5	4	no	—
71	C₅	—	4	1	no	—
72	C₅	C₅×C₂₉×C₃⋊Dic₃	1	1	yes	characteristic, complemented
73	C₅	C₂₉×C₃⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic, direct product factor
74	C₄	—	45	1	no	Sylow
75	C₃	C₅×C₂₉×ΓL(1,𝔽₁₆)	1	4	yes	complemented
76	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₂₉	C₃⋊ΓL(1,𝔽₁₆)
commutator, hypocenter	C₃²×C₅	C₄×C₅×C₂₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₂₉	C₄
prime radical	C₃²×C₅×D₅×C₂₉	C₂
cosocle	C₃²×D₅	C₂×C₅×C₂₉
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₅×C₂₉

Complements

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

N	H ≅ G/N	type
3. C₃²×C₅²×C₂₉	C₄	semidirect
4. C₂₉×C₃⋊ΓL(1,𝔽₁₆)	C₅	direct (N × H)
10. C₃×C₅²×C₂₉	Dic₃	semidirect
15. C₃²×C₅×C₂₉	C₄×C₅	semidirect
16. C₃²×C₅×C₂₉	AGL(1,𝔽₅)	semidirect
18. C₅×C₃⋊ΓL(1,𝔽₁₆)	C₂₉	direct (N × H)
21. C₅²×C₂₉	C₃⋊Dic₃	semidirect
27. C₃×C₅×C₂₉	C₅×Dic₃	semidirect
28. C₃×C₅×C₂₉	ΓL(1,𝔽₁₆)	semidirect
33. C₃²×C₂₉	C₅×AGL(1,𝔽₅)	semidirect
34. C₃²×C₅²	C₄×C₂₉	semidirect
35. C₃⋊ΓL(1,𝔽₁₆)	C₅×C₂₉	direct (N × H)
40. C₅×C₂₉	C₅×C₃⋊Dic₃	semidirect
41. C₅×C₂₉	C₃⋊ΓL(1,𝔽₁₆)	direct (N × H)
46. C₃×C₂₉	C₅×ΓL(1,𝔽₁₆)	semidirect
47. C₃×C₅²	Dic₃×C₂₉	semidirect
53. C₃²×C₅	C₄×C₅×C₂₉	semidirect
54. C₃²×C₅	AGL(1,𝔽₅)×C₂₉	semidirect
58. C₂₉	C₅×C₃⋊ΓL(1,𝔽₁₆)	direct (N × H)
59. C₅²	C₂₉×C₃⋊Dic₃	semidirect
64. C₃×C₅	C₅×Dic₃×C₂₉	semidirect
65. C₃×C₅	C₂₉×ΓL(1,𝔽₁₆)	semidirect
69. C₃²	C₅×AGL(1,𝔽₅)×C₂₉	semidirect
72. C₅	C₅×C₂₉×C₃⋊Dic₃	semidirect
73. C₅	C₂₉×C₃⋊ΓL(1,𝔽₁₆)	direct (N × H)
75. C₃	C₅×C₂₉×ΓL(1,𝔽₁₆)	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅×D₅×C₂₉	2
C₅×C₂₉×ΓL(1,𝔽₁₆)	3
C₂₉×C₃⋊ΓL(1,𝔽₁₆)	5
C₅×C₂₉×C₃⋊Dic₃	5
C₅×C₃⋊ΓL(1,𝔽₁₆)	29

Subgroups — C5×C29×C3⋊ΓL(1,𝔽16) #39908192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₂₉×C₃⋊ΓL(1,𝔽₁₆) #39908192